Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter July 27, 2017

Design of experiments in liquid chromatography (HPLC) analysis of pharmaceuticals: analytics, applications, implications and future prospects

  • Saurabh B. Ganorkar EMAIL logo and Atul A. Shirkhedkar

Abstract

This review presents the essential brief annals, crucial analytics, precise applications and noteworthy implications of design of experiments which enrouted to liquid chromatography (LC) in the midst of utmost focus on high-performance liquid-chromatography (HPLC) and broadened its impressions on allied techniques in pharmaceutical analysis. Being most widely applied statistical methodologies for such purpose, its use was started in 1970 and heightened after Fischer’s precious input in 1981. The persistent use of statistical approaches one after another led to the efficient attention of pharmaceutical analysts. Hence, in order to fine-tune the trail impressed by the cumulative trends, the use of statistical designs in HPLC analysis has been reviewed and efforts were made to recognize its relative impact and corresponding future prospects. Applications of precise methodologies have been reassessed with respect to the need established by recent regulatory perspectives with a fanatical and the consequent stance on prominent historical advancements and concrete purposes. An effort was also made to state an arbitrary classification of diverse design types and succinct line of application in LC and associated analyses.

Introduction

Pharmaceutical analysis usually involves experiments for the measurement of the concentration of drug as an active pharmaceutical ingredient (API) or component of a pharmaceutical formulation. Such determination is performed with the help of a simple analytical method or a stability-indicating method for quantification of one or more degradation products (DPs) and/or impurities (IMPs). Pharmaceutical bioanalytical methods are constantly designed for the determination of drugs and/or metabolites as well as potential IMPs that may be present along with drug and may interfere with its pharmacological potential; further both of these methods need to be accurate, selective and precise (Kettaneh-Wold 1991). The range of chromatographic and spectroscopic techniques alone or as hyphenated modifications has been used for decades in pharmaceutical analysis. Liquid chromatographic techniques used for such a purpose have gained inimitable importance in this process of drug analysis as a baseline for the determination of drugs, followed by its separation from the other interfering chemical entities that may be either metabolites and/or IMPs.

Unique omnipresent and multifaceted chromatographic techniques having a pronounced position in drug analysis are high-performance liquid chromatography (HPLC), high-performance thin-layer liquid chromatography (HPTLC) and associated hyphenations. Challenging and proving the efficiencies of these techniques can be best accomplished and applied with a fundamental focus on steps linked with them such as preparation of samples of analytes and quantification which requires a usual procedure of development, followed by optimization and validation of methods (Ferreira et al. 2007a). Being a determining step in the pharmaceutical analysis, HPLC, or simply chromatographic development can be seen as a time-consuming and subjective process in most cases which may affect all the processes in the life cycle of a potential drug molecule ahead.

The development of the HPLC method in the past was principally a manual practice requiring a vast literary and chemical exercise to understand the nature of a drug and subsequently to develop a mobile phase and further determination. In the past, most of the chromatographic analyses were based on the one factor at a time (OFAT) approach. This approach involves varying a single system parameter affecting chromatographic efficiency in any sense and keeping others constant followed by the recording of the resultant recital of the method and associated setup (Sandford & Shelver, 2009). This process needs a large number of experimental runs, and in a number of cases, once developed, the method still may need additional efforts when validated. A similar situation arises during the stability studies and so on up to technology transfer while determination, identification, resolution (RS), isolation and characterization of IMPs. Thus, such an approach used for HPLC analysis may ultimately lead to retardation of the overall process pertaining to drug development and pharmaceutical analysis. This will also affect the post-marketing surveillance and may hinder therapeutic abilities of drugs and pharmaceuticals to some point (Monks, Rieger & Molnár, 2011). “The art of extracting chemically relevant information from data produced in chemical experiments is stated as Chemometrics” by Svante Wold has become a major drive for various disciplines of chemistry as well as analysis (Wold 1995). The applications of pattern recognition techniques and multicomponent analysis have been started actually in the late 1970s (Jellum, 1977; McConnell et al., 1979). Alike through the years chemometrics has proved to be a powerful tool in chromatography and its applications are continuing to increase till date. The importance of chemometrics in chromatography and growing volume of combined applications all over the world became the driving force for the interest of pharmaceutical analysts and/or chemist in the aforementioned area (Araujo & Grung, 2012). Chemometric experimental design (ED) can be defined as the rational process of scheduling experiments with enough statistical supremacy, sample size and adequate type of data in order to provide maximum information from chemical data and efficiently address the challenges and goals imposed by intended research (Araujo & Janagap, 2012). Contrary to the OFAT approach, the chemometric ED uses multivariate statistical techniques. Such multivariate statistical techniques have advantages, namely, reduction in a number of experiments that need to be performed resulting in lower reagent consumption and considerably less laboratory work allows development of mathematical models that permit assessment of relevance as well as statistical significance of the communication effects in between factors. If significant interaction exists amongst factors, the optimal conditions indicated by the OFAT approach or univariate studies will be different from the correct results of multivariate optimization. The interaction effect between the factors is directly proportional to the difference that will be found using univariate and multivariate techniques in HPLC analysis as the effect of one variable may be dependent on other variables. In contrast to this, a multivariate strategy involves EDs for which levels of variables are also changed simultaneously to encounter the interaction effects of potential variables affecting drug analyses (Ferreira et al. 2007). The first step of multivariate optimization is screening the factors in order to obtain the significant effects on the analytical system, followed by obtaining favorable operation conditions with the appliance of other statistical designs such as central composite designs (CCD), Doehlert matrix (DM), Box-Behnken design (BBD) and much more (Box, Hunter & Hunter, 2005; Bruns, Scarminio & de Barros Neto, 2006). Therefore, the obvious advantages as well as changing scientific and regulatory scenario have generated the need for the thorough understanding as well as the application of chemometrics as the design of experiments (DoE) in HPLC analysis.

The aim of this explorative review is to trace the use of ED as a chemometric tool for the betterment of chromatography, specifically, HPLC. The diverse applications of DoE during HPLC method development, optimization, validation, robustness determination as well as stress studies, and impurity profiling of drugs have also been enlightened with the help of prototype citations from the literature. Identification of suitability of particular design type from its use in the literature has been addressed as conclusive remarks. All this is supposed to benefit the researchers who are planning to apply DoE in HPLC analysis and will lead to establishing a way to explore the potential of design strategies to contribute to the betterment of drug analysis. The trend observed right from the discovery of concept up to date for the application of the DoE strategy for HPLC analysis of pharmaceuticals has been studied. Pubmed and Scopus searches were performed on September 9, 2015, to address the development during the consecutive 5-year period. The paradigm shift that one can witness from Figure 1A and B added toward our interest in creating and putting forth this review based on the design applications in HPLC.

Figure 1: Trend in the application of experimental design methodologies in HPLC analysis of pharmaceuticals as evidenced in (A) Pubmed and (B) Scopus Search Engines.
Figure 1:

Trend in the application of experimental design methodologies in HPLC analysis of pharmaceuticals as evidenced in (A) Pubmed and (B) Scopus Search Engines.

Design of experiments

The approach of fitting multivariate data into an empirical function as linear or quadratic with interaction terms, which is then used to obtain useful information related to the system, such as minima and maxima and trend observed when the parameters are subjected to change simultaneously, can be referred collectively as the DoE (Hibbert 2012). HPLC analysis requires experimentation which should achieve objectives efficiently and accurately that too with few experiments. DoE can be utilized as multivariate optimization stratagem to fulfill this goal with the following general steps:

  1. Choosing a statistical design to investigate a region of experimental interest.

  2. Perform experiments in random order.

  3. Perform statistical interpretations based on the regression results to choose the most appropriate model (Bianchini, Castellano & Kaufman, 2009).

Various updated statistical computer programs are available as evidenced by a methodical literature search to execute the steps listed above, which represents a wide variety of software packages that can be efficiently used by researchers. Some of these programs are Design Expert from Stat-Ease Inc. Pat Whitcomb, Minneapolis, MN, USA (Beser et al., 2011; Bianchini, Castellano & Kaufman, 2009; Davies, De Biasi & Perrett, 2004; Deshpande et al., 2011), MINITAB by Minitab Inc., F. Ryan, Thomas A. Ryan, Jr., and Brian L. Joiner, State College, Pennsylvania University, University Park, FL, USA (Cao et al., 2010; Coscollà et al., 2009; Costa et al., 2010; Guo, Srinivasan & Gaiki, 2007), Fusion pro from S-Matrix corporation, Eureka, CA, USA (den Brok et al., 2003; Nistor et al., 2011; Quiming et al., 2008), SAS’s JMP, John Sall and team, Cary, North Carolina, USA (Martendal, Budziak & Carasek, 2007; Switzar et al., 2011), StatSoft’s STATISTICA, Dell Software, Round Rock, TX, USA (Gruendling, Guilhaus & Barner-Kowollik, 2009; Hadjmohammadi & Nazari, 2010), Matlab by The Mathworks Inc., Natick, MA, USA (Moberg, Bergquist & Bylund, 2006; Pous-Torres et al., 2009), Modde from Umetrics, Sartorius Stedim Biotech, Goettingen, Germany (Lin et al., 2008; Verma, Hartonen & Riekkola, 2008), Unscrambler from CAMO AS, Harald Martens, Gaustadalléen, Oslo, Norway (Duarte & Duarte, 2011; Prieto et al., 2007) and Virtual Column by ACROSS and the University of Tasmania, Tasmania, Australia (Madden et al., 2002).

Wish to apply design in HPLC? Let us check this out (Hibbert 2012 )

The basic statistical terminologies involved in DoE and their understanding is a key to get well versed with the concept of ED. First amongst them is “experimental designs,” defined as statistical techniques for planning, conducting, analyzing and interpreting data from experiments. This has the major counterpart, a “response” dependent variable, which is a measured or observed quantity that is subject of study or optimization; for example, during chromatographic method development and validation the responses may be retention time, peak area, number of theoretical plates, recovery, RS among chromatographic peaks for an analyte. A “factor,” predictor or parameter which can have a discrete or continuous value may be controlled/independent or uncontrolled/dependent. Independent variables are experimental variables that can be changed independently of each other. Typical independent variables comprise the pH, temperature, concentration of reagents, microwave irradiation time, flow rate, temperature and elution strength among others. Levels of a variable are different values of the variable at which the experiments must be carried out. “Residual” is the difference between the calculated and experimental results for a determinate set of conditions. A good mathematical model fitted to experimental data must present low residual values. “Randomization” of the order of experiments during a study will assist for the exact idea about the fact that whether the repeatability variance of the response is undergoing changes due to effects of uncontrolled factors, examples of factors for HPLC may be mobile-phase proportions, stationary phase, temperature, etc. “Factor level” justifies the value of a factor that was assigned during DoE; this also decides the type of design selected, for example, two-level or three-level design. “Response surface” is a relationship of various responses which consist of a function fitted to experimental data, plotted mostly as a three-dimensional or sometimes two-dimensional graph or curvature. “Response surface methods” (RSM) are used to conclude the details related to the chromatographic system (Bezerra et al., 2008). “DoE model” is a mathematical polynomial equation that may be either first order or second order; it is mostly empirical based on polynomials of factors or may be based on theoretical understanding of the designated chromatographic system. If the model is based on two factors, then it is represented as linear (equation 1) or quadratic (equation 2) depending upon the factors chosen and whether the interaction terms are negligible or have a significant value, respectively (Ferreira et al. 2007a).

(1)y=b0+b1x1+b2x2+b3x3+b12x1x2
(2)y=b0+b1x1+b2x2+b3x3+b12x1x2+b13x1x3+b23x2x3+b11x12+b22x22+b33x32

where “y” is the measured response (dependent variable) associated with the each factor-level combination, “b0” represents the polynomial equation intercept representing the average arithmetic mean of all quantitative outcomes of runs and “b1b33” are regression coefficients computed from the observed experimental values of “y”. “x1,” “x2” and “x3” represent the coded levels of independent variables. The last term effect is regarded as a coefficient for the coded level. Most probably for HPLC analyses “x1,” “x2” and “x3” may be mobile-phase composition, flow rate, temperature and pH of mobile phase (Ficarra et al. 2002).

Regulatory perspectives for application of DoE

According to a recent guidance issued by FDA’s Pharmaceutical CGMPs for the Twenty-First Century: A Risk-Based Approach (2004), which has its encryption that principles of process validation should be aligned with the product lifecycle. FDA’s Guidance for Industry. Process Validation: General Principles and Practices (2011) addressed concerns with previous approaches for process validation where multiple batch processing at a time ensured controlled manufacturing. Thus, the traditional approach always had a scope for continuous improvement for quality and efficacy during process validation as it fosters the shuffling of the process not at all or to a negligible extent to a prior validated process and hence may hamper continuous improvement.

Issues pertaining to process validation have its attributes parallel to analytical method development and validation. HPLC being a widespread technique in pharmaceutical analysis and its basic counterpart chromatographic method development and validation can be considered to have an analogous concern. Validation of analytical methods is predominantly performed according to guidance issued by ICH Harmonised Tripertite Guideline (2003) or at the most with guidelines laid by United States Pharmacopeia (The United State Pharmacopeia USP 24 2000). Method development and validation being an event limited by and to a specific phase of time without any guidance for evaluation of continuous method performance. The guidance on suitable acceptance criteria is also required; hence, there is a scope for the method validation process to be traced more. Validation documents thus prepared will withstand regulatory requirements and assure consistent method performance during the development phase along with application of the method for usual analytical evaluations. The ICH Q2 (2005) guideline, Validation of Analytical Procedures: Text and Methodology, for pharmaceutical products is considered by pharmaceutical industry and regulatory authorities which provide guidance on philosophy for the analytical method. The development and validation of the method for pharmaceutical product is considered as a one-time event without any focus on continuous assessment and screening for criteria to establish desired purposes (criteria for method acceptance). Hence, there is a scope for determining the ability of the method to be more convenient during validation documentation and regulatory screenings as well, besides the fact that the method should perform well during custom analysis.

Transfer of an analytical method after it is developed and validated by the developing analyst has become a regular protocol nowadays. This should ensure transfer of implicit knowledge related to analytical method development and validation to persons who will use the method for routine analysis and responsible for possible documentation that both sending and receiving laboratories are obtaining akin results for the said method. The lack of illustrated and well-defined statistical approaches during method development and validation may lead to a deficient transfer of facts of development analysts. Thus it may cause method failures to perform in receiving laboratories. Many efforts are then required from all sides in identifying the factors crucial toward affecting method performance characteristics. A hidden risk of transfer of analytical reports is more vulnerable than ensuring the ability of the receiving laboratory to run the method accurately and reliably to ensure the continuity and integrity of analytical results. Considering analytical methods for the analysis of APIs and/or finished pharmaceutical products (FFPs) as a “process”, which needs to have an output predefined mostly in the form of data that affect the acceptable quality of APIs and/or FFPs, resulted in taking quality by design (QbD) concepts designed for manufacturing processes and showed the effectiveness of these when employed for analytical methods Borman et al. (2007). Consequently, the concepts of lifecycle validation being developed for manufacturing processes might also be applicable to analytical method development and validation too.

The concept of equipment qualification in the USP, consisting of equipment design, followed by operational and performance qualification, proposed by Landy and Vuolo-Schuessler (Landy, 2002; Vuolo-Schuessler et al., 2014 ) aligns well with the lifecycle and with analytical method validation activities. Further, ICH in its Q8 (Pharmaceutical Development) (2009), Q9 (Quality Risk Management) (2005) and Q10 (Pharmaceutical Quality System) (2008) gave stringent requirements regarding quality of product, and United States Food and Drug Administration (USFDA) also stated the importance of quality of pharmaceutical products by offering process analytical technology (PAT), which is supposed to be a framework for innovative pharmaceutical development, manufacturing and quality assurance. DoE either alone or along with QbD ultimately helps to implement Q8 and Q9. FDA’s view of QbD is that “QbD is a systematic approach to product and process design and development”. This concept was accepted by FDA in 2004 and detailed description was given in Pharmaceutical cGMPs for the Twenty-First Century: A Risk-Based Approach (Sangshetti et al., 2014).

In a nutshell:

  1. Designing effective analytical method development and validation will assure quality similarly as designing an efficient manufacturing process can assure product quality.

  2. Application of design will foster scientific understanding of problems associated with analytical method development and validation.

  3. A risk-based assessment will still enhance the regulatory attributes further although regulatory approaches are there.

  4. Some modifications to accommodate scientific knowledge may be experienced by the related regulatory policies and measures.

  5. Thus, either DoE or QbD is not implied directly in guidelines but they may seek a statistical support further as an advancement.

Use of DoE in chromatography (HPLC): history and purposes

Use of statistical modeling and design of experiments (SMDE) was reported earliest by Kettaneh-Wold in 1991 as an essential tool for the development and understanding of complicated processes and products with efficient experimentation (Kettaneh-Wold 1991). He further stated that chemical analysis requires the use of accurate, selective and precise analytical methods that optimize recovery, chromatographic peak separation as well as robustness. To achieve the stated objectives for the requirements aforementioned, experimentation is required. Such experimentation will suggest that the negative and positive factors are crucial for such a process. Fischer in 1925 solved the problem of efficiently selecting a set of best experiments which later spurred the concept of SMDE (Fischer 1925).

Preliminary design strategies applied for chromatography mentioned the use of orthogonal designs as factorial designs. These were applied as a full factorial or fractional factorial designs (FFD) depending on the purpose. In 1950, Plackett-Burman developed orthogonal designs with “N” being multiple of 4 which allowed only the measurement of the main effects (confounding of interactions of two factors with each other and with main effects). Due to the ability to screen many variables, these proved to be good designs for robustness testing during HPLC. This has been followed by the development of classical response surface designs which were introduced as CCD (Box & Hunter, 1978). A face-centered CCD was developed and used with the application of partial least square (PLS), as a generalized regression model to fit data obtained through experimentation to a quadratic model (Weld 1982). Mixture designs were introduced in 1955 which included classical mixture designs, namely, axial designs for screening factors and simplex lattice and simplex centroid for response surface determination (RSD) to visualize the effect of various variables on method robustness (Comell 1990). One of the major techniques used for the method development of ternary and quaternary HPLC systems has been to use mixture designs, often referred to as “Glajch’s Triangle”. This technique does not allow for the systematic and simultaneous optimization of other factors such as gradient time, pH and temperature that affect the quality of separations; hence, an alternative approach is used such as spherical coordinate representations (Morris, Hughes & Marriott, 2003). The use of mixture designs in chromatography was limited due to constraints that the factors do not always have values between 0% and 100% (Ferreira et al., 2007; Hibbert, 2012); it may be assumed that fractional values in this situation were solved with the advent of D-optimal designs for the limited number of runs and when the classical design was not applicable (Atkinson & Tobias, 2008). Taguchi designs were introduced to optimize the response while at the same time minimizing variability. These are continued for their use in the development of robust pharmaceutical manufacturing processes; their use in chromatography and thereby in HPLC was rare and extremely limited (André et al., 2013; Araujo & Janagap, 2012; Kettaneh-Wold, 1991; Vasselle, Gousset & Bounine, 1999). Plackett-Burman designs (PBD) are well-balanced and randomized screening designs (Chen et al., 2001) which were employed to solve the research objective of checking the robustness of HPLC methods (Goupy 2005). The first purpose of using such designs is to rule out screening to assure that the factors being evaluated are affecting response, may be in the negative or positive way. The subsequent optimization can be performed with many of factorial and FFD. The second purpose for which these designs were applied is to test the ruggedness (different normal conditions introduced) and robustness (deliberate small changes are introduced) of the method (Stojanović et al. 2013). These designs should be used cautiously. The method repeatability is assured usually by adding several measurements at the center point and to assure that the response surface has no curvature; if the response surface has curvature, PBD are not suitable to check robustness and other EDs should be used (Li et al. 2005). The literature also depicts the use of PBD using a two-level, non-geometric, orthogonal array, which were applied to determine the ruggedness of laboratory test methods (Waters & Dovletoglou, 2003). Optimization of chromatographic conditions is a crucial step of chromatographic method development and validation which affects the method performance at all stages. The BBD was one of the design strategies suggested in the literature for optimization of mobile phase during chromatographic analysis (Ferreira et al., 2007; Mustafa et al., 2013). The effective use of this kind of design strategy has also been justified along with Derringer’s desirability function in the fine tuning of gradient programs (Vemić et al., 2013) as well as along with RSM to evaluate main, interaction and quadratic effects of the selected factors on responses during optimization (Awotwe-Otoo et al. 2012). Even there is a reference in the literature about the use of BBD in development and robustness testing during LC-separation also as proved by Kristoffersen et al. (2007) .

The statistical experimental design (SED) was developed by Fischer to solve the problem of efficiently selecting best experiments, which later led to orthogonal/factorial designs (Fischer 1925). These designs were later, known from late 1991, for their applicability in improving drug solubilities as evidenced by Kettaneh-Wold (1991). Usually, factorial designs are meant in HPLC to model the response or to optimize the response and/or criteria. Recently, full factorial design was used during forced degradation experiments, and the factors/combination of factors which were most likely to affect degradation of luliconazole under various conditions were identified and further optimized using RSM (Sonawane & Gide 2011a; 2011b; 2016). Determination of relationships between the chromatographic conditions and retention behavior of the analytes has also been investigated using a full factorial design by Acevska et al. (2012). Classical screening designs mostly PBD or saturated FFD can be employed to evaluate the influence of procedure-related factors such as pH and temperature, which can assume a high or low value. In contrast, non-procedure-related factors such as chromatographic column manufacturer for which examination at two levels is not significant. In this case to examine both types of factors at the same time Addelman’s main effect plan for asymmetrical factorials has to be used which was mentioned by Hund et al. (2000). These designs are referred to as asymmetrical because they contain factors to be examined at different number of levels (Hund et al. 2000). Yet the factorial designs are not over; there is something more interesting and applicable, that is, reduced factorial design or FFD which have been applied for the determination of robustness with asymmetric factorial designs (Hund et al. 2000) as well as simply for robustness determination (Bianchini, Castellano & Kaufman, 2009; Goupy, 2005; Romero et al., 2001). The application of FFD to evaluate the considered variables and to identify them as significant factors affecting chromatographic analysis has also been reported by some authors (Iriarte et al., 2006; Torrealday et al., 2003). The rare application of such a design strategy which was observed in the literature was for evaluation of intermediate precision along with robustness as reported before (Ye et al., 2000). Full factorial designs, on the other hand, were also functional toward the determination of robustness (Kristoffersen et al. 2007). A full factorial design was found to estimate all higher order interaction effects as well as main effects during chromatographic analysis (Ragonese, Mulholland & Kalman, 2000). Besides the determination of robustness as that of other designs, full factorial design has also been pointed out for optimization of micellar liquid chromatographic separation statistically assisted with regression models (Hadjmohammadi & Ebrahimi, 2004). The full factorial design was equally applied during the development of HPLC methods (Al-Hamdi et al., 2006). The influence of factors affecting chromatographic analysis was found in the literature with the help of a full factorial design, and a report for estimation of coefficients of a linear regression model developed as a part of the optimization of chromatographic conditions with the help of PBD is also available (Petkovska, Cornett & Dimitrovska, 2008a; Rao et al., 2008). Intermediate precision has been reported by Barmpalexis, Kanaze, and Georgarakis (2009). The highest degree of fractionation is possible with the use of a saturated factorial design, which has been used previously during HPLC analysis to screen the highest number of factors and to quantitatively observe the effects of these factors (Fabre 1996). Robustness of the analytical method was evaluated using a two-level saturated factorial design by Molina, Nechar, and Bosque-Sendra (1998) .

As evidenced by Jacques Goupy in his publication in early 2005, star designs (Brereton, 2003; Massart et al., 1988; Otto, 1999) although seem strange but are the best way to verify method robustness and these are OFAT designs which are simplest and very easy to carry out. With a star design a new factor can be added at the end of experiments to check whether that factor is robust or not (Goupy 2005).

Sequential designs are one of the rare designs investigated in the late 1990s. These designs suggested to be used when the experimenter was supposed to have limited knowledge about how far the optimum region is from the starting experimental point. Araujo and Brereton (1996a) suggested several types of sequential designs for their application listed above in chromatography, which were simplex design, steepest ascent design and evolutionary optimization design. Doehlert designs comprise another class of EDs with which different factors can be studied at different numbers of levels (Barros Neto, Scarminio & Bruns, 2006; Massart et al., 1997). Ferreira et al. (2004) described Doehlert designs or DM as a tool in the optimization of methods in analytical chemistry where the authors quoted the first application of DM/design in the optimization of the separation process using HPLC (Ferreira et al. 2004). Such a design has been suggested in the literature during systematic and simultaneous optimization of the gradient solvent system with parallel optimization of instrumental and experimental variables (Araujo 2000). Doehlert designs are easily applied to optimize the variables during chromatographic separation (Massart et al. 1997). Further, in HPLC analysis, the Doehlert design has been used for finding the optimal chromatographic condition for the simultaneous determination of analytes (Djang'eing'a Marini et al. 2003). An alternative and very useful ED for second-order models is the uniform shell design which was proposed by Doehlert in 1970. Because the points are uniformly distributed on a spherical shell, Doehlert suggested that these designs be called uniform shell designs (Doehlert 1970). Araujo and Janagap (2012) have discussed in detail the principles of Doehlert uniform shell designs (aka Doehlert designs) and their purpose in chromatography. Along with it, they have concluded that Doehlert uniform shell designs are generally used for determining the optimal combination of the factors that have the strongest influence on selected single or multiple experimental responses although the chromatographic system is influenced by more than 50 factors (Van Leeuwen et al. 1991). Doehlert designs should not be used for more than three factors as this would lead to a high number of experiments and complications in predictions (Araujo and Janagap 2012). Recently Hibbert (2012) suggested in his review that Doehlert designs are becoming more popular due to greater efficiency in optimizing chromatographic conditions.

Some other designs with unprecedented and mysterious status in pharmaceutical and thereby in the chromatographic analysis are supersaturated designs, nested designs or nested analysis of variance (ANOVA) and split-plot designs. The application of supersaturated designs in pharmaceutical analysis is not very common. Being recently developed designs although, these may be used as screening designs. A supersaturated design when applied for multiple factor effects of main factors is confounded and cannot be estimated unconfounded anymore (Dejaegher and Vander Heyden 2011). A supersaturated design may be constructed as a two-level, multi-level or mixed-level design, any of which can be applied thereafter depending on experiments (Dejaegher and Vander Heyden 2008). Nested design or nested ANOVA (Vander Heyden and Massart 1996) as referred before in 2007 only by Dejaegher and Vander Heyden (2007) is proved to be useful during ICH robustness and ruggedness testing to determine the influence of factors at several levels. Split-plot EDs are uncommon in chemistry and hence in the chromatographic analysis (Cornell 1988). The use of such designs involves performing a block of experiments to investigate a system usually followed by an identical replicate block to measure experimental errors (Bortoloti et al., 2004). Split-plot designs normally involve a large number of factors. Several applications in chemistry involved both process and mixture variables (Bortoloti, Borges & Bruns, 2005), but applications of such design specifically in chromatography or HPLC are yet to be untouched. Figure 2 depicts the dominance of various designs employed in the literature for HPLC as a recent trend. The data were generated based on scifinder search for the years 2014 and 2015. CCD can be seen as the design of choice and employed in most of the publications involving the use of DoE during HPLC determination of pharmaceutical drugs and drug products.

Figure 2: Dominancy of designs for the application in HPLC analysis.
Figure 2:

Dominancy of designs for the application in HPLC analysis.

Arbitrary classification for various types of EDs used in HPLC analysis

Based on the existing research articles in the literature, the various types of EDs applied in chromatography till date can be classified arbitrarily for the sake of better understanding of their applicability into screening designs, response surface designs and mixture designs. These three types are again divided into subtypes. The various types and associated subtypes of designs employed in the betterment of chromatography are represented in Figure 3.

Figure 3: Arbitrary classification for various types of EDs used in the literature for chromatographic studies.
Figure 3:

Arbitrary classification for various types of EDs used in the literature for chromatographic studies.

General methodology for application of ED during chromatographic analyses

Preliminary studies

Preliminary investigations need to be carried out in the same way as that of the regular protocol for the liquid chromatographic method development and validation, while aspiring for application of ED during chromatographic analyses, which includes steps such as selection of initial HPLC conditions and optimization of the mobile phase. Even optimization of the HPLC mobile phase has been addressed with application of DoE by some authors in the literature (Hadjmohammadi & Nazari, 2010; Torrealday et al., 2003; Vemić et al., 2013) along with a selection of a column, pH range and organic solvents (Hafez et al., 2015). Decisions related to the feasibility of organic solvents such as acetonitrile, methanol and water in various compositions by isocratic or gradient elution mode and need of the optimal flow rate to achieve the pre-decided goals of the intended method as well as to obtain good peak shape and/or RS are addressed in depth by Ribeiro et al. (2004) .

Critical factors as independent variables and their selection

Factors related to the chromatographic analytical procedure can be considered as operational factors or environmental factors. Operational factors are based upon the operating procedure during chromatographic analysis, whereas the environmental factors are not necessarily specified explicitly in the analytical method. The selected factors can be quantitative (continuous), qualitative (discrete) or mixture factors (Vander Heyden et al., 2001). Qualitative and/or quantitative factors by which the penultimate results of the analysis are affected can be referred to as critical factors or independent variables. Such 50 factors or independent variables have been mentioned in the previous literature which are supposed to influence HPLC methods and related analyses (Van Leeuwen et al., 1990). Mixtures of solvents are often used in analytical methods. In HPLC analysis the mobile phase can contain, besides the aqueous phase, one to three organic modifiers, yielding mixtures of two to four components (Vander Heyden, Questier & Massart, 1998). If one component of a mixture is found to be important, this means in practice that the mixture composition as a whole is important. Because it is not possible to control only one of the components of a mixture, the composition of the mixture as a whole should be more strictly controlled (Vander Heyden et al. 2001).

Moreover, the list continues further if the analysis is supported by pre-column or post-column derivatization (Fabre et al., 1989). These factors are related to the sample preparation step (sample weight, internal standard concentration, sonication time, the volume of extraction solvent, the age of the solutions, etc.), separation and detection. Typical factors are, for example, the flow rate and mobile-phase composition (buffer pH and concentration, the smallest component in the solvent mix, additive concentration, etc.) injected or applied volume, batch, or age of column in HPLC. As the changes in level values are small, limited numbers of factors are expected to affect the results. Due to the time constraints and practical limitations, the number of factors is limited up to eight and it is important to perform experiments over a limited period of time to obtain reliable results (Fabre 1996).

Selection of factors during the development and validation of the HPLC method may vary depending upon the step of analytical determination; for example, the proportion of organic phase and flow rate are usually responsible for RS and peak shape. Although the wavelength maximum is usually considered for analytical method development, the drugs depicting absorbance at more than one wavelength create a choice for the selection of suitable wavelength. Studies involving determination of two analytes at a time required to a have a common wavelength at which the detection of both drugs can be carried out effectively. Hence, the effect of wavelength selected on chromatographic analysis can be taken into consideration, and one wavelength can be preferred depending on whether it is a critical factor and the effects, positive or negative, it is depicting on the responses to be measured (Ribeiro et al. 2004). Examples of quantitative factors are the pH of a solution, the temperature or the concentration of a solution, for qualitative factors the batch of a reagent or the manufacturer of a chromatographic column and for mixture factors the fraction of organic modifier in a mobile phase. The selected factors should represent those that are most likely to be changed when a method is transferred between laboratories, analysts or instruments and that potentially could influence the response(s) of the method (Vander Heyden et al. 2001). As referred earlier several variables may influence the response of the system studied, and it is practically impossible to recognize and control the small contributions from each one. Hence, it is necessary to select those variables with major effects. Screening designs should be carried out to determine which of the several experimental variables and their interactions present more significant effects. Full or fractional two-level factorial designs may be used for this objective principally because they are efficient and economical (Lundstedt et al. 1998). Factors to be studied may be obvious from the nature of the system. Ruggedness tests in method validation will have had the factors for the study prescribed in the protocol (Hibbert and Gooding 2006). If it is known that a factor has a great effect of the separation (perhaps column temperature), there is no point in discovering this information in a screening design. It can be included immediately in the factors for optimization. Discrete-valued factors such as column type might be studied separately rather than as part of a design. Thus mobile-phase composition, flow rates and gradients might be optimized for a C8 column and then for a C18 column (Hibbert 2012).

Selection of factor levels and coded levels or level numbers

The variations encountered in different laboratories due to the use of different instruments, stationary phases, environmental conditions, analysts, etc. should be reflected in the factor levels. Preferably, the number of levels tested for each factor is three (low, high and nominal levels/center point) but five levels can also be considered depending on the situation and to obtain a more accurate surface response. It should be kept in mind that a two-level factorial design implies a linear relationship between the factor and the response, which is not always verified. This is because the method has already been optimized and the nominal level for one or several factors may be close to the optimum, yielding a non-linear response between the two extreme levels tested apart from this value (Fabre 1996). The main effect of wavelength will not be disclosed by comparing the two extreme levels if the two wavelengths are situated on each side of the maximum absorbance wavelength. The comparison of the responses at low and high levels without running experiments at the nominal level (center point) should not be the rule (Caporal-Gautier et al. 1992). The factor levels are usually defined symmetrically around the nominal level prescribed in the operating procedure. The interval chosen between the extreme levels represents the (somewhat exaggerated) limits between which the factors are expected to vary when a method is transferred. In most case studies, the analyst defines the levels according to one’s personal opinion. However, selection of the levels can also be based on the precision or the uncertainty with which a factor can be set and reset (Morgan 1991). Recently, as quoted by Hibbert (2012), the choice of factor levels in a design is most important, possibly more than the design itself. Obtaining information using only a small number of factor levels is the strength of DoE, but also a potential weakness. Each level must be appropriate and lead to useful information. Values too close together do not allow sufficient variation in the response to be observed, and in this case, RSM will have a plateau. However, points that are at the extremes of a reasonable range will give poor responses that might not differ from each other, that is, RSM will depict a maximum response (Hibbert 2012). Not all combinations of factor levels may be practical. Sometimes the improper selection of levels leads to the depiction of maxima in RSM at the edges and the saddle. The selection of factor levels according to the category, that is, whether level needs to be decided for qualitative factor, quantitative factor and/or mixture factors, has been explained in relation to the principle of uncertainty. A clarification for the less applicability of the principle of uncertainty while selecting factor levels and justification of the need of a simple alternative for the same has been stated effectively by Vander Heyden et al. (2001) .

Coded variables are used to represent EDs. The situation is explained by Hibbert (2012) by giving an example of a design that requires only two values of a variable (so-called “two-level” design); factor values are usually given as a series of +1 and −1 indicating whether one value (+1) or the other value (−1) is to be chosen along with the nominal or center point value. The reasons he has stated for this practice is mathematical but also a practical use is that designs can be written independently of the particular factors under study. For designs where there are more than two levels, the values indicate the relative magnitude of the levels. If the temperature is considered as the factor and the range to be studied was decided to be 50°C–100°C, then the required design points would be 50, 57, 75, 93 and 100. Note that this can only be done for continuous variables that can be set as predefined values (Hibbert 2012).

Another example for the coded factor level is as stated by Stojanović et al. (2013) in which 12 experiments defined by the Plackett-Burman experimental plan were performed by varying the five real factors and six dummy factors around the nominal level. The included real factors and their intervals were acetonitrile content in the mobile phase (from 43% to 45%), sodium dodecyl sulfate content in water phase (from 5.5 to 6.5 mM), column temperature (from 40°C to 50°C), pH of the mobile phase (from 4.3 to 4.7) and flow rate (from 0.9 to 1.1 ml/min). Values given in the brackets present the low (−1) and high (+1) levels (Stojanović et al. 2013).

Various factors were chosen while the applications of design procedures during different purposes of pharmaceutical HPLC analyses are as represented in Figure 4. Readers interested in gaining in-depth knowledge about the factors, selection of factors and specific references for the use of particular factor in analysis can refer the cross-citations of an article published by Dejaegher and Vander Heyden (2007) .

Figure 4: Various factors chosen while the application of design procedures during pharmaceutical HPLC analyses.
Figure 4:

Various factors chosen while the application of design procedures during pharmaceutical HPLC analyses.

Choosing response(s) and purpose

The effect of selected factors has to be measured in terms of response which is in turn more essential to understand the chromatographic process. This creates the main goal of optimization of responses in analytical chemistry with frequent objectives of maximizing sensitivity, minimization of the limit of detection. Some others are an increase of accuracy and precision, assessment of reproducibility, reduction of cost, identification of important variables, quantification of variable effects, mathematical modeling, ruggedness testing, method validation and mixture formulation (Olivero, Seshadri & Deming, 1993). Another concern associated with HPLC is its relation to trade and optimum separation is desired with considerations such as time, cost, required measurement uncertainty and the ultimate applicability of analytical information. Measurement of multiple responses at a time can be considered as a most important advantage of DoE and models developed that arrive at the desired overall optimum without extra experiments (Hibbert 2012).

Chromatographic responses as stated earlier can be quantitative responses such as peak areas, peak heights and qualitative chromatographic or electrophoretic parameters (plate count, symmetry factor, RS and retention or migration times) which are typically assessed during analysis (Fabre 1996). Both qualitative and quantitative responses are taken into consideration in chromatographic analysis depending on the purpose (Li et al. 2005). According to experiments performed earlier, various responses can be selected as stated earlier. For chromatographic methods, responses describing a quantity such as the content of main substance and by-products and/or peak areas or peak heights are the more evident. For a separation method, one should also consider one or more parameters describing the quality of the separation, such as, for example, the RS or the relative retention. The evaluation of these separation parameters may also lead to the establishment of system suitability test (SST) limits as required by the ICH. When determining SST limits, other responses such as capacity factors or retention times, asymmetry factors (USP tailing) and a number of theoretical plates can also be studied (Vander Heyden et al. 2001). In conclusion, choosing a response during the application of DoE in chromatography depends on the purpose of analysis; the response may be simply drug content as a quantitative response or retention time as qualitative response while purpose is just the identification of some chemical components as stated by Destandau et al. (2006) while a stability-indicating method will require resolution (RS) as an important response to be studied as explained by Debrus et al. (2011) . The use of RS of the critical pair (i.e. the two most proximate peaks in a chromatogram) as the response of the model can be hazardous due to its non-linear and discontinuous behavior (Lebrun et al. 2008). The thing to be remembered is that the success of getting the right chromatographic condition by DoE depends on the selection of responses (Kumar et al. 2012). Table 1 depicts the classes and number of responses that can be taken into account while applying DoE in HPLC.

Table 1:

Potential responses examined while applying DoE in HPLC (chromatography) (Dejaegher and Vander Heyden 2007).

Chromatographic responses
S. no.QualitativeS. no.Quantitative
I.Retention factor (k)I.Concentration or percent recovery
II.Tailing factor (Asf or T); symmetry factor (S) or asymmetry factor (As)II.Ratio of compounds concentration
III.Plate height (H)III.Peak area (A), height (h), width (w)
IV.Number of theoretical plates (N) (efficiency)IV.Retention time (tr)
V.Background noiseV.Relative retention time; selectivity (α)
VI.Chromatographic response function (separation quality)VI.Resolution
VII.Reproducibility (% RSD) of peak areaVII.Kaiser peak separation index

Choosing an appropriate ED

Analytical researchers often deal with the predicaments of choosing an approach for ED for research. The decision taken is mostly based on the things which are known about the system, needs to be known, the available resources, situations and knowledge of specific EDs. Although several situations in chromatographic research can be addressed with common design solutions, researchers lacking a strong background in statistical design must have to go through scattered literature sources. As it is not possible for all researchers to get acquainted with the knowledge of all the available designs as well as to become the expertise to discriminate among potential EDs, it is usually difficult to decide abruptly about the type of design to be chosen. Even many of researchers do not always have access to experts in the field of ED who can recognize the characteristics of a problem that relate to the selection of a design. Hence, the application of apparently refined statistical methods to the analysis of data acquired from poor selection of EDs may lead to unnoticed erroneous conclusions about the results (Mark 1986).

The oldest literature available for the selection of design which we came across during our literature search was by Olivero (1987), who investigated problem-solving ability of an expert in the domain of ED for chemical research and embedded in a custom-written computer program (named DXPERT). The work led to the development of a computerized tool to help researchers in the preliminary evaluation of various ED classes for a given project. The tool is intended to provide advice in a way similar to an expert in the field, integrating knowledge and experience. It should efficiently gather information about the project, use the information to rank the EDs according to suitability and provide help to the researcher. The scope of the software is the selection of appropriate ED types and does not include setting specific experimental parameters once an approach has been selected (Olivero, Seshadri, and Deming 1993).

Despite the use of the computer program the general criteria for the selection of a design have been discussed by Debrus et al. (2011), and according to their views, selected design needs to have good statistical properties as orthogonality and/or rotatability to maintain the number of experiments as low as possible as a prime consideration. DoE can be split up into two categories as screening designs which allow estimation of the factors’ effect on the selected response. When too many factors seem to affect the response (i.e. four or more), these designs are mainly used to select factors that have the higher effects (i.e. the factors that create the higher response variation). In this category, a well-known design which has been applied in chromatography is the PBD (Debrus et al. 2011). In liquid chromatography (LC), PBD are also used to estimate the robustness of an optimal separation (Dejaegher et al., 2007c). The second category corresponds to optimization designs (i.e. used to model the response and to optimize response and/or criteria). The EDs in this class are mainly full factorial (i.e. complete combination of all factor levels), FFD (i.e. a statistically selected subpart of full factorial design), D-optimal (i.e. tend to minimize the parameter estimates covariance and then maximize the D factor) and CCD (i.e. tend to place the experiments on a circular/spherical shape around the experimental domain center to obtain a good rotatability property) (Atkinson and Donev 1992). Although the path directed by the previous researchers seems to be an interesting option while selecting a design for chromatographic investigation, the authors here wish to suggest that along with a literature search for various types of designs used, a preliminary computer search using software packages available can be used to determine the EDs according to the analyst’s choices. The combined efforts will lead to the better understanding and hence the proper application of EDs as per the requirements.

Conducting actual experiments

The main research goals of any analytical investigation are to optimize the desired response and to understand the underlying process. The subsidiary objectives are modeling the phenomenon and/or screening followed by optimization. After choosing an appropriate design for the chromatographic and thereby analytical investigation, various pre-chromatographic requirements need to be fulfilled as usual. For the evaluation of the critical chromatographic parameters, a mixed standard solution is needed; for an assay, standard and test solutions are prepared and need to be injected in the sequence as specified in the procedure accordingly (Olivero, Seshadri, and Deming 1993). Replicate injections should be preferred, except if the time is restricted, to estimate the order of experiments; it has been stated that randomization is not necessary when one is primarily concerned with using screening designs with one observation per run (Wheeler 1989); however, it is the opinion of the author from the literature review that the different experiments should preferably be carried out in a random order (selected from a table of random order or generated by software) to take into account uncontrolled factors likely to introduce a bias into the responses. Randomization is essential if a center point is used. Quantitative (peak areas, peak heights) and qualitative chromatographic responses (plate count, symmetry factor, RS and retention or migration times) are typically measured during the tests (Araujo and Brereton 1996a). Results obtained for the quantitative factors (chosen responses) as per the design during actual experiments are subjected to statistical analyses to check validity of the predicted model with the experimental model through evaluation of various statistical parameters such as coefficient of regression, standard deviation, coefficient of variations, degrees of freedom, sum of squares, mean sum of squares, Fischer’s ratio for the variable or selected factors (Ganorkar, Dhumal & Shirkhedkar, 2017).

Statistical analysis of the responses and interpretation

As stated previously in Section “Choosing response(s) and purpose”, the actual response values obtained after conducting the actual experiments given by design software or generated manually depending on the type of design are subjected to statistical analysis after computation. All the associated software packages (today) or manual statistical analysis (past) uses ANOVA to fit the data to select a model and to evaluate the two-factor interaction effects usually practical in chromatography (Gilmour 2006).

The statistical analysis of the selected responses and associated interpretation can be categorized as qualitative and quantitative (Figure 5), while for further convenience it can again be divided as numerical, graphical and calculations of percent errors sometimes.

Figure 5: Ways of statistical analyses and interpretations applied in the literature for chromatographic experimental designs.
Figure 5:

Ways of statistical analyses and interpretations applied in the literature for chromatographic experimental designs.

Qualitative analysis of SEDs employed in chromatography
Response surface plots/surface response curves

RSM was developed by Box and collaborators in the 50th century (Bruns, Scarminio, and de Barros Neto 2006), which led to the generation of response surface plots or curves. The introductory definition of a response surface plot or a response surface curve has already been stated in Section “Wish to apply design in HPLC? Let us check this out (Hibbert 2012)”. Just to add to it, a response surface is a three-dimensional or two-dimensional plot or a curve of a function/response fitted to experimental data generated by a factor(s) or variable(s) or combinations of them, which is principally used to deduce the information about the system with most precise visual graphics (Skartland, Mjøs & Grung, 2011). Response surface plots can be used to optimize a single response at ease, but when one needs to optimize multiple responses (two to five responses or should not be very large in number) at a time, it can be done by simply visual observation of the various response surfaces obtained for a particular single response respectively and overlapping them to find out the experimental region which is supposed to satisfy all the responses to be studied (Sivertsen et al., 2007). Qualitative interpretation of the chromatographic data can be done mostly using a response surface plot or curve. A response surface is a visualization for the predicted model equation (usually quadratic). It is a graphical representation of an n-dimensional surface with (n + 1)-dimensional space, which is usually a two-dimensional representation of a three-dimensional plot. The plot can be visualized for three or more variables only if one of the variables is set to a constant value; depending on the factors selected and the response to be optimized or studied, a response surface may vary as depicted in Figure 6 by Bezerra et al. (2008) for two factors. The figure states the role of response surface plots generated for a quadratic model during optimization of factors. The figure is about optimizing response “y” by varying factors “x1,” “x2” and “x3”. The optimum response shown by the maximum point in the response surface can be within the experimental region as in Figure 6A and B, while if there is a plateau for one of the variables, then the variation of that variable does not affect the system (Figure 6B). Displacement in the initial design is needed if the maximum (optimum) point is outside the experimental region (Figure 6C). Sometimes minima may be obtained (needed) to define a response; in this case, the response surface plot will look like the one shown in Figure 6D. If there exists an inflection point between a relative maximum and a relative minimum, then it represents a saddle which is considered to be critical, coordinates of which will not serve as optimal values. Hence, in this case, it is possible to find the optimum region through visual inspection of the surfaces and to make necessary changes in design applied. In a nutshell, the application of DoE in chromatography and thereby the application of response surface plots for the interpretation of data generated by the quadratic model may result in possible shapes as depicted in Figure 6A–E and will need to be observed as suggested above. The literature (Eldin, Shalaby & El-Tohamy, 2011) search revealed the use of response surface plots for separation and optimization associated with HPLC methods (Dewé et al., 2004; Acevska et al., 2012; Bezerra et al., 2008; Ferreira et al., 2007; Khamanga & Walker, 2011; Krishna et al., 2016; Kumar et al., 2012; Petkovska, Cornett & Dimitrovska, 2008a), exploring robustness of a chromatographic system, mostly HPLC (Ficarra et al., 2002; Ganorkar, Dhumal & Shirkhedkar, 2017; Petkovska, Cornett & Dimitrovska, 2008a; Rao et al., 2008; Srinubabu et al., 2007).

Figure 6: Response surfaces: some profiles of surface response generated from a quadratic model in the optimization of two variables.(A) maximum, (B) plateau, (C) maximum outside the experimental region, (D) minimum and (E) saddle surfaces (Bezerra et al. 2008).
Figure 6:

Response surfaces: some profiles of surface response generated from a quadratic model in the optimization of two variables.

(A) maximum, (B) plateau, (C) maximum outside the experimental region, (D) minimum and (E) saddle surfaces (Bezerra et al. 2008).

Contour plots

The application of EDs to explore potential pharmaceutical analytical relationships leads to the generation of the data sets, which need to be represented, understood, studied and interpreted further. Pharmaceutical analysis when subjected to DoE involves generation of large multivariate data sets, and hence needs to be plotted as a first step prior to understanding. For such large data sets a contour plot (two-dimensional) is an alternative to a three-dimensional response surface plot. The plot is a graph between z (iso-response values); represented as lines against (x, y) coordinates (variables) which are plotted instead of longitude, latitude and elevation (Dejaegher and Vander Heyden 2011). Nowadays variations available to be incorporated in contour plots to pinpoint the deliverables specify the contour levels, choosing lines or filled areas (custom coloring schemes), showing or hiding data points and labeling contours with response values. A sample two-dimensional contour plot and one that is generated by the authors for optimization of a capacity factor during HPLC method development are depicted in Figure 7. The effect of two independent variables “X” and “Y” on the respective axes toward a response is represented collectively as iso-response lines (grids) as a function of levels of two factors in Figure 7A, while Figure 7B is the visualization for the effect of tetrabutylammonium hydroxide (TBAH) on the capacity factor, which depicts that the increase in the concentration of TBAH increases the capacity factor for separation of eberconazole nitrate (Krishna et al. 2016). Generation of “z” values and iso-response lines from them is performed by the respective software program. The readers interested in the mathematical calculations pertaining to contour plots and their generation should refer to the articles published by Araujo and Brereton (1996b, 1997) , Araujo and Frøyland (2006). The use of contour plots for the optimization of chromatographic conditions has been stated effectively by Ferreira et al. (2007a). Various applications for the graphical interpretation of contour plots as described in the literature are development and optimization of chromatographic conditions (Araujo & Grung, 2012; Awotwe-Otoo et al., 2012; Barmpalexis, Kanaze & Georgarakis, 2009; Chen et al., 2001; Dejaegher & Vander Heyden, 2007; Khamanga & Walker, 2011; Krishna et al., 2016; Kristoffersen et al., 2007; Outinen et al., 1998; Székely et al., 2012), RS of drug and DPs (Murthy et al. 2013) and optimization of stress conditions (Sonawane & Gide 2011a; 2011b; 2016).

Figure 7: Contour plots: (A) effect of two independent variables X and Y on the respective axis toward a response represented collectively as iso-response lines (Grids). (B) Effect of concentration of TBAH on the capacity factor of eberconazole nitrate (Murthy et al. 2013).
Figure 7:

Contour plots: (A) effect of two independent variables X and Y on the respective axis toward a response represented collectively as iso-response lines (Grids). (B) Effect of concentration of TBAH on the capacity factor of eberconazole nitrate (Murthy et al. 2013).

Polynomial equations

The use of EDs for various purposes in chromatography, which is discussed previously, usually results in the generation of a linear (first-order or first-degree) and/or quadratic (second-order or second-degree) polynomial equation depending on the number of coded factors or variables and the responses to be optimized chosen during a particular study. A literature search reveals that the polynomial equation generated fits best the selected model/design used for the study. The equation usually assumes the forms as represented in equations (1) and (2). The model if based on two factors is then represented as linear (equation 1) or quadratic (equation 2) or as linear and quadratic depending on the factors chosen and whether the interaction terms are negligible or have a significant value, respectively, as stated previously in Section “Wish to apply design in HPLC? Let us check this out (Hibbert 2012)”. The role of these equations in the interpretation of the effect of variables for a response can be studied by readers by referring to some of the published articles cited (Ficarra et al., 2002; Khamanga & Walker, 2011; Kumar et al., 2012; Milovanović et al., 2012; Petkovska, Cornett & Dimitrovska, 2008a; Rafamantanana et al., 2012; Rao et al., 2008; Torrealday et al., 2003; Srinubabu et al., 2007; Vemić et al., 2013).

Conclusive remarks regarding the application of polynomial model equations of all types are focused on the magnitude and the sign of the coefficients of the variables in the equation. The positive sign indicates the positive impact of changes in variables according to designated levels and a negative sign indicates a negative impact. The similar is also true for the sign and magnitude of the coefficients for the interaction effects of two or more variables. A rare recent report by Sonawane and Gide (2016) exists in the literature for the application of Yates analysis to retain significant coefficients in polynomial equations followed by generation of RSM and optimization of the percentage of degradation during forced degradation studies of luliconazole.

Normal and half-normal probability plots

The earliest report for the application of normal probability plots for supplementation of statistical results for visualization of critical factors was published by Box, Hunter, and Hunter (2005) followed by some others later (Box, Hunter & Hunter, 2005; Morgan, 1991), while a later report on the use of it in LC has been stated by Fabre (1996) and others (Davies, 1993; Fabre, 1996; Vander Heyden & Massart, 1996).

The graphical interpretation of imperative effects can be revealed with a normal or half-normal probability plot. It is necessary to decide that the numerical limits obtained after statistical interpretation are significant or not, which can be easily decided by representing values graphically with the aforementioned plots. These are always applied in pharmaceutical chromatography to differentiate significant and non-significant effects during an analysis (Dejaegher and Vander Heyden 2011). Typical plots applied for describing ruggedness or robustness tests of HPLC, capillary electrophoretic, gas chromatographic (GC), supercritical fluid chromatographic and ultra-performance liquid chromatographic (UPLC) assay methods can be shown in Figure 8A and B (Dejaegher and Vander Heyden 2007). Essential details about the values (rankits) utilized in generating plots along with construction visualization and interpretation may be obtained by referring Vander Heyden et al. (2001). Diverse modern literal applications of such plots include the study of the effects of variables on chromatographic responses such as optimization of the mobile phase or its components (Awotwe-Otoo et al. 2012), RS (Romero et al., 2001; Sivakumar et al., 2007), optimization of retention time (Khamanga and Walker 2011), capacity factor (Murthy et al. 2013) and robustness determination (Dejaegher et al., 2006; Inglot et al., 2013; Li et al., 2005; Pyka, Budzisz & Dołowy, 2013). The half-normal probability plots are also referred to in the literature as “Birnbaun plots” (Dejaegher et al. 2006).

Figure 8: (A) Normal and (B) half-normal probability plots for an N = 12, f = 11 experimental design.A straight line is drawn through the non-significant effects. The significant effects are encircled; adapted from (Dejaegher and Vander Heyden 2007).
Figure 8:

(A) Normal and (B) half-normal probability plots for an N = 12, f = 11 experimental design.

A straight line is drawn through the non-significant effects. The significant effects are encircled; adapted from (Dejaegher and Vander Heyden 2007).

Pareto charts

Graphical supplementation of the statistical results can also be achieved with the help of Pareto charts (Fabre 1996). Along with the interaction plots, Pareto charts provide rapid visual information on the size of effects produced by each variable to categorize them as significant and not significant (Altria and Filbey 1994). It can be concluded from the literature search that the Pareto charts were used best to assist the screening designs such as Plackett-Burman. The primary line of applicability for Pareto charts runs parallel to other graphical modes of visualization as stated earlier as the statistical significance used to categorize variables in Pareto charts. The levels of EDs used after the application of screening designs can be decided easily depending on the size of the effect produced by the variable as demonstrated by Araujo and Janagap (2012). These are used in the literature while tracing factors having significant effects on the robustness of a chromatographic method, RS, optimization of system suitability parameters and few other applications as cited for rest of the graphical optimization ways stated just above in this article. Readers interested in exploring the applications of Pareto charts as screening designs may refer to the recently published article by Agrahari et al. (2014). Figure 9A depicts the use of Pareto charts for the determination of the influence of variables on the capacity factor during HPLC analysis of eberconazole, while Figure 9B depicts the use of the Pareto chart for chromatographic optimization.

Figure 9: Pareto charts: (A) simultaneous influence of numerous variables on the capacity factor of eberconazole (Krishna et al. 2016). (B) A Pareto chart used for chromatographic optimization depicting the t-value effect and ranking generated by a computer program (Agrahari et al. 2014).
Figure 9:

Pareto charts: (A) simultaneous influence of numerous variables on the capacity factor of eberconazole (Krishna et al. 2016). (B) A Pareto chart used for chromatographic optimization depicting the t-value effect and ranking generated by a computer program (Agrahari et al. 2014).

Overlay plots

Rare reports were observed by the authors for the application of overlay plots for interpretation with designs applied to evaluate chromatography or HPLC. Overlay plots were brought to play as a statistical tool for the interpretation of EDs in pharmaceutical analysis and thereby in HPCL in 2009. They were traced from the article published by Barmpalexis, Kanaze, and Georgarakis (2009) during the literature search by the authors of this article, where those referred to as overlay contour plots applied for the optimization of chromatographic RS and generated by feeding data for statistical design in Design Expert Version 6.0.4 (Stat-Ease Inc., Minneapolis, MN, USA). The rest of the graphs were made using SigmaPlot Version 8.0 (Systat Software Inc., San Jose, CA, USA) (Barmpalexis, Kanaze, and Georgarakis 2009). The overlay plot of effects obtained from the search of the design space depicting optimum conditions for the retention, recovery, column temperature and mobile-phase composition as investigated by Kumar et al. (2012) is represented in Figure 10 (Kumar et al. 2012).

Figure 10: Overlay plot: an example used in the literature for the interpretation of a chromatographic design during the HPLC method development and optimization of multiple variables.
Figure 10:

Overlay plot: an example used in the literature for the interpretation of a chromatographic design during the HPLC method development and optimization of multiple variables.

Residual plots

The use of residual plots in chromatography is suggested if one must guarantee that the actual optimum experimental conditions have to be found (Ferreira et al. 2007a). A typical residual plot is depicted in Figure 11, which shows optimization of retention behavior of chlordiazepoxide as demonstrated by Hadjmohammadi and Ebrahimi (2004). Readers interested in exploring the residual plots are suggested to refer to the article by Debrus et al. (2011). The application of residual plots for the optimization of the capacity factor can be explored by referring to the article by Srinubabu et al. (2007) .

Figure 11: Residual plot: an example for predicted retention times according to the regression models generated after the application of face-centered cube response surface design (Hadjmohammadi and Ebrahimi 2004).
Figure 11:

Residual plot: an example for predicted retention times according to the regression models generated after the application of face-centered cube response surface design (Hadjmohammadi and Ebrahimi 2004).

Perturbation plots, bar plots, desirability, sweet spot plots and main effect plots

Perturbation plots are employed in chromatographic design to gain a better understanding of the investigated procedure. These show the effect of individual factors on a specific response, with a remaining factor held constant at a constant reference point (Sivakumar et al. 2007). Figure 12 depicts a perturbation plot for the optimization of the RS between the critical pair as investigated by Barmpalexis, Kanaze, and Georgarakis (2009). The lines presented in a graph for a particular variable represent the sensitivity of that factor toward the response; hence, the primary purpose may be screening of the variables at a later stage to determine most influential factors. The application of bar plots as means of graphical visualization for qualitative determination in statistical designs for chromatography was observed to be rare and was restricted in Owens et al. (2002), Furlanetto et al. (2002), and Yekkala et al. (2006). Other modes of graphical visualizations used for interpretative designs in chromatography (HPLC) were bar plots for studying robustness (Yekkala et al. 2006), desirability plots (Agrahari et al. 2014) and sweet spot plots for chromatographic optimization (Orlandini et al. 2014) and main effect plots generated by MINITAB to observe the effect of various factors affecting chromatographic sensitivity simultaneously (Figure 13) (Li and Rasmussen 2003).

Figure 12: Perturbation plot generated for the optimization of resolution between critical pairs in chromatography depicting sensitivity of response toward variations in variables (Sivakumar et al. 2007).
Figure 12:

Perturbation plot generated for the optimization of resolution between critical pairs in chromatography depicting sensitivity of response toward variations in variables (Sivakumar et al. 2007).

Figure 13: Main effect plots generated by MINITAB to predict the effect of variables placed on the x-axis on chromatographic sensitivity (Li and Rasmussen 2003).
Figure 13:

Main effect plots generated by MINITAB to predict the effect of variables placed on the x-axis on chromatographic sensitivity (Li and Rasmussen 2003).

Quantitative analysis of SEDs employed in chromatography
Regression

As previously suggested by Ferreira et al. (2007a) in their article, due to the availability of statistical computing programs generating regression equations and lack of user interventions in actual regression analysis, it is not under the scope of this article to describe mathematical steps involved in generating regression. Readers interested for the same are requested to refer to the basic sources (Acevska et al., 2012; Box, Hunter & Hunter, 2005; Bruns, Scarminio & de Barros Neto, 2006; Wieling et al., 1996). The purpose for a description of regression analysis here is to explore the applications for which it has been used during ED in chromatography.

Regression as anywhere is applied in pharmaceutical analysis and thereby in chromatography to estimate the relationship between variables, quantitatively, which may be simple or multiple regression analysis. The casual effect of one variable on the other, as well as the statistical significance, can be estimated by both. Simple regression implies to regression analysis with one single explanatory variable (concentration) for a single response (area), as in HPLC. Multiple-linear regression (MLR) is a technique that allows additional factors to enter the analysis separately so that the effect of each on a single response can be estimated at a time which is valuable for quantifying the impact of various simultaneous influences on a single dependent variable. Further, because of omitted variable bias with simple regression, multiple regression is often essential even when the investigator is only interested in the effects of one of the independent variables (Rodrıguez et al., 1998).

The analyst needs to study the linear and quadratic regression functions to be applied for the response, which need to be optimized or evaluated during the application of statistical EDs for screening or optimization in chromatography (Outinen et al. 1998). Chromatographic applications involved the use of either the PLS or MLR; when examined factors are interdependent the correlated PLS deals far better than MLR (Dejaegher and Vander Heyden 2007). Various applications of regressions analysis we came across during the literature search were the use of multiple regression during screening of factors using orthogonal factorial designs as well as PLS regression to fit the quadratic model to data (Kettaneh-Wold 1991) and MLR for robustness (Romero et al. 2001). Molina, Nechar, and Bosque-Sendra (1998) mentioned the use of robust regression. The use of simultaneous designs in chromatographic optimization was reported by Araujo and Brereton (1996a). Quadratic regression models to show dependence between eluent composition and retention times and linear regressions for prediction of RS was reported by Outinen et al. (1998). Evaluation of bench top stability as a part of pre-validation in bioanalytical methods was carried out by Wieling et al. (1996). Application of least square multiple regression for robustness study was assessed by Rodrıguez et al. (1998). The estimation of coefficients of second-order polynomial model was utilized during the LC method validation by Sivertsen et al. (2007). The optimization of assay during HPLC analysis of ethambutol HCl as method optimization was reported by Derringer (1980).

ANOVA

ANOVA is used on the regression results so that the most appropriate model with no evidence of lack of fit can be generated to represent the data. The model used to represent the data should be validated, and this task requires decisions by the researcher, as suggested by Ferreira et al. (2007a). Almost every author, who have published an article in the last decade or so before that, with the application of DoE in chromatography had used MLR with ANOVA as a tool for quantitative interpretation to evaluate the significance of the model fitted to the design of choice (Dejaegher and Vander Heyden 2007). The authors here wish to report the peculiarities associated while interpreting data, different ways used for the same and especial cases if any. A linear, quadratic or cubic model should be tested to fit the data of a design and to investigate it. The computer programs available nowadays give probability values for the model used on the basis of which one could find the appropriateness of the selected model easily. More details about the selection of a linear, quadratic or cubic model and appropriate application of them, based on ANOVA are mentioned as part of review crafted by (Ferreira et al. 2007a).

Desirability, desirability indices and desirability function

While reviewing applications of designs in chromatography, the authors of this article came across some articles which have effectively employed the desirability approach or desirability function for varied purposes in chromatography. Ferreira et al. (2007b) reviewed the literature for the specific applications of the desirability approach and stated the desirability function as a popular form for the treatment of multiple responses which was proposed by Derringer and Suich in 1980. This article describes the conversion of predicted values generated by a design for each response surface and its conversion to the dimensionless scale di, followed by the application of algorithms to determine the set of variable values maximizing desirability (D) as well as a review of some existing applications (Ferreira et al. 2007b). The approach was developed to establish the suitability of a particular design type for definite purpose and has been evaluated by assigning desirability index to each design type; the approach was proposed to be useful for the researchers in the concentration of further efforts in most applicable designs. Desirability was assigned values in between 0% and 100% and central composite, full factorial, BBD with values of 96%, 95% and 95%, respectively, were final recommendations (Olivero, Seshadri, and Deming 1993). Various desirability functions have earlier been used in separation science to improve the quality of separations (Deming 1991). Outinen et al. (1998) have combined Desirability with PRISMA mixture design and employed to enhance the quality of HPLC separations. The desirability function converted the calculated value (Rs) into the desirability value (D), and the overall optimum was then defined by means of the overall desirability. Individual desirabilities for responses can be combined by various ways; if the criterion is a simple arithmetic mean, then it is called the “utility function,” and if it is a geometric function, then it is referred to as the “Derringer’s desirability function”. Sivakumar et al. (2007) published a paper using multiple response simultaneous optimization using Derringer’s desirability function for the development of a reversed-phase HPLC (RP-HPLC) method for the simultaneous determination of domperidone and pantoprazole in commercial pharmaceutical preparations. The plan of combining desirabilities as a geometric mean was first offered by Harrington (1965), but it was put into a more general form by Derringer (1980). The advantage of Derringer’s desirability function is that if one of the criteria has an unacceptable value, then the overall product will also be unacceptable, while for the utility functions, this is not the case. Further, Derringer’s method offers the user flexibility in the definition of desirability functions. Harrington et al. explained the use of desirability (denoted by “d” for each response; d = 0 for completely undesirable response and d = 1 for completely desirable response) to optimize the combination of factor levels that jointly optimize a set of responses by satisfying the requirement of each response in the set; the desirabilities for individual response were combined to give composite or combined desirability (D) (Harrington 1965). Various characteristic chromatographic applications of the desirability function can be stated as shown in Table 2.

Table 2:

Characteristic chromatographic applications of desirability function.

S. no.Chromatographic purpose for employing desirability functionReferences
1Deming introduced desirability in chromatography by implementation to resolution and analysis time as objective functions to improve separation qualityDeming (1991)
2During the screening of studies to select factors and composite desirability to obtain an optimum set of conditions for the development and optimization of an HPLC method for protamine sulfateAwotwe-Otoo et al. (2012)
3Separation of pridinol mesylate and process-related impurities using HPLCBianchini, Castellano, and Kaufman (2009)
4Optimization of isocratic reversed-phase HPLC separation conditions of nimodipine and impurities in tabletsBarmpalexis, Kanaze, and Georgarakis (2009)
5Optimization of retention time and recovery during the development of an RP-LC method for a diastereomeric drug valganciclovirKumar et al. (2012)
6Optimization of each chromatographic parameter and overall desirability for the final optimization of the HPLC methodDewé et al. (2004)
7Maximization of resolution and minimization of retention time during the RP-UPLC analysis of darifenacin hydrobromide, its related compounds and degradation productsMurthy et al. (2013)
8Optimization of selectivity in HPLCOutinen et al. (1998)
9Simultaneous optimization of resolution and analysis time in micellar LC separation of a group of nine phenyl thiohydantoin amino acidsSafa and Hadjmohammadi (2005)
10Optimization of HPLC conditions while determination of tetranortriterpenoids in Carapa guianensis seed oilRomero et al. (2001)
11Optimizing the analytical method for the final tuning of the gradient program and for the simultaneous analysis of levodopa, carbidopa, entacapone and their impuritiesVemić et al. (2013)
12Optimization of mobile phase for HPLC-PDA analysis of ACE inhibitors, hydrochlorothiazide and indapamideDawud and Shakya (2014)
13Optimization of conditions for the LC analysis of topical HIV microbicides stampidine and HI443Agrahari et al. (2014)
Dong’s approach or Dong’s algorithm

The identification of significant variables from screening designs can be performed using graphical or statistical methods as revealed from the literature. Most of the statistical methods which use a t-test require estimation of error. The cases where about 50% factor effects are significant Dong’s algorithm is hardly capable of indicating any effect as significant (Dejaegher et al. 2006). This can be achieved by defining an effect as negligible with the help of Lenth’s or Dong’s algorithm (Dong 1993). Very rare and discrete reports were found in the literature for the application of Dong’s approach or Dong’s algorithm during the use of DoE in HPLC analysis. The authors here wish to represent them chronologically as per the purpose they were used in chromatography. Li et al. (2005) mentioned the use of the algorithm during robustness studies assisted with DoE in relation to the variability observed in different types of designs used while assessing method robustness. The approach has been mentioned there seems to be significant due to the one of its counterparts that is the principle of effect sparsity (less than 50% of effects were significant) (Li et al. 2005). A later report for the use of the same was found to be published by Dejaegher and Vander Heyden (2011) while describing the advances in the use of DoE and mentioned the use of critical values obtained from Dong’s approach or from adapted Dong’s approach. These values were plotted as a function of the Fixing Effect and Adding Rows (FEAR) steps. The adapted algorithm of Dong was used to indicate significant effects in classic screening designs in cases when many significant factors are present (Dejaegher and Vander Heyden 2011); the FEAR method was developed by the authors to estimate all factor effects from supersaturated design results (Dejaegher, Capron & Vander Heyden 2007a; 2007b). Adapted Dong’s approach was developed by Dejaegher, Durand, and Vander Heyden (2009) for the especial situations, as the algorithm of Dong requires the effect of sparsity, and if this is violated, then problems of detecting significant effect arise. This may lead to overestimation, resulting in significant effects incorrectly considered non-significant (Dejaegher, Durand, and Vander Heyden 2009). A recent report for the approach was published by Stojanović et al. (2013), where the approach has been mentioned for the determination of non-significant intervals for the significant factors while optimization of various responses during LC determination of raloxifene hydrochloride (Stojanović et al. 2013). Hund et al. (2000) utilized the algorithm as one of the criteria to decide on the significance of effects in a robustness test with an asymmetrical factorial design for the RP-HPLC method to determine the total content of triadimenol to estimate the critical effects from the distribution of the non-significant effects. Inglot et al. (2013) used Dong’s algorithm along with a graphical approach to identify significant effects during the development of a new HPLC method with ED and fluorescence detection for the analytical study of an antihypertensive mixture of amlodipine and valsartan. Vander Heyden et al. (2001) stated the application of the algorithm of Dong for the estimation of error from the distribution of effects, suggested the use of the algorithm when t-tests are unable to detect any significance of factors and explained the same with the help of a case study.

Lenth’s algorithm

As quoted earlier, Lenth’s algorithm was utilized for the estimation of error by defining negligible effects (Nijhuis et al., 1999). The literature revealed the use of Lenth’s algorithm by Hund et al. (2000) as one of the criteria to decide on the significance of effects in a robustness test with an asymmetrical factorial design for the RP-HPLC method to determine the total content of triadimenol to estimate the critical effects from the distribution of the non-significant effects. The application of this algorithm has been further stated duly by Dejaegher et al. (2006) in comparison with Dong’s algorithm.

Uniform mapping algorithm of Kennard and Stones

Asymmetrical designs used in chromatography while examination of an asymmetrical domain or elsewhere are constructed based on the uniform mapping algorithm of Kennard and Stone (1969). Dejaegher and Vander Heyden (2011) mentioned about this algorithm while describing advances in setup and data interpretation for EDs. The article also cited the necessary articles need to be referred while applying it. Exact applications of this algorithm in relation to optimization and validation of separation methods can be found in detail in de Aguiar, Bourguignon, and Massart (1997) and Torres-Lapasió et al. (2000) .

Yates algorithm

For an analytical method which is fast and requires the testing of a few factors (three or lesser), a fine alternative for robustness testing may be well accomplished by the factorial design proposed by Yates and Mather in 1963 (Rao et al., 2008; Yates and Mather 1963). This algorithm was widely employed because of its high efficiency with respect to the number of runs required. An update of these in the form of the Yates algorithm or Yates analysis was found to be used by Sonawane and Gide (2011a) for the optimization of forced degradation conditions during the development of a stability-indicating method for eplerenone. The authors also performed the Yates analysis to determine significant factors affecting percent degradation, and F-values were generated (Sonawane and Gide 2011b) to retain significant coefficient for the percent degradation of luliconazole (Sonawane and Gide 2016).

Atypical algorithms used in some cases

Besides the popular and precisely investigated algorithms stated before, in this article some atypical algorithms or methods found in some of the publications are also stated briefly as analysts would need them in coming future for one or more purposes in chromatography. Other methods or algorithms used purposefully were algorithms based on D-optimal design searches (Li and Jeff Wu 1997), evolutionary or genetic algorithms (Cela, Martınez & Carro, 2000), Galois field theory (Lu and Meng 2000) on cyclic balanced incomplete block designs (Liu & Zhang, 2000; Nguyen, 1996), an optimal foldover plan (Fang, Lin & Qin, 2003) and the use of Bayesian D-optimality (Allen and Bernshteyn 2003).

Function of mutual information (FUMI) theory

Hayashi and Matsuda (1994) proposed a chemometric tool based on the FUMI theory to improve the prediction of the uncertainty in HPLC. Kotani et al. (2003) employed the FUMI theory for the prediction of measurement RSD and detection limits in the HPLC-electrochemical detection of catechins without repetitive measurement of chromatograms, saving considerable amounts of chemicals and experimental time.

HPLC analytical procedures-opted design strategies

Method development or optimization of chromatographic conditions

Development and/or optimization of liquid chromatographic (HPLC, HPTLC, LC-MS and LC-MS/MS) methods using the chemometric approach were revealed to be the prime purpose of the application of design strategies in chromatography. The authors wish to represent here some of the imperative contributions in this regard. The articles thus published in the literature over the period of time may contribute as the vital approach to proceed with the application of ED for chromatographic development and optimization. An assortment of reports published on the same line of work is being stated in the subsequent discussion.

The various purposes for which chemometry was applied during the HPLC method development and optimization were to optimize the mobile phase, screen factors, study main interaction and quadratic effects, and achieve optimum retention. Some representative reports for the development and optimization of HPLC methods using the chemometric approach are as stated in Table 3.

Table 3:

Representative reports for the development and optimization of chromatographic methods using the chemometric approach.

Technique/analyte(s)Applied designFactorsOptimization objectiveReferences
SI-HPTLCBox-BehnkenNot stated in the articleMethod optimizationMustafa et al. (2013)
Gradient RP-HPLC/levodopa, carbidopa, entacapone and IMPsBox-Behnken and Derringers desirability functionPercentage of methanolMethod optimization and fine tuning of gradient programVemić et al. (2013)
HPLC/protamine sulfatePlackett-Burmana and Box-BehnkenbpH, flow rate, temperature, injection volume, methanol concentrationScreen effectsa and main interaction and quadratic effectsbAwotwe-Otoo et al. (2012)
HPLC-DAD/opium alkaloidsFull factoriala and central composite circumscribedbTemperature, pH, flow rateEstablish relationship between chromatographic conditions, retentiona and method optimizationbAcevska et al. (2012)
HPLC/pridinol mesylateFull factoriala and fractional factorialb(pH and % of organic phase)a, (temperature, flow rate, pH, organic phase %)bMobile-phase compositiona and robustnessbBianchini, Castellano, and Kaufman (2009)
SPE-HPLC-UV-fluorescence/valsartan, valeryl-4-hydroxy-valsartan, candesartanFractional factoriala and central compositebFlow rate, temperature, pH, gradient steepness, percentage of Acetonitrile, percentage of Trifluoroacetic acid Investigation of significant factorsa, optimize significant factorsbIriarte et al. (2006)
Isocratic RP-HPLC/bilirubin and biliverdinFull factorial designLength of the analytical column, pH, composition and mobile phase flow rateSet factors during method developmentAl-Hamdi et al. (2006)
RP-HPLC-UV/leflunomidePlackett-BurmanaAutosampler temperature, column oven temperature, detector wavelength, (percentage v/v of acetonitrile in mobile phase, flow rate and pH)bFactor optimizationa, robustnessb and intermediate precisionRao et al. (2008)
RP-LC/valganciclovirCentral compositeMobile-phase ratio, flow rate, column temperatureMaximum dRT, maximum recovery and minimum RTKumar et al. (2012)
SI-HPLC/eberconazole nitrateFull factorialTetrabutyl ammonium hydroxide (mM), pH, organic phase (v/v)Chromatography, mobile phaseKrishna et al. (2016) and Petkovska, Cornett, and Dimitrovska (2008a) )
RP-HPLC/atorvastatin and RSFull factoriala and central composite face-centeredbOrganic phase variation during gradient elution and gradient timeMethod optimizationa and robustnessbPetkovska, Cornett, and Dimitrovska (2008a)
SI-RP-UPLC/darifenacin hydrobromide and IMPCentral compositePercentage of organic modifier, temperature, pHLC-conditions, separation, main effects and interaction effectsMurthy et al. (2013)
Simultaneous RP-HPLC-PDA/biogenic aminesPRISMA mixture designs and desirability functionsConcentrations of Acetonitrile, Tetrahydrofuran and MethanolMobile-phase optimization (solvent compositions) for good separationOutinen et al. (1998)
RP-HPLC/stampidine and HI443Plackett-Burmana and Box-BehnkenbFlow rate, injection volume, detection wavelength, gradient ration of AcetonitrileScreeninga, and main and interaction effectsbAgrahari et al. (2014)
HPLC-PDAPlackett-BurmanColum temperature, injection volume, methanol in mobile phase, initial gradient organic total, gradient slope, detection wavelength, columns of different lots, different instrument, methanol in sample solventMethod development/optimization of mobile phaseLi and Rasmussen (2003)
HPLC-PDA/hydrochlorothiazide and indapamideCentral compositeVolume fraction of organic solvents in mobile phase and bufferMethod development and optimizationDawud and Shakya (2014)
Ion pair-LC-MS/1-naphthyl phosphate (1), 1-naphthalenesulfonic acid (2), 2-naphthalenesulfonic acid (3) and (1-naphthoxy)acetic acid (4)Full factorial and modified factorialConcentration of ion-pair reagent, solution pH and acid used for pH adjustmentOptimization of the aqueous LC mobile phaseSeto, Bateman, and Gunter (2002)
Ternary and quaternary HPLC/phenols and corticosteroidsCentral composite and factorialTemperature, percentage of organic component in mobile phase and ratio of Tetrahydrofuran/Acetonitrile/Methanol in the mobile phaseSimultaneous optimization of mobile-phase compositionMorris, Hughes, and Marriott (2003)
RP-LC/metformin and glibenclamideFull factorialAcetonitrile percentage, pH of the mobile phase, temperatureScreening factorsDemiralay (2012)
RP-HPLC/2-arylammidoFull factorialTemperature, pH of mobile phase and percentage of AcetonitrileHPLC conditionsVučićević et al. (2009)
RP-HPLC/antipsychoticsFull factorialpH, column chemistry (acquity C18, Ethylene Bridged Hybrid-BEH shield RP18, fluorophenyl, BEH phenyl) and level of organic modifier (Acetonitrile and Methanol)Method development: column screening and selectivity; column geometry for resolutionDebrus, Guillarme, and Rudaz (2013)
  1. Where, a, b and c are used to correlate the columns for applied designs with optimization objectives respectively.

Validation steps: robustness, precision, assay

Chemometric approaches as various types of designs have also been applied successfully during method validation. Among the various validation parameters, robustness evaluation was at prime focus from the beginning till the date. The reproducibility of chromatographic techniques as required in pharmaceutical analysis and technology transfer processes along with strict regulatory compliance demanded by the regulatory authorities may be the probable reason behind it. PBD, central composite, factorial designs either as full factorial or fractional factorial and Taguchi designs were the most widely used for the same (in descending order of use). Rare reports were seen for the optimization or evaluation of other validation parameters except robustness such as pharmaceutical assay bias and intermediate precision. The Table 4 depicts the selected applications of DoE during pharmaceutical HPLC method validation.

Table 4:

Unique applications of experimental design during HPLC validation.

Technique/analyte(s)Applied designFactorsOptimization objectiveReferences
SI-gradient-HPLC/synercid–streptogramin, quinupristin, dalfopristinTaguchiMobile phase (Acetonitrile in A and B, pH, weight of potassium salt), flow rate, accuracy of gradient, column temperature, wavelengthMethod validation/robustness studiesVasselle, Gousset, and Bounine (1999)
HPLC/ginsenosidesPlackett-BurmanHydrophobicity of API, amount and type of excipient, size of capsule shells or tablet coating material, amount of organic solvent and inorganic buffer in the sample solvent, and amount of solvent used in preparing the sampleHPLC assay-biasLi et al. (2005)
RP-HPLC/pneumocandin BoPlackett-BurmanWavelength, injection volume, flow rate, mobile-phase composition, column temperature and column lotRobustnessWaters and Dovletoglou (2003)
HPLC/pridinol mesylate process-related impuritiesFull factoriala, Fractional factorialb(pH and % of organic phase)a, (temperature, flow rate, pH, organic phase %)bMobile-phase compositiona, and robustnessbBianchini, Castellano, and Kaufman (2009)
HPLC/biogenic aminesFractional factorialGradient, column temperature, concentrations of buffer, pH of buffer used in mobile phase, wavelength, % of TriethylamineMethod validation/robustness studiesRomero et al. (2001)
RP-HPLC-UV/leflunomidePlackett-BurmanaAutosampler temperature, column oven temperature, detector wavelength, (percentage v/v of acetonitrile in mobile phase, flow rate and pH)bFactor optimizationa, validation of robustnessb and intermediate precisionRao et al. (2008)
RP-HPLC/clopidogrel and RSFull factoriala and central composite face-centeredbAcetonitrile content (v/v %) in the mobile phase, pH value of mobile phase, and column temperatureMethod optimizationa and robustnessbPetkovska, Cornett, and Dimitrovska (2008b)
RP-HPLC/carboxylic acidsCentral compositeDetection wavelength, column temperature, Acetonitrile ratio, plateau before gradient and gradient slopeRobustnessDestandau et al. (2006)
RP-HPLC-PDA/zileutonCentral compositeMethanol content, flow rate, concentration of orthophosphoric acidRobustnessGanorkar, Dhumal, and Shirkhedkar (2017)
HPLC-fluorescence–Plackett-BurmanMethanol content, pH of the buffer, flow rate, detection wavelengths and column temperatureRobustnessInglot et al. (2013)
HPLC-PDA/hydrochlorothiazide and indapamideCentral compositeVolume fraction of organic solvents in mobile phase and bufferMethod development and optimizationDawud and Shakya (2014)
RP-HPLC/atorvastatin and RSFull factoriala and central composite face-centeredbOrganic phase variation during gradient elution and the gradient timeMethod optimizationa and robustnessbPetkovska, Cornett, and Dimitrovska (2008a)
RP-HPLC-PDA/zafirlukastPlackett-BurmanPercentage of organic modifier, temperature, flow rateMethod validation/robustnessFicarra et al. (2000)
RP-HPLC/griseofulvin and IMPsFull factorialDetection wavelength, column temperature, flow rate and injection volumeRobustnessKahsay et al. (2013)
RP-HPLC/ambrisentanFull factorial designWavelength, flow rate and Orhthophosphoric acid % in mobile phaseRobustnessAdiki et al. (2014)
SI-RP-HPLC/naftopidilPlackett-BurmanStrength of buffer, flow rate, column temperature, pH of mobile phase, detection wavelengthRobustnessSatheeshkumar et al. (2014)
  1. Where, a, b and c are used to correlate the columns for applied designs with optimization objectives respectively.

RS/separation of APIs and/or IMPs during stability studies

Stability-indicating LC methods are an integral component of pharmaceutical analysis. These have their own importance in pharmaceutical sciences. Advances in the determination of IMPs and/or DPs were the factors evoking the curiosity of pharmaceutical analysts in this regard. The parallel rise in the interest of the pharmacological profile of drug during pre-clinical and post-clinical evaluations, developments as well as post-marketing surveillance was another reason. Both of these spurred the interest of pharmaceutical analysts in impurity profiling or fate mapping of pharmaceuticals. The separation of the drug from these IMPs, followed by identification and characterization, is key to unlock the said interest. The RS of the component at the conditions of analysis was the main complication for such investigations. The EDs entered at this point and helped to optimize the conditions of chromatography for best RS of APIs from IMPs and thereby most precise stability-indicating methods as well. To get acquainted with the type of designs that has been used prominently to optimize RS should be focused in coming future. Then only it will lead to creative modifications and through applications later. In this regard, we wish to represent here a concise account of the designs used, factors screened or selected and optimization objective for the particular LC technique as in Table 5.

Table 5:

Assorted applications of designs applied for the resolution of APIs from IMPs in HPLC and hyphenated techniques.

Technique/analyte(s)Applied designFactorsOptimization objectiveReferences
UPLC/nine isocyanatesTaguchiProportion of solvent, percent triethylamine, temperature and flow rateSeparation/resolutionAndré et al. (2013)
Micellar-LC (MLC)/benzodiazepine anticonvulsantsFace-centered cube response surface and Pareto optimalityOrganic modifier concentration in the mobile phase, the length of the alkyl chain of the organic modifier, the concentration of sodium dodecyl sulfate (SDS) and Brij-35, pH of the mobile phase and temperatureSeparationHadjmohammadi and Ebrahimi (2004)
Isocratic RP-HPLC/nimodipine and impuritiesFull factorial a, central compositebType of the organic modifier: methanol or acetonitrile, concentration, column temperature, mobile-phase flow rate and pHScreeninga, separationbBarmpalexis, Kanaze, and Georgarakis (2009)
HPLC/acetaminophen, phenylephrine, chlorpheniramineFull factorialMobile-phase composition, gradient time, mobile-phase pHSeparationDebrus et al. (2011)
HPLC-ECD/captoprilCCD combined with fractional factorialIndependent buffer pH, buffer molarity organic solvent concentrationSeparationKhamanga and Walker (2011)
SI-RP-UPLC/darifenacin hydrobromide and IMPsCentral composite% of organic modifier, temperature, pHLC-conditions, separation, main effects and interaction effectsMurthy et al. (2013)
LC-MS/MS/4-dimethylaminopyridineCentral compositeFlow, gradient and injection volume as LC factors and cone voltage and collision energy as MS factorsSeparationSzékely et al. (2012)
RP-HPLC-PDA/biogenic aminesPRISMA mixture designs and desirabilityConcentrations of Acetnitrile, Tetrahydrofuran and MethanolMobile-phase optimization (solvent compositions) for good separationOutinen et al. (1998)
HPLC-UV/aporphine alkaloidsFull factorialMobile-phase pH, the initial proportion of methanol and the gradient slopeSeparationRafamantanana et al. (2012)
RP-HPLC/domperidone and pantoprazoleCentral composite and Derringer’s desirability functionMobile-phase composition, buffer molarity and flow rateHPLC separationSivakumar et al. (2007)
HPLC/tetranortriterpenoids in Carapa guianensis seed oilCentral compositeFlow, volume of injected sample and composition of mobile phase expressed as the amount of acetonitrileChromatographic resolutionTappin et al. (2008)
HPLC/moxifloxacin and RSCentral composite face-centeredpH, % of Acetonitrile and % of MethanolSeparationKalariya et al. (2014)
RP-HPLC-CAD/sucrose caprate regioisomersFace-centered compositeConcentration of acetonitrile and corresponding time for gradient runSeparationLie, Wimmer, and Pedersen (2013)
RP-HPLC/antipsychoticsFull factorialpH, column chemistry (acquity C18, BEH shield RP18, fluorophenyl, BEH phenyl) and level of organic modifier (ACN and MeOH)Method development: column screening and selectivity; column geometry for resolutionDebrus, Guillarme, and Rudaz (2013)
HPLC/pramipexole API and IMPsMulti factorial spaceGradient time, temperature, buffer pHSeparationSchmidt, Stanic, and Molnár (2014)
  1. Where, a, b and c are used to correlate the columns for applied designs with optimization objectives respectively.

Optimization of stress/forced degradation studies

Applications of DoE in the optimization of conditions used to degrade the bulk drug and/or formulation so as to achieve optimum degradation of 5% to 30% as suggested by ICH were noticed recently. Sonawane and Gide (2011a, 2011b, 2016) justified the chemometric approach for the forced degradation of pharmaceuticals. Factorial designs either alone or assisted with the Yates analysis were used to identify significant factors. These factors are supposed to affect the desired degradation of the sample, and later subjected to optimization. As the variations in the conditions applied to degrade the sample may lead to the changes in the amount and type of DPs, the same may influence the drug-drug interaction at accelerated conditions along with the drug-excipient interaction leading to the formation of adducts. The possibility of future complications in identification, separation, characterization, isolation as well as toxicity determination has been said to be avoided using the chemometric approach. Conditions for the forced degradation of eplerenone, rebamipide and luliconazole have been optimized by the authors during the development of LC-MS, RP-HPLC and stability-indicating HPLC methods for the drugs, respectively. The authors also mentioned the use of microwave irradiation first time for the forced degradation studies (Sonawane and Gide 2016).

HPLC bioanalytical methods and extraction steps

Substantial differences do not exist in the validation of a chromatographic method for the analysis or bioanalysis. Hence, analyst usually may think of the application of the design of an experiment for the development and validation of a bioanalytical method, similarly as it is applied for various purposes in analytical methods. We wish to report here some of the typical preliminary, central and latest applications of chemometric approaches for bioanalytical methods. An SPE-HPLC-UV-fluorescence method was developed and validated for the metabolite in plasma samples; the method involved the use of FFD and CCD for the optimization of the extraction and separation of the antihypertensive drug valsartan and its metabolite valeryl-4-hydroxy-valsartan (Iriarte et al. 2006). Torrealday et al. (2003) applied the ED approach for the validation of the bioanalytical method of telmisartan in spiked human urine and the design applied was CCD. Wieling et al. (1996) discussed the choice of a rational ED in the validation of the bioanalytical method by using HPLC determination of captopril in human plasma assisted with nested designs and ANOVA for the evaluation of the lack of fit and goodness of fit. Dawes et al. (2012) investigated DoE in an effort to optimize the extraction procedure of the bioanalytical assay; factors selected were extraction buffer pH (two pHs), volume ratio of organic solvent to plasma (two ratios) and extraction shake time (three times); optimization was achieved using 23 full factorial and Latin square design.

Derivatization reactions during chromatography

Sometimes during HPLC, a chemical reaction, like derivatization (pre-or post-column), between an analyte and reagent to change the chemical and physical properties of the analyte is required. This is done to improve detectability, change molecular structure or polarity, change matrix or stabilize a sensitive analyte for better chromatography as defined by Snyder, Kirkland, and Glajch (1997). It needs to be rapid, reproducible and quantitative, with minimal by-products or IMPs. Being a complicated step, it may increase the chances of errors in analysis and analysis time. Although these procedures can be automated, the use of the ED has led to a reduction of all or some drawbacks associated with derivatization. We wish to report here some of the assorted reports which have applied DoE to assist chromatographic derivatization.

Romero et al. (2001) used FFD during derivatization of biogenic amines via the dabsylation reaction during HPLC determination (Romero et al. 2001). Stafiej et al. (2006) used BBD for optimization of the derivatization reaction established during the development of a method proposed for the determination of aliphatic aldehydes by HPLC. Petz and co-workers proposed a GC-MS method for the determination of aminoglycoside antibiotics. BBD was used for the optimization of the derivatization reaction (Preu, Guyot & Petz, 1998). Vannecke et al. (2002) found optimum conditions required for the chemical derivatization for HPLC determination using quarter-fraction factorial design with 16 experiments. den Brok et al. (2003) used DoE for the derivatization of the marine anticancer agent in bulk and its pharmaceutical dosage form. A typical study was recently reported by Patil, Patil, and Wani (2016) for the use of DoE for the chemical derivatization of pregabalin for the optimization of the condensation reaction. p-Dimethylamino benzaldehyde was employed as a complexing agent to form a colored complex followed by its determination with visible spectrophotometry (Patil, Patil, and Wani 2016).

Modern applications of design stratagems in chromatographic advancements

Applications of design strategies in chromatographic analysis are still the point of recent attention for pharmaceutical analysts. Hence, a vital update of current prospects needs to be addressed at once in this review. The selected modern applications, specific design type and corresponding purposes are as follows.

A 26−2 FFD was applied to study the influence variables (extracting and dispersing solvents, pH, ionic strength, extraction time and centrifugation time) to optimize the dispersive liquid-liquid microextraction during the HPLC-UV analysis of melatonin in plasma and then the significant variables were optimized by using a CCD (Talebianpoora et al. 2014). BBD and RSM were used effectively to optimize the chromatographic conditions for impurity profiling of valacyclovir and its related products by RP-HPLC (Katakam et al. 2014). Elkhoudarya, Abdel Salam, and Hadad (2014) explored the robustness testing in the HPLC analysis of clarithromycin, norfloxacin, doxycycline, tinidazole and omeprazole in pharmaceutical dosage forms by using 2-level FFD, and the significance of column temperature, pH, concentrations of ion pairing agent and buffer and the fraction of mobile-phase B (during various time levels of gradient optimization) was illustrated by using a half-normal plot. Optimization of forced degradation conditions was achieved during the development of a stability-indicating method for furosemide by 2n FFD, which helped to obtain the targeted 20%–30% drug degradation and also to enrich levels of DPs.

The CCD was applied for the optimization of the mobile phase, saturation time and retention factor by Shah et al. (2016) during simultaneous HPTLC analysis of clonazepam and paroxetine. The optimization of main effects and interaction effects was executed during the development of the mobile phase with the use of a 23-level full factorial design for the simultaneous HPTLC analysis of aliskiren, amlodipine and hydrochlorothiazide in a synthetic mixture (Patel et al., 2015). FFD was used to evaluate the effect of four independent variables, methanol content in the total mobile phase, wavelength, chamber saturation time and solvent front during evaluation of robustness, while simultaneous thin-layer chromatography (TLC)-densitometric estimation of nadifloxacin, mometasone furoate and miconazole nitrate in creams by Patel et al. (2016). HPLC determination of diclofenac potassium and its IMPs was carried out by using CCD to investigate the influence of critical parameters (concentrations of methanol and PHP, pH of aqueous phase). Monte Carlo simulation was used to evaluate the risk of uncertainty in model predictions, to adjusting process parameters and to identify design space. The study also employed FFD to the test method (Tumpa et al., 2015). The application of Taguchi ED was performed to evaluate the effects of seven independent chromatographic parameters and to screen the factors having critical effects on theoretical plates and peak tailing as critical analytical attributes (CAAs) while the interaction effects of responsible factors were also studied using CCD during the HPLC analysis of ketoprofen in Bulk Drug and Proniosomal Vesicular System (Yadav et al. 2015).

Robustness was determined during the HPLC evaluation of pravastatin using BBD to assess the concurrent effects of various parameters on retention time of drug (Ahmad et al., 2016). Khurana et al. (2016) reported the application of face-centered cubic design for the optimization of volume-loaded and plate dimensions as the critical method parameters selected from screening studies employing D-optimal and PBD, followed by evaluating their effect on the CAAs during the thin-layer densitometric bioanalytical method for the estimation of mangiferin (Khurana et al. 2016). The optimization of the derivatization procedure for the analysis of biogenic amines by HPLC-UV was performed by applying CCD using multiple response analysis by Argotty Salazar and Lozada Castro (2016). Shengyun Dai et al. (2016) successfully used the Monte Carlo simulation method to build the chromatographic design space and the process capability index Cp was introduced to evaluate the robustness of the design space to develop an HPLC method to separate five components of the Panax notoginseng. Sandhu et al. (2016) made the use of a 7-factor 8-run Taguchi design for factor screening studies followed by systematic optimization by employing BBD for the estimation of tamoxifen by HPLC. The combination of ED and quantitative structure-retention relationship was applied recently in order to investigate the retention behavior and to select optimal experimental conditions for the separation of ziprasidone and its five IMPs by TLC with initial support of a central composite face-centered design to examine the influence of four factors (the developing distance, the amount of toluene in the mobile phase, the amount of acetic acid in the mobile phase and the spot band size). The study also used the coefficient plots to signify the interaction effects (Obradovic et al., 2016).

HPLC with or without EDs

HPLC analysis experienced the upbeat changes right from sensitive identification toward quantitative estimation drugs, IMPs and/or metabolites in bulk samples as well as mixtures and biological fluids individually or as hyphenated alignments. The efforts were continuously made to reduce the time, the cost of analysis and increase the efficiency of determination. The trend started to adopt the design strategies since the investigation of design application in the early 1980s, as a seedling which has grown into a giant tree with multifaceted views and the same number of sights as branches and much more. The numbers of publications have grown consistently year by year, and hence the decision regarding the following queries may not be easy to understand yet.

  • Whether to apply design in HPLC analysis?

  • Should it be applied to simple analysis or is it a primary need for complex analysis?

  • Which step of HPLC analysis requires design?

  • How to apply the design? Manually or using software packages?

  • What kind of software? Which is most suitable?

  • What kind of design?

  • What kind of methods to analyze data?

  • Which is a most suitable method for data analysis?

  • How to interpret the data?

Chromatography at its peak for the pharmaceutical analysis is expecting the high throughput during these days. Analysts are making all their possible efforts toward it. The future thus seems to be filled with the ample accessories assisting quality attributes of chromatography and thereby HPLC. Prospects of statistical design in HPLC are likely to be bright, but it will be when the questions stated above as a representative are addressed or studied better, established and stated appropriately by the period of time. Thus the need of authenticated and validated ED methodologies or approaches and a well-defined protocol along with a regulatory compliance should be there.

Conclusions

The present review deals with specific applications of the DoE in the LC (HPLC) analysis of pharmaceuticals. As the vast literature is available from stretched duration, we felt it necessary to study the trend toward the use of the statistical designs in HPLC as chemometric approaches. OFAT approaches were prevalent in the literature until 2005, but still the concepts like QbD and DoE were establishing their impressions in publications as newer strategies. It started becoming prominent in appearance in the literature pertaining to HPLC analysis in late 2008. It has been vital at this moment to plan the HPLC assisted pharmaceutical analysis bestowed with design strategies. The conclusions that we need to summarize at the end are closely related to the common queries to which an HPLC analyst comes across while thinking of about chemometry in HPLC.

Multivariate stratagem involving EDs to encounter simultaneous interaction effects of potential variables affecting drug analysis is more useful than OFAT. This is required to assure patient-centric quality and leading research mindset to evolve better strategy as evidenced by the literature search. The application of multivariate optimization needs identification of suitability of a particular design type while exploring the potential of design strategies to contribute toward superior pharmaceutical analysis of tomorrow. It is necessary to get well acquainted with the terms used and mathematical meanings of them.

The choice of factor and factor levels and response to be measured is more important even than the design itself. The choice of critical factors and their interaction effects having significant consequence toward analysis can be sorted using screening designs. The same can be achieved more efficiently with a full or fractional two-level factorial design that can be used pertaining to their economy. The level should be decided according to the type of factor: qualitative or quantitative. The principle of uncertainty can help out in the selection of a factor level. Response to be chosen depends on the type of analysis (assay method: content, peak area, peak height; separation method: RS and relative retention). Statistical analyses of responses and interpretation can be performed using ANOVA and response surface plots at ease without going in depth of meticulous mathematics.

The type of design to be chosen for the purpose of HPLC analysis cannot be decided abruptly due to insufficient access all and on time to experts in the field of ED. Although the path directed by previous researchers seems to be an interesting option as far as the trend is considered if an analyst can find the solution for the selection of a design such as DXPERT (does not include setting specific experimental parameters), there will be a scope for the comparison and it can be stated here that there is a need for computer programs devoted to the selection of ED modified for setting parameters simultaneously for effective HPLC analysis.

Design Expert by Stat-Ease Inc. with all its versions was found to be highly applied software for the application of a design in HPLC followed by MINITAB by Minitab Inc. with least articles available for the manual application without using any software. The selection of the type of designs for the particular purpose during HPLC analysis can be predicted from the literature; for example, PBD can be used as a well-balanced screening design during the development of HPLC methods.

The optimization of critical factors and their interaction effects can be performed best with the help of CCD being a leader in the series while one may apply factorial or BBD. PBD, central composite, factorial designs either as full factorial or fractional factorial and Taguchi designs were the most widely used for the same (in descending order of use) validation steps, such as evaluation of HPLC robustness, precision and assay. Full factorial, central composite and Taguchi designs (in descending order of use) were meant for achieving better RS in HPLC. Factorial designs assisted with Yates analysis were proved to be effective strategies of designs for optimization of stress or forced degradation reactions. Factorial design (full or fractional), CCD and Latin square design were among the highly used designs for the optimization of extraction steps in HPLC bioanalytical procedures. The optimization of pre-column and post-column derivatization reactions during HPLC analysis was achieved in the literature using BBD to a highest extent with some cases of applied FFD. Still the authors have not found any reports about the comparison of more than one design software package or program, comparison and evaluation of more than one design type for a particular purpose in HPLC as well as in chromatography in general. Thus, simultaneous RS of the drugs from every drug-related substance will add toward their characterization. This will be followed by thorough prediction and determination of toxicity and drug-like properties of all related substances of a drug using computer-aided drug design. This may ultimately lead to a pathway for new drug discovery from the parent drug itself. Hence, accurate, efficient, economical LC analysis is the base for the successive laddering to reach to the apex of drug discovery. Chemometry as EDs in the form of QBD and/or DoE nowadays is crawling to create chromatography as sturdy as possible.

Acknowledgments

The authors wish to express sincere gratitude toward University Grants Commission (UGC) New Delhi for financial assistance in the form of UGC-Minor Research Project for motivational support in the form of funding, as this review was effectively generated as a part of literature searches required for the research proposals funded through the aforementioned scheme. The authors wish to thank the Principal of the R. C. Patel Institute of Pharmaceutical Education and Research, Shirpur, Maharashtra, India, for providing constant encouragement and essential amenities.

References

Acevska, J., Stefkov, G., Petkovska, R., Kulevanova, S. & Dimitrovska, A. (2012). Chemometric approach for development, optimization, and validation of different chromatographic methods for separation of opium alkaloids. Analytical and Bioanalytical Chemistry, 403, 1117–1129.10.1007/s00216-012-5716-1Search in Google Scholar

Adiki, S. K., Prashanti, M., Dey, B., Katakam, P., Assaleh, F. H., Hwisa, N. T., Singla, R. K. & Chandu, B. R. (2014). Design of experiment assisted UV-visible spectrophotometric and RP-HPLC method development for ambrisentan estimation in bulk and formulations. World Journal of Analytical Chemistry, 2, 23–30.10.12691/wjac-2-2-2Search in Google Scholar

Agrahari, V., Meng, J., Zhang, T. & Youan, B.-B. C. (2014). Application of design of experiment and simulation methods to liquid chromatography analysis of topical HIV microbicides stampidine and HI443. Journal of Analytical and Bioanalytical Techniques, 5, 180.Search in Google Scholar

Ahmad, A., Raish, M., Alkharfy, K. M., Mohsin, K. & Shakeel, F. (2016). Box-Behnken supported development and validation of robust RP-HPLC method: an application in estimation of pravastatin in bulk and pharmaceutical dosage form. Journal of the Chilean Chemical Society, 61, 2963–2967.10.4067/S0717-97072016000200022Search in Google Scholar

Al-Hamdi, A., Williams, J., Al-Kindy, S. & Pillay, A. (2006). Optimization of a high-performance liquid chromatography method to quantify bilirubin and separate it from its photoproducts. Applied Biochemistry and Biotechnology, 135, 209–218.10.1385/ABAB:135:3:209Search in Google Scholar

Allen, T. T. & Bernshteyn, M. (2003). Supersaturated designs that maximize the probability of identifying active factors. Technometrics, 45, 1–8.10.1198/004017002188618734Search in Google Scholar

Altria, K. & Filbey, S. (1994). The application of experimental design to the robustness testing of a method for the determination of drug-related impurities by capillary electrophoresis. Chromatographia, 39, 306–310.10.1007/BF02274518Search in Google Scholar

André, C., Jorge, F., Castanheira, I. & Matos, A. (2013). Optimizing UPLC isocyanate determination through a Taguchi experimental design approach. Journal of Chemometrics, 27, 91–98.10.1002/cem.2496Search in Google Scholar

Araujo, P. (2000). A new high performance liquid chromatography multifactor methodology for systematic and simultaneous optimisation of the gradient solvent system and the instrumental/experimental variables. Trends in Analytical Chemistry, 19, 524–529.10.1016/S0165-9936(00)00035-2Search in Google Scholar

Araujo, P. W. & Brereton, R. G. (1996a). Experimental design II. Optimization. Trends in Analytical Chemistry, 15, 63–70.10.1016/0165-9936(96)80762-XSearch in Google Scholar

Araujo, P. W. & Brereton, R. G. (1996b). Experimental design III. Quantification. Trends in Analytical Chemistry, 15, 156–163.10.1016/0165-9936(95)00086-0Search in Google Scholar

Araujo, P. W. & Brereton, R. G. (1997). Visualisation of confidence in two-factor designs where model, replication and star points are varied. Analyst, 122, 621–630.10.1039/a700135eSearch in Google Scholar

Araujo, P. & Frøyland, L. (2006). Hierarchical classification designs for the estimation of different sources of variability in proficiency testing experiments. Analytica Chimica Acta, 555, 348–353.10.1016/j.aca.2005.09.024Search in Google Scholar

Araujo, P. & Grung, B. (2012). Chemometrics in chromatography. Journal of Chromatography B, 910, 1.10.1016/j.jchromb.2012.10.042Search in Google Scholar

Araujo, P. & Janagap, S. (2012). Doehlert uniform shell designs and chromatography. Journal of Chromatography B, 910, 14–21.10.1016/j.jchromb.2012.05.019Search in Google Scholar PubMed

Argotty Salazar, A. K. & Lozada Castro, J. J. (2016). Central composite design to optimizate the derivatization procedure for analysis of biogenic amines by HPLC-UV. Journal of the Brazilian Chemical Society, DOI: 10.5935/0103-5053.20160200.Search in Google Scholar

Atkinson, A. C. & Tobias, R. D. (2008). Optimal experimental design in chromatography. Journal of Chromatography A, 1177, 1–11.10.1016/j.chroma.2007.11.045Search in Google Scholar PubMed

Atkinson, A. & Donev, A. (1992). Optimum Experimental Designs. Oxford: Clarendon.Search in Google Scholar

Awotwe-Otoo, D., Agarabi, C., Faustino, P. J., Habib, M. J., Lee, S., Khan, M. A. & Shah, R. B. (2012). Application of quality by design elements for the development and optimization of an analytical method for protamine sulfate. Journal of Pharmaceutical and Biomedical Analysis, 62, 61–67.10.1016/j.jpba.2012.01.002Search in Google Scholar PubMed

Barmpalexis, P., Kanaze, F. I. & Georgarakis, E. (2009). Developing and optimizing a validated isocratic reversed-phase high-performance liquid chromatography separation of nimodipine and impurities in tablets using experimental design methodology. Journal of Pharmaceutical and Biomedical Analysis, 49, 1192–1202.10.1016/j.jpba.2009.03.003Search in Google Scholar PubMed

Barros Neto, B. D., Scarminio, I. S. & Bruns, R. E. (2006). 25 years of chemometrics in Brazil, Quím. Nova, 29, 1401–1406.Search in Google Scholar

Beser, M. I., Pardo, O., Beltrán, J. & Yusà, V. (2011). Determination of per-and polyfluorinated substances in airborne particulate matter by microwave-assisted extraction and liquid chromatography-tandem mass spectrometry. Journal of Chromatography A, 1218, 4847–4855.10.1016/j.chroma.2011.04.082Search in Google Scholar PubMed

Bezerra, M. A., Santelli, R. E., Oliveira, E. P., Villar, L. S. & Escaleira, L. A. (2008). Response surface methodology (RSM) as a tool for optimization in analytical chemistry. Talanta, 76, 965–977.10.1016/j.talanta.2008.05.019Search in Google Scholar PubMed

Bianchini, R. M., Castellano, P. M. & Kaufman, T. S. (2009). Development and validation of an HPLC method for the determination of process-related impurities in pridinol mesylate, employing experimental designs. Analytica Chimica Acta, 654, 141–147.10.1016/j.aca.2009.09.022Search in Google Scholar

Borman, P., Chatfield, M., Nethercote, P., Thompson, D. & Truman, K. (2007). The application of quality by design to analytical methods. Pharmacy Technology, 31, 142–152.Search in Google Scholar

Bortoloti, J. A., Bruns, R. E., de Andrade, J. C. & Vieira, R. K. (2004). Split-plot design optimization for trace determination of lead by anodic stripping voltammetry in a homogeneous ternary solvent system. Chemometrics and Intelligent Laboratory Systems, 70, 113–121.10.1016/j.chemolab.2003.09.004Search in Google Scholar

Bortoloti, J. A., Borges, C. N. & Bruns, R. E. (2005). Split-plot designs and normal probability graphs for the optimization of chemical systems. Analytica Chimica Acta, 544, 206–212.10.1016/j.aca.2005.01.021Search in Google Scholar

Box, G. E. & Hunter, W. G. (1978). Statistics for Experimenters. New York: Wiley.Search in Google Scholar

Box, G. E, Hunter, J. S. & Hunter, W. G. (2005). Statistics for experimenters: design, innovation, and discovery. AMC, 10, 12.Search in Google Scholar

Brereton, R. G. (2003). Chemometrics: Data Analysis for the Laboratory and Chemical Plant. Chichester: John Wiley & Sons.10.1002/0470863242Search in Google Scholar

Statistical design: chemometrics. Bruns, R. E., I. S. Scarminio & B. de Barros Neto (Eds.), (2006). Data Handling in Science and Technology(pp. xx + 412) (25)Amsterdam: Elsevier.Search in Google Scholar

Cao, J., Covarrubias, V. M., Straubinger, R. M., Wang, H., Duan, X., Yu, H., Qu, J. & Blanco, J. G. (2010). A rapid, reproducible, on-the-fly orthogonal array optimization method for targeted protein quantification by LC/MS and its application for accurate and sensitive quantification of carbonyl reductases in human liver. Analytical Chemistry, 82, 2680–2689.10.1021/ac902314mSearch in Google Scholar

Caporal-Gautier, J., Nivet, J., Algranti, P., Guilloteau, M., Histe, M., Lallier, M., N'Guyen-Huu, J. & Russotto, R. (1992). Guide de validation analytique: rapport d'une commission SFSTP. I: méthodologie. STP Pharma Pratiques, 2, 205–226.Search in Google Scholar

Cela, R., Martınez, E. & Carro, A. (2000). Supersaturated experimental designs. New approaches to building and using it: Part I. Building optimal supersaturated designs by means of evolutionary algorithms. Chemometrics and Intelligent Laboratory Systems, 52, 167–182.10.1016/S0169-7439(00)00091-5Search in Google Scholar

Chen, J.-G., Glancy, K., Chen, X. & Alasandro, M. (2001). Investigation of pharmaceutical high-performance liquid chromatography assay bias using experimental design. Journal of Chromatography A, 917, 63–73.10.1016/S0021-9673(01)00670-7Search in Google Scholar

Comell, J. A. (1990). Experiments with Mixtures (2nd ed.). New York: Wiley.Search in Google Scholar

Cornell, J. A. (1988). Analyzing data from mixture experiments containing process variables: a split-plot approach. Journal of Quality Technology, 20, 2–23.10.1080/00224065.1988.11979079Search in Google Scholar

Coscollà, C., Yusà, V., Beser, M. I. & Pastor, A. (2009). Multi-residue analysis of 30 currently used pesticides in fine airborne particulate matter (PM 2.5) by microwave-assisted extraction and liquid chromatography-tandem mass spectrometry. Journal of Chromatography A, 1216, 8817–8827.10.1016/j.chroma.2009.10.040Search in Google Scholar PubMed

Costa, S., Barroso, M., Castañera, A. & Dias, M. (2010). Design of experiments, a powerful tool for method development in forensic toxicology: application to the optimization of urinary morphine 3-glucuronide acid hydrolysis. Analytical and Bioanalytical Chemistry, 396, 2533–2542.10.1007/s00216-009-3447-8Search in Google Scholar PubMed

Dai, S., Xu, B., Zhang, Y., Sun, F., Li, J., Cui, Y., Shi, X. & Qiao, Y. (2016). Robust design space development for HPLC analysis of five chemical components in Panax notoginseng saponins. Journal of Liquid Chromatography and Related Technologies, 39, 504–512.10.1080/10826076.2016.1198914Search in Google Scholar

Davies, L. (1993). Efficiency in Research, Development, and Production: The Statistical Design and Analysis of Chemical Experiments. Cambridge: Royal Society of Chemistry.Search in Google Scholar

Davies, M. P., De Biasi, V. & Perrett, D. (2004). Approaches to the rational design of molecularly imprinted polymers. Analytica Chimica Acta, 504, 7–14.10.1016/S0003-2670(03)00812-2Search in Google Scholar

Dawes, M. L., Bergum, J. S., Schuster, A. E. & Aubry, A.-F. (2012). Application of a design of experiment approach in the development of a sensitive bioanalytical assay in human plasma. Journal of Pharmaceutical and Biomedical Analysis, 70, 401–407.10.1016/j.jpba.2012.06.011Search in Google Scholar

Dawud, E. R. & Shakya, A. K. (2014). HPLC-PDA analysis of ACE-inhibitors, hydrochlorothiazide and indapamide utilizing design of experiments. Arabian Journal of Chemistry, DOI:10.1016/j.arabjc.2014.10.052.Search in Google Scholar

de Aguiar, P., Bourguignon, B. & Massart, D. (1997). Comparison of models and designs for optimisation of the pH and solvent strength in HPLC. Analytica Chimica Acta, 356, 7–17.10.1016/S0003-2670(97)00516-3Search in Google Scholar

Debrus, B., Lebrun, P., Ceccato, A., Caliaro, G., Rozet, E., Nistor, I., Oprean, R., Rupérez, F. J., Barbas, C. & Boulanger, B. (2011). Application of new methodologies based on design of experiments, independent component analysis and design space for robust optimization in liquid chromatography. Analytica Chimica Acta, 691, 33–42.10.1016/j.aca.2011.02.035Search in Google Scholar PubMed

Debrus, B., Guillarme, D. & Rudaz, S. (2013). Improved quality-by-design compliant methodology for method development in reversed-phase liquid chromatography. Journal of Pharmaceutical and Biomedical Analysis, 84, 215–223.10.1016/j.jpba.2013.06.013Search in Google Scholar PubMed

Dejaegher, B. & Vander Heyden, Y. (2007). Ruggedness and robustness testing. Journal of Chromatography A, 1158, 138–157.10.1016/j.chroma.2007.02.086Search in Google Scholar PubMed

Dejaegher, B. & Vander Heyden, Y. (2008). Supersaturated designs: set-ups, data interpretation, and analytical applications. Analytical and Bioanalytical Chemistry, 390, 1227–1240.10.1007/s00216-007-1641-0Search in Google Scholar PubMed

Dejaegher, B. & Vander Heyden, Y. (2011). Experimental designs and their recent advances in set-up, data interpretation, and analytical applications. Journal of Pharmaceutical and Biomedical Analysis, 56, 141–158.10.1016/j.jpba.2011.04.023Search in Google Scholar PubMed

Dejaegher, B., Capron, X., Smeyers-Verbeke, J. & Vander Heyden, Y. (2006). Randomization tests to identify significant effects in experimental designs for robustness testing. Analytica Chimica Acta, 564, 184–200.10.1016/j.aca.2006.01.101Search in Google Scholar

Dejaegher, B., Capron, X. & Vander Heyden, Y. (2007a). Fixing effects and adding rows (FEAR) method to estimate factor effects in supersaturated designs constructed from Plackett-Burman designs. Chemometrics and Intelligent Laboratory Systems, 85, 220–231.10.1016/j.chemolab.2006.06.017Search in Google Scholar

Dejaegher, B., Capron, X. & Vander Heyden, Y. (2007b). Generalized FEAR method to estimate factor effects in two-level supersaturated designs. Journal of Chemometrics, 21, 303–323.10.1002/cem.1065Search in Google Scholar

Dejaegher, B., Dumarey, M., Capron, X., Bloomfield, M. & Vander Heyden, Y. (2007c). Comparison of Plackett-Burman and supersaturated designs in robustness testing. Analytica Chimica Acta, 595, 59–71.10.1016/j.aca.2006.11.077Search in Google Scholar

Dejaegher, B., Durand, A. & Vander Heyden, Y. (2009). Identification of significant effects from an experimental screening design in the absence of effect sparsity. Journal of Chromatography B, 877, 2252–2261.10.1016/j.jchromb.2008.10.019Search in Google Scholar

Deming, S. N. (1991). Multiple-criteria optimization. Journal of Chromatography A, 550, 15–25.10.1016/S0021-9673(01)88527-7Search in Google Scholar

Demiralay, E. Ç. (2012). An experimental design approach to optimization of the liquid chromatographic separation conditions for the determination of metformin and glibenclamide in pharmaceutical formulation. Acta Chimica Slovenica, 59, 307–314.Search in Google Scholar

den Brok, M. W., Nuijen, B., Miranda, E., Floriano, P., Munt, S., Manzanares, I. & Beijnen, J. H. (2003). Development and validation of a liquid chromatography-ultraviolet absorbance detection assay using derivatisation for the novel marine anticancer agent ES-285·HCl [(2S, 3R)-2-amino-3-octadecanol hydrochloride] and its pharmaceutical dosage form. Journal of Chromatography A, 1020, 251–258.10.1016/j.chroma.2003.08.094Search in Google Scholar PubMed

Derringer, G. (1980). Simultaneous optimization of several response variables. Journal of Quality Technology, 12, 214–219.10.1080/00224065.1980.11980968Search in Google Scholar

Deshpande, G. R., Roy, A. K., Rao, N. S., Rao, B. M. & Reddy, J. R. (2011). Rapid screening of volatile ion-pair reagents using UHPLC and robust analytical method development using DoE for an acetyl cholinesterase inhibitor: galantamine HBr. Chromatographia, 73, 639–648.10.1007/s10337-011-1970-1Search in Google Scholar

Destandau, E., Vial, J., Jardy, A., Hennion, M.-C., Bonnet, D. & Lancelin, P. (2006). Robustness study of a reversed-phase liquid chromatographic method for the analysis of carboxylic acids in industrial reaction mixtures. Analytica Chimica Acta, 572, 102–112.10.1016/j.aca.2006.05.016Search in Google Scholar PubMed

Dewé, W., Marini, R., Chiap, P., Hubert, P., Crommen, J. & Boulanger, B. (2004). Development of response models for optimising HPLC methods. Chemometrics and Intelligent Laboratory Systems, 74, 263–268.10.1016/j.chemolab.2004.04.016Search in Google Scholar

Djang'eing'a Marini, R., Chiap, P., Boulanger, B., Dewe, W., Hubert, P. & Crommen, J. (2003). LC method for the simultaneous determination of R-timolol and other closely related impurities in S-timolol maleate: optimization by use of an experimental design. Journal of Separation Science, 26, 809–817.10.1002/jssc.200301367Search in Google Scholar

Doehlert, David H. (1970). Uniform Shell Designs. Applied Statistics, 19(3), 231–231. DOI: 10.2307/2346327.Search in Google Scholar

Doehlert, D. H. (1970). Uniform shell designs. Journal of Applied Statistics, 231–239.10.2307/2346327Search in Google Scholar

Dong, F. (1993). On the identification of active contrasts in unreplicated fractional factorials. Statistica Sinica, 3, 209–217.Search in Google Scholar

Duarte, R. M. & Duarte, A. C. (2011). Optimizing size-exclusion chromatographic conditions using a composite objective function and chemometric tools: application to natural organic matter profiling. Analytica Chimica Acta, 688, 90–98.10.1016/j.aca.2010.12.031Search in Google Scholar

Eldin, A. B., Shalaby, A. A. & El-Tohamy, M. (2011). Development and validation of a HPLC method for the determination of montelukast and its degradation products in pharmaceutical formulation using an experimental design. Acta Pharmaceutica Science, 53, 45–56.Search in Google Scholar

Elkhoudarya, M. M., Abdel Salam, R. A. & Hadad, G. M. (2014). Robustness testing in HPLC analysis of clarithromycin, norfloxacin, doxycycline, tinidazole and omeprazole in pharmaceutical dosage forms using experimental design. Current Pharmaceutical Analysis, 10, 58–70.10.2174/157341291001140102111733Search in Google Scholar

Fabre, H. (1996). Robustness testing in liquid chromatography and capillary electrophoresis. Journal of Pharmaceutical and Biomedical Analysis, 14, 1125–1132.10.1016/S0731-7085(96)01770-0Search in Google Scholar

Fabre, H., Sekkat, M., Blanchin, M. & Mandrou, B. (1989). Determination of aminoglycosides in pharmaceutical formulations—II. High-performance liquid chromatography. Journal of Pharmaceutical and Biomedical Analysis, 7, 1711–1718.10.1016/0731-7085(89)80185-2Search in Google Scholar

Fang, K.-T., Lin, D. K. & Qin, H. (2003). A note on optimal foldover design. Statistics and Probability Letters, 62, 245–250.10.1016/S0167-7152(03)00008-7Search in Google Scholar

Ferreira, S. C., Bruns, R., Ferreira, H., Matos, G., David, J., Brandao, G., da Silva, E. P., Portugal, L., Dos Reis, P. & Souza, A. (2007). Box-Behnken design: an alternative for the optimization of analytical methods. Analytica Chimica Acta, 597, 179–186.10.1016/j.aca.2007.07.011Search in Google Scholar PubMed

Ferreira, S. L., Dos Santos, W. N., Quintella, C. M., Neto, B. C. B. & Bosque-Sendra, J. M. (2004). Doehlert matrix: a chemometric tool for analytical chemistry—review. Talanta, 63, 1061–1067.10.1016/j.talanta.2004.01.015Search in Google Scholar

Ferreira, S. L. C., Bruns, R. E., da Silva, E. G. P., dos Santos, W. N. L., Quintella, C. M., David, J. M., de Andrade, J. B., Breitkreitz, M. C., Jardim, I. C. S. F. & Neto, B. B. (2007a). Statistical designs and response surface techniques for the optimization of chromatographic systems. Journal of Chromatography A, 1158, 2–14.10.1016/j.chroma.2007.03.051Search in Google Scholar

Ferreira, S. L. C., Bruns, R. E., Ferreira, H. S., Matos, G. D., David, J. M., Brandão, G. C., da Silva, E. G. P., Portugal, L. A., dos Reis, P. S., Souza, A. S. & dos Santos, W. N. L. (2007b). Box-Behnken design: an alternative for the optimization of analytical methods. Analytica Chimica Acta, 597, 179–186.10.1016/j.aca.2007.07.011Search in Google Scholar

Ficarra, R., Ficarra, P., Tommasini, S., Melardi, S., Calabro, M., Furlanetto, S. & Semreen, M. (2000). Validation of a LC method for the analysis of zafirlukast in a pharmaceutical formulation. Journal of Pharmaceutical and Biomedical Analysis, 23, 169–174.10.1016/S0731-7085(00)00266-1Search in Google Scholar

Ficarra, R., Calabro, M., Cutroneo, P., Tommasini, S., Melardi, S., Semreen, M., Furlanetto, S., Ficarra, P. & Altavilla, G. (2002). Validation of a LC method for the analysis of oxaliplatin in a pharmaceutical formulation using an experimental design. Journal of Pharmaceutical and Biomedical Analysis, 29, 1097–1103.10.1016/S0731-7085(02)00151-6Search in Google Scholar

Fischer, R. A. (1925). Statistical Methods for Research Workers. Oxford: Oxford University Publications.Search in Google Scholar

Furlanetto, S., Orlandini, S., La Porta, E., Coran, S. & Pinzauti, S. (2002). Optimization and validation of a CZE method for rufloxacin hydrochloride determination in coated tablets. Journal of Pharmaceutical and Biomedical Analysis, 28, 1161–1171.10.1016/S0731-7085(02)00054-7Search in Google Scholar

Ganorkar, S. B., Dhumal, D. M. & Shirkhedkar, A. A. (2017). Development and validation of simple RP-HPLC-PDA analytical protocol for zileuton assisted with design of experiments for robustness determination. Arabian Journal of Chemistry, 10(2), 273–282. DOI:10.1016/j.arabjc.2014.03.009.Search in Google Scholar

Gilmour, S. G. (2006). Response surface designs for experiments in bioprocessing. Biometrics, 62, 323–331.10.1111/j.1541-0420.2005.00444.xSearch in Google Scholar PubMed

Goupy, J. (2005). What kind of experimental design for finding and checking robustness of analytical methods. Analytica Chimica Acta, 544, 184–190.10.1016/j.aca.2005.01.051Search in Google Scholar

Gruendling, T., Guilhaus, M. & Barner-Kowollik, C. (2009). Design of experiment (DoE) as a tool for the optimization of source conditions in SEC-ESI-MS of functional synthetic polymers synthesized via ATRP. Macromolecular Rapid Communications, 30, 589–597.10.1002/marc.200800738Search in Google Scholar PubMed

Guo, Y., Srinivasan, S. & Gaiki, S. (2007). Investigating the effect of chromatographic conditions on retention of organic acids in hydrophilic interaction chromatography using a design of experiment. Chromatographia, 66, 223–229.10.1365/s10337-007-0264-0Search in Google Scholar

Hadjmohammadi, M. & Ebrahimi, P. (2004). Optimization of the separation of anticonvulsant agents in mixed micellar liquid chromatography by experimental design and regression models. Analytica Chimica Acta, 516, 141–148.10.1016/j.aca.2004.04.019Search in Google Scholar

Hadjmohammadi, M. R. & Nazari, S. (2010). Separation optimization of quercetin, hesperetin and chrysin in honey by micellar liquid chromatography and experimental design. Journal of Separation Science, 33, 3144–3151.10.1002/jssc.201000326Search in Google Scholar

Hafez, H. M., Elshanawane, A. A., Abdelaziz, L. M. & Mohram, M. S. (2015). Design of experiment utilization to develop a simple and robust RP-UPLC method for stability indicating method of anti-glaucoma ophthalmic drops. European Journal of Analytical Chemistry, 10, 46–67.Search in Google Scholar

Harrington, E. (1965). The desirability function. Industrial Quality Control, 21, 494–498.Search in Google Scholar

Hayashi, Y. & Matsuda, R. (1994). Uncertainty structure, information theory, and optimization of quantitative analysis in separation science. Advances in Chromatography, 34, 347.Search in Google Scholar

Hibbert, D. B. & Gooding, J. J. (2006). Analysis of Variance. In Data Analysis for Chemistry: An Introductory Guide for Students and Laboratory Scientists (pp. 99–125) (pp. 1–173). Oxford, Newyork: Oxford University Press. http://gen.lib.rus.ec/book/index.php?md5=79AC8C1472D2E33337897CC2F9A17588.Search in Google Scholar

Hibbert, D. B. (2012). Experimental design in chromatography: a tutorial review. Journal of Chromatography B, 910, 2–13.10.1016/j.jchromb.2012.01.020Search in Google Scholar

Hund, E., Vander Heyden, Y., Haustein, M., Massart, D. & Smeyers-Verbeke, J. (2000). Comparison of several criteria to decide on the significance of effects in a robustness test with an asymmetrical factorial design. Analytica Chimica Acta, 404, 257–271.10.1016/S0003-2670(99)00716-3Search in Google Scholar

ICH Harmonised Tripertite Guideline. (2003). Stability Testing of New Drug Substances and Products, Q1A (R2). Geneva, Switzerland: ICH.Search in Google Scholar

Inglot, T., Gumieniczek, A., Mączka, P. & Rutkowska, E. (2013). New HPLC method with experimental design and fluorescence detection for analytical study of antihypertensive mixture, amlodipine and valsartan. American Journal of Analytical Chemistry, 4, 17.10.4236/ajac.2013.41003Search in Google Scholar

Iriarte, G., Ferreiros, N., Ibarrondo, I., Alonso, R. M., Maguregi, M. I., Gonzalez, L. & Jimenez, R. M. (2006). Optimization via experimental design of an SPE-HPLC-UV-fluorescence method for the determination of valsartan and its metabolite in human plasma samples. Journal of Separation Science, 29, 2265–2283.10.1002/jssc.200600093Search in Google Scholar

Jellum, E. (1977). Profiling of human body fluids in healthy and diseased states using gas chromatography and mass spectrometry, with special reference to organic acids. Journal of Chromatography B, 143, 427–462.10.1016/S0378-4347(00)81792-2Search in Google Scholar

Kahsay, G., Adegoke, A. O., Van Schepdael, A. & Adams, E. (2013). Development and validation of a reversed phase liquid chromatographic method for analysis of griseofulvin and impurities. Journal of Pharmaceutical and Biomedical Analysis, 80, 9–17.10.1016/j.jpba.2013.02.035Search in Google Scholar PubMed

Kalariya, P. D., Namdev, D., Srinivas, R. & Gananadhamu, S. (2014). Application of experimental design and response surface technique for selecting the optimum RP-HPLC conditions for the determination of moxifloxacin HCl and ketorolac tromethamine in eye drops. Journal of Saudi Chemical Society, 21, S373–S382. DOI:10.1016/j.jscs.2014.04.004.Search in Google Scholar

Katakam, P., Dey, B., Hwisa, N. T., Assaleh, F. H., Babu Chandu, R., Singla, R. K. & Mitra, A. (2014). An experimental design approach for impurity profiling of valacyclovir-related products by RP-HPLC. Scientia Pharmaceutica, 82, 617–630.10.3797/scipharm.1403-20Search in Google Scholar

Kennard, R. W. & Stone, L. A. (1969). Computer aided design of experiments. Technometrics, 11, 137–148.10.1080/00401706.1969.10490666Search in Google Scholar

Kettaneh-Wold, N. (1991). Use of experimental design in the pharmaceutical industry. Journal of Pharmaceutical and Biomedical Analysis, 9, 605–610.10.1016/0731-7085(91)80185-CSearch in Google Scholar

Khamanga, S. M. & Walker, R. B. (2011). The use of experimental design in the development of an HPLC-ECD method for the analysis of captopril. Talanta, 83, 1037–1049.10.1016/j.talanta.2010.11.025Search in Google Scholar PubMed

Khurana, R. K., Rao, S., Beg, S., Katare, O. P. & Singh, B. (2016). Systematic development and validation of a thin-layer densitometric bioanalytical method for estimation of mangiferin employing analytical quality by design (AQbD) approach. Journal of Chromatographic Science, 54(5), 829–841. DOI:10.1093/chromsci/bmw001.Search in Google Scholar PubMed PubMed Central

Kotani, A., Hayashi, Y., Matsuda, R. & Kusu, F. (2003). Optimization of HPLC-ECD conditions for determination of catechins with precision and efficiency based on the FUMI theory. Analytical Sciences, 19, 865–869.10.2116/analsci.19.865Search in Google Scholar PubMed

Krishna, M. V., Dash, R. N., Reddy, B. J., Venugopal, P., Sandeep, P. & Madhavi, G. (2016). Quality by design (QbD) approach to develop HPLC method for eberconazole nitrate: application oxidative and photolytic degradation kinetics. Journal of Saudi Chemical Society, 20, S313–S322. DOI:10.1016/j.jscs.2012.12.001.Search in Google Scholar

Kristoffersen, L., Oiestad, E. L., Opdal, M. S., Krogh, M., Lundanes, E. & Christophersen, A. S. (2007). Simultaneous determination of 6 beta-blockers, 3 calcium-channel antagonists, 4 angiotensin-II antagonists and 1 antiarrhythmic drug in post-mortem whole blood by automated solid phase extraction and liquid chromatography mass spectrometry: method development and robustness testing by experimental design. Journal of Chromatography B, 850, 147–160.10.1016/j.jchromb.2006.11.030Search in Google Scholar PubMed

Kumar, R. S., Hariram, B., Divya, G., Srinivasu, M., Srinivas, K. & Sagyam, R. R. (2012). Development of a RP-LC method for a diastereomeric drug valganciclovir hydrochloride by enhanced approach. Journal of Pharmaceutical and Biomedical Analysis, 70, 101–110.10.1016/j.jpba.2012.06.010Search in Google Scholar PubMed

Landy, J. (2002). Encyclopedia of Pharmaceutical Technology (2nd ed.). New York: Dekker.Search in Google Scholar

Lebrun, P., Govaerts, B., Debrus, B., Ceccato, A., Caliaro, G., Hubert, P. & Boulanger, B. (2008). Development of a new predictive modeling technique to find with confidence equivalence zone and design space of chromatographic analytical methods. Chemometrics and Intelligent Laboratory Systems, 91, 4–16.10.1016/j.chemolab.2007.05.010Search in Google Scholar

Li, W. W. & Jeff Wu, C. (1997). Columnwise-pairwise algorithms with applications to the construction of supersaturated designs. Technometrics, 39, 171–179.10.1080/00401706.1997.10485082Search in Google Scholar

Li, W. & Rasmussen, H. T. (2003). Strategy for developing and optimizing liquid chromatography methods in pharmaceutical development using computer-assisted screening and Plackett-Burman experimental design. Journal of Chromatography A, 1016, 165–180.10.1016/S0021-9673(03)01324-4Search in Google Scholar

Li, Y.-G., Liu, H., Vander Heyden, Y., Chen, M., Wang, Z.-T. & Hu, Z.-B. (2005). Robustness tests on the United States Pharmacopoeia XXVI HPLC assay for ginsenosides in Asian and American ginseng using an experimental design. Analytica Chimica Acta, 536, 29–38.10.1016/j.aca.2004.12.071Search in Google Scholar

Lie, A., Wimmer, R. & Pedersen, L. H. (2013). Design of experiments and multivariate analysis for evaluation of reversed-phase high-performance liquid chromatography with charged aerosol detection of sucrose caprate regioisomers. Journal of Chromatography A, 1281, 67–72.10.1016/j.chroma.2013.01.079Search in Google Scholar

Lin, J., Su, M., Wang, X., Qiu, Y., Li, H., Hao, J., Yang, H., Zhou, M., Yan, C. & Jia, W. (2008). Multiparametric analysis of amino acids and organic acids in rat brain tissues using GC/MS. Journal of Separation Science, 31, 2831–2838.10.1002/jssc.200800232Search in Google Scholar

Liu, M. & Zhang, R. (2000). Construction of E (s2)-optimal supersaturated designs using cyclic BIBDs. Journal of Statistical Planning and Inference, 91, 139–150.10.1016/S0378-3758(00)00136-1Search in Google Scholar

Lu, X. & Meng, Y. (2000). A new method in the construction of two-level supersaturated designs. Journal of Statistical Planning and Inference, 86, 229–238.10.1016/S0378-3758(99)00169-XSearch in Google Scholar

Lundstedt, T., Seifert, E., Abramo, L., Thelin, B., Nystrom, A., Pettersen, J. & Bergman, R. (1998). Experimental design and optimization. Chemometrics and Intelligent Laboratory Systems, 42, 3–40.10.1016/S0169-7439(98)00065-3Search in Google Scholar

Madden, J. E., Shaw, M. J., Dicinoski, G. W., Avdalovic, N. & Haddad, P. R. (2002). Simulation and optimization of retention in ion chromatography using virtual column 2 software. Analytical Chemistry, 74, 6023–6030.10.1021/ac020280wSearch in Google Scholar PubMed

Mark, H. (1986). Comparative study of calibration methods for near-infrared reflectance analysis using a nested experimental design. Analytical Chemistry, 58, 2814–2819.10.1021/ac00126a051Search in Google Scholar

Martendal, E., Budziak, D. & Carasek, E. (2007). Application of fractional factorial experimental and Box-Behnken designs for optimization of single-drop microextraction of 2,4,6-trichloroanisole and 2,4,6-tribromoanisole from wine samples. Journal of Chromatography A, 1148, 131–136.10.1016/j.chroma.2007.02.079Search in Google Scholar

Massart, D. L., Vandeginste, B. G., Buydens, L., Lewi, P. & Smeyers-Verbeke, J. (1997). Handbook of Chemometrics and Qualimetrics: Part A. Amsterdam: Elsevier.Search in Google Scholar

Massart, D., Vandeginste, B., Deming, S., Michotte, Y. & Kaufman, L. (1988). Chemometrics: a textbook. New York: Elsevier.Search in Google Scholar

McConnell, M. L., Rhodes, G., Watson, U. & Novotný, M. (1979). Application of pattern recognition and feature extraction techniques to volatile constituent metabolic profiles obtained by capillary gas chromatography. Journal of Chromatography B, 162, 495–506.10.1016/S0378-4347(00)81830-7Search in Google Scholar

Milovanović, S., Otašević, B., Zečević, M., Živanović, L. & Protić, A. (2012). Development and validation of reversed phase high performance liquid chromatographic method for determination of moxonidine in the presence of its impurities. Journal of Pharmaceutical and Biomedical Analysis, 59, 151–156.10.1016/j.jpba.2011.09.029Search in Google Scholar

Moberg, M., Bergquist, J. & Bylund, D. (2006). A generic stepwise optimization strategy for liquid chromatography electrospray ionization tandem mass spectrometry methods. Journal of Mass Spectrometry, 41, 1334–1345.10.1002/jms.1108Search in Google Scholar

Molina, M. A. F., Nechar, M. & Bosque-Sendra, J. M. (1998). Determination of zinc in environmental samples by solid phase spectrophotometry: optimization and validation study.s. Analytical Sciences, 14, 791–797.10.2116/analsci.14.791Search in Google Scholar

Monks, K., Rieger, H.-J. & Molnár, I. (2011). Expanding the term “Design Space” in high performance liquid chromatography (I). Journal of Pharmaceutical and Biomedical Analysis, 56, 874–879.10.1016/j.jpba.2011.04.015Search in Google Scholar

Morgan, E. (1991). Chemometrics: Experimental Design, Analytical Chemistry by Open Learning. Chichester: Wiley.Search in Google Scholar

Morris, V., Hughes, J. & Marriott, P. (2003). Spherical coordinate representations of solvent composition for liquid chromatography method development using experimental design. Journal of Chromatography A, 1008, 43–56.10.1016/S0021-9673(03)01021-5Search in Google Scholar

Murthy, M. V., Krishnaiah, C., Srinivas, K., Rao, K. S., Kumar, N. R. & Mukkanti, K. (2013). Development and validation of RP-UPLC method for the determination of darifenacin hydrobromide, its related compounds and its degradation products using design of experiments. Journal of Pharmaceutical and Biomedical Analysis, 72, 40–50.10.1016/j.jpba.2012.09.013Search in Google Scholar PubMed

Mustafa, G., Ahuja, A., Baboota, S. & Ali, J. (2013). Box-Behnken supported validation of stability-indicating high performance thin-layer chromatography (HPTLC) method: an application in degradation kinetic profiling of ropinirole. Saudi Pharmaceutical Journal, 21, 93–102.10.1016/j.jsps.2011.11.006Search in Google Scholar PubMed PubMed Central

Nguyen, N. K. (1996). An algorithmic approach to constructing supersaturated designs. Technometrics, 38, 69–73.10.1080/00401706.1996.10484417Search in Google Scholar

Nijhuis, A., Van der Knaap, H., De Jong, S. & Vandeginste, B. (1999). Strategy for ruggedness tests in chromatographic method validation. Analytica Chimica Acta, 391, 187–202.10.1016/S0003-2670(99)00113-0Search in Google Scholar

Nistor, I., Cao, M., Debrus, B., Lebrun, P., Lecomte, F., Rozet, E., Angenot, L., Frederich, M., Oprean, R. & Hubert, P. (2011). Application of a new optimization strategy for the separation of tertiary alkaloids extracted from Strychnos usambarensis leaves. Journal of Pharmaceutical and Biomedical Analysis, 56, 30–37.10.1016/j.jpba.2011.04.027Search in Google Scholar

Obradovic, D., Filipic, S., Nikolic, K. & Agbaba, D. (2016). Optimization of the thin-layer chromatography method for the separation of ziprasidone and its impurities. Journal of Planar Chromatography, 29, 239–246.10.1556/1006.2016.29.4.1Search in Google Scholar

Olivero, R. (1987). Selection of experimental designs for analytical chemistry with the aid of an expert system. Dissertation Abstracts International. B, The Sciences and Engineering, 48.Search in Google Scholar

Olivero, R. A., Seshadri, S. & Deming, S. N. (1993). Development of an expert system for selection of experimental designs. Analytica Chimica Acta, 277, 441–453.10.1016/0003-2670(93)80455-TSearch in Google Scholar

Orlandini, S., Pasquini, B., Gotti, R., Giuffrida, A., Paternostro, F. & Furlanetto, S. (2014). Analytical quality by design in the development of a cyclodextrin-modified capillary electrophoresis method for the assay of metformin and its related substances. Electrophoresis, 35, 2538–2545.10.1002/elps.201400173Search in Google Scholar

Otto, M. (1999). Chemometrics: Statistics and Computer Application in Analytical Chemistry. New York: Wiley-VCH.Search in Google Scholar

Outinen, K., Haario, H., Vuorela, P., Nyman, M., Ukkonen, E. & Vuorela, H. (1998). Optimization of selectivity in high-performance liquid chromatography using desirability functions and mixture designs according to PRISMA. European Journal of Pharmaceutical Sciences, 6, 197–205.10.1016/S0928-0987(97)10016-1Search in Google Scholar

Owens, P. K., Wikström, H., Någård, S. & Karlsson, L. (2002). Development and validation of a capillary electrophoresis method for ximelagatran assay and related substance determination in drug substance and tablets. Journal of Pharmaceutical and Biomedical Analysis, 27, 587–598.10.1016/S0731-7085(01)00578-7Search in Google Scholar

Patel, T. R., Patel, T. B., Suhagia, B. N. & Shah, S. A. (2015). HPTLC method for simultaneous estimation of aliskiren, amlodipine and hydrochlorothiazide in synthetic mixture using quality by design approach. Journal of Liquid Chromatography and Related Technologies, 38, 1546–1554.10.1080/10826076.2015.1076461Search in Google Scholar

Patel, K. G., Shah, P. M., Shah, P. A. & Gandhi, T. R. (2016). Validated high-performance thin-layer chromatographic (HPTLC) method for simultaneous determination of nadifloxacin, mometasone furoate, and miconazole nitrate cream using fractional factorial design. Journal of Food and Drug Analysis, 24, 610–619.10.1016/j.jfda.2016.02.011Search in Google Scholar PubMed

Patil, D. D., Patil, M. S. & Wani, Y. B. (2016). Spectrophotometric method for pregabalin determination: an experimental design approach for method development. Journal of the Association of Arab Universities for Basic and Applied Sciences, 21, 31–37. DOI:10.1016/j.jaubas.2015.03.002.Search in Google Scholar

Petkovska, R., Cornett, C. & Dimitrovska, A. (2008a). Development and validation of rapid resolution RP-HPLC method for simultaneous determination of atorvastatin and related compounds by use of chemometrics. Analytical Letters, 41, 992–1009.10.1080/00032710801978566Search in Google Scholar

Petkovska, R., Cornett, C. & Dimitrovska, A. (2008b). Experimental design approach for the development and validation of an enantiospecific RP-HPLC method for simultaneous determination of clopidogrel and related compounds. Macedonian Journal of Chemistry and Chemical Engineering, 27, 53–64.10.20450/mjcce.2008.247Search in Google Scholar

Pous-Torres, S., Torres-Lapasió, J., Baeza-Baeza, J. & García-Álvarez-Coque, M. (2009). Alternating iterative regression method for dead time estimation from experimental designs. Analytical and Bioanalytical Chemistry, 394, 625–636.10.1007/s00216-009-2735-7Search in Google Scholar

Preu, M., Guyot, D. & Petz, M. (1998). Development of a gas chromatography-mass spectrometry method for the analysis of aminoglycoside antibiotics using experimental design for the optimisation of the derivatisation reactions. Journal of Chromatography A, 818, 95–108.10.1016/S0021-9673(98)00537-8Search in Google Scholar

Prieto, A., Zuloaga, O., Usobiaga, A., Etxebarria, N. & Fernández, L. (2007). Development of a stir bar sorptive extraction and thermal desorption-gas chromatography-mass spectrometry method for the simultaneous determination of several persistent organic pollutants in water samples. Journal of Chromatography A, 1174, 40–49.10.1016/j.chroma.2007.07.054Search in Google Scholar

Pyka, A., Budzisz, M. & Dołowy, M. (2013). Validation thin layer chromatography for the determination of acetaminophen in tablets and comparison with a pharmacopeial method. BioMed Research International, 2013, 1–10.10.1155/2013/545703Search in Google Scholar

Quiming, N. S., Denola, N. L., Saito, Y., Catabay, A. P. & Jinno, K. (2008). Chromatographic behavior of uric acid and methyl uric acids on a diol column in HILIC. Chromatographia, 67, 507–515.10.1365/s10337-008-0559-9Search in Google Scholar

Rafamantanana, M. H., Debrus, B., Raoelison, G. E., Rozet, E., Lebrun, P., Uverg-Ratsimamanga, S., Hubert, P. & Quetin-Leclercq, J. (2012). Application of design of experiments and design space methodology for the HPLC-UV separation optimization of aporphine alkaloids from leaves of Spirospermum penduliflorum Thouars. Journal of Pharmaceutical and Biomedical Analysis, 62, 23–32.10.1016/j.jpba.2011.12.028Search in Google Scholar

Ragonese, R., Mulholland, M. & Kalman, J. (2000). Full and fractionated experimental designs for robustness testing in the high-performance liquid chromatographic analysis of codeine phosphate, pseudoephedrine hydrochloride and chlorpheniramine maleate in a pharmaceutical preparation. Journal of Chromatography A, 870, 45–51.10.1016/S0021-9673(99)00972-3Search in Google Scholar

Rao, S., Rao, A. A., Maheswari, I. & Srinubabu, G. (2008). Development and validation of LC method for the determination of leflunomide in pharmaceutical formulations using an experimental design. African Journal of Pure and Applied Chemistry, 2, 10–17.Search in Google Scholar

Ribeiro, R. L., Bottoli, C. B., Collins, K. E. & Collins, C. H. (2004). Reevaluation of ethanol as organic modifier for use in HPLS-RP mobile phases. Journal of the Brazilian Chemical Society, 15, 300–306.10.1590/S0103-50532004000200022Search in Google Scholar

Rodrıguez, L. C., Garcı́a, R. B., Campana, A. M. G. & Sendra, J. M. B. (1998). A new approach to a complete robustness test of experimental nominal conditions of chemical testing procedures for internal analytical quality assessment. Chemometrics and Intelligent Laboratory Systems, 41, 57–68.10.1016/S0169-7439(98)00036-7Search in Google Scholar

Romero, R., Sánchez-Viñas, M., Gázquez, D., Bagur, M. & Cuadros-Rodriguez, L. (2001). Robustness study for the determination of biogenic amines by HPLC. Chromatographia, 53, 481–484.10.1007/BF02491607Search in Google Scholar

Safa, F. & Hadjmohammadi, M. R. (2005). Simultaneous optimization of the resolution and analysis time in micellar liquid chromatography of phenyl thiohydantoin amino acids using Derringer's desirability function. Journal of Chromatography A, 1078, 42–50.10.1016/j.chroma.2005.04.081Search in Google Scholar

Salazar, Ángela K. Argotty & Castro, Juan J. Lozada (2016). Central Composite Design to Optimizate the Derivatization Procedure for Analysis of Biogenic Amines by HPLC-UV. Journal of the Brazilian Chemical Society, . DOI:10.5935/0103-5053.20160200.Search in Google Scholar

Sandford, L. & Shelver, G. (2009). Using a design of experiments approach to develop fast LC methods for automated scale-up to preparative chromatography of sulfa drugs. Application Note, Fusion AE Method Development, 95501, 1–8.Search in Google Scholar

Sandhu, P. S., Beg, S., Katare, O. P. & Singh, B. (2016). QbD-driven development and validation of a HPLC method for estimation of tamoxifen citrate with improved performance. Journal of Chromatographic Science, 54(8), 1373–1384. DOI:10.1093/chromsci/bmw090.Search in Google Scholar

Sangshetti, J. N., Deshpande, M., Zaheer, Z., Shinde, D. B. & Arote, R. (2014). Quality by design approach: regulatory need. Arabian Journal of Chemistry. DOI:10.1016/j.arabjc.2014.01.025.Search in Google Scholar

Satheeshkumar, N., Spandana, V., Shantikumar, S. & Srinivas, R. (2014). Experimental design approach to optimize stability indicating liquid chromatography method for the determination of naftopidil in its bulk and tablet dosage form. Journal of Young Pharmacists, 6, 1–7.10.5530/jyp.2014.1.1Search in Google Scholar

Schmidt, A. H., Stanic, M. & Molnár, I. (2014). In silico robustness testing of a compendial HPLC purity method by using of a multidimensional design space build by chromatography modeling-Case study pramipexole. Journal of Pharmaceutical and Biomedical Analysis, 91, 97–107.10.1016/j.jpba.2013.12.023Search in Google Scholar

Seto, C., Bateman, K. P. & Gunter, B. (2002). Development of generic liquid chromatography-mass spectrometry methods using experimental design. Journal of the American Society for Mass Spectrometry, 13, 2–9.10.1016/S1044-0305(01)00334-8Search in Google Scholar

Shah, P., Patel, J., Patel, K. & Gandhi, T. (2016). Development and validation of an HPTLC method for the simultaneous estimation of clonazepam and paroxetine hydrochloride using a DOE approach. Journal of Taibah University for Science, 11, 121–132.10.1016/j.jtusci.2015.11.004Search in Google Scholar

Sivakumar, T., Manavalan, R., Muralidharan, C. & Valliappan, K. (2007). Multi-criteria decision making approach and experimental design as chemometric tools to optimize HPLC separation of domperidone and pantoprazole. Journal of Pharmaceutical and Biomedical Analysis, 43, 1842–1848.10.1016/j.jpba.2006.12.007Search in Google Scholar PubMed

Sivertsen, E., Bjerke, F., Almøy, T., Segtnan, V. & Næs, T. (2007). Multivariate optimization by visual inspection. Chemometrics and Intelligent Laboratory Systems, 85, 110–118.10.1016/j.chemolab.2006.05.005Search in Google Scholar

Skartland, L. K., Mjøs, S. A. & Grung, B. (2011). Experimental designs for modeling retention patterns and separation efficiency in analysis of fatty acid methyl esters by gas chromatography-mass spectrometry. Journal of Chromatography A, 1218, 6823–6831.10.1016/j.chroma.2011.07.077Search in Google Scholar PubMed

Snyder, L. R., Kirkland, J. J. & Glach, J. L. (1997). Completing the HPLC method. In Practical HPLC method development (2nd ed.) (pp. 424-428) (pp. 1–800). Newyork: Wiley-Interscience.10.1002/9781118592014Search in Google Scholar

Sonawane, S. & Gide, P. (2011a). An experimental design approach for the forced degradation studies and development of a stability-indicating LC method for eplerenone in tablets. Journal of Liquid Chromatography and Related Technologies, 34(17), 2020–2031. DOI:10.1080/10826076.2011.582913.Search in Google Scholar

Sonawane, S. & Gide, P. (2011b). Optimization of forced degradation using experimental design and development of a stability-indicating liquid chromatographic assay method for rebamipide in bulk and tablet dosage form. Scientia Pharmaceutica, 79, 85.10.3797/scipharm.1011-06Search in Google Scholar PubMed PubMed Central

Sonawane, S. & Gide, P. (2016). Application of experimental design for the optimization of forced degradation and development of a validated stability-indicating LC method for luliconazole in bulk and cream formulation. Arabian Journal of Chemistry, 9, S1428–S1434. DOI:10.1016/j.arabjc.2012.03.019Search in Google Scholar

Srinubabu, G., Raju, C. A., Sarath, N., Kumar, P. K. & Rao, J. S. (2007). Development and validation of a HPLC method for the determination of voriconazole in pharmaceutical formulation using an experimental design. Talanta, 71, 1424–1429.10.1016/j.talanta.2006.04.042Search in Google Scholar PubMed

Stafiej, A., Pyrzynska, K., Ranz, A. & Lankmayr, E. (2006). Screening and optimization of derivatization in heating block for the determination of aliphatic aldehydes by HPLC. Journal of biochemical and biophysical methods, 69(1), 15–24.10.1016/j.jbbm.2006.02.009Search in Google Scholar PubMed

Stojanović, B. J., Rakić, T., Slavković, B., Kostić, N., Vemić, A. & Malenović, A. (2013). Systematical approach in evaluation of LC method for determination of raloxifene hydrochloride and its impurities employing experimental design. Journal of Pharmaceutical Analysis, 3, 45–52.10.1016/j.jpha.2012.09.007Search in Google Scholar PubMed PubMed Central

Switzar, L., Giera, M., Lingeman, H., Irth, H. & Niessen, W. (2011). Protein digestion optimization for characterization of drug–protein adducts using response surface modeling. Journal of Chromatography A, 1218, 1715–1723.10.1016/j.chroma.2010.12.043Search in Google Scholar

Székely, G., Henriques, B., Gil, M., Ramos, A. & Alvarez, C. (2012). Design of experiments as a tool for LC-MS/MS method development for the trace analysis of the potentially genotoxic 4-dimethylaminopyridine impurity in glucocorticoids. Journal of Pharmaceutical and Biomedical Analysis, 70, 251–258.10.1016/j.jpba.2012.07.006Search in Google Scholar

Talebianpoora, M.S., Khodadoust, S., Rozbehi, A., Akbartabar Toori, M., Zoladl, M., Ghaedi, M., Mohammadi, R. & Hosseinzadeh, A. S. (2014). Application of optimized dispersive liquid-liquid microextraction for determination of melatonin by HPLC-UV in plasma samples. Journal of Chromatography B, 960, 1–7.10.1016/j.jchromb.2014.04.013Search in Google Scholar

Tappin, M. R. R., Nakamura, M. J., Siani, A. C. & Lucchetti, L. (2008). Development of an HPLC method for the determination of tetranortriterpenoids in Carapa guianensis seed oil by experimental design. Journal of Pharmaceutical and Biomedical Analysis, 48, 1090–1095.10.1016/j.jpba.2008.08.027Search in Google Scholar

The United State Pharmacopeia USP 24. (2000). The National Formulary NF 19. I. United States Pharmacopeial Convention (Ed.) (pp. 1876–1878). Rockville, MD.Search in Google Scholar

Torrealday, N., Gonzalez, L., Alonso, R., Jimenez, R. & Lastra, E. O. (2003). Experimental design approach for the optimisation of a HPLC-fluorimetric method for the quantitation of the angiotensin II receptor antagonist telmisartan in urine. Journal of Pharmaceutical and Biomedical Analysis, 32, 847–857.10.1016/S0731-7085(03)00187-0Search in Google Scholar

Torres-Lapasió, J., Massart, D., Baeza-Baeza, J. & García-Alvarez-Coque, M. (2000). A three-factor optimisation strategy for micellar liquid chromatography. Chromatographia, 51, 101–110.10.1007/BF02490703Search in Google Scholar

Tumpa, A., Miladinović, T., Rakić, T., Stajić, A. & Jančić-Stojanović, B. (2015). Quality by design determination of diclofenac potassium and its impurities by high-performance liquid chromatography. Analytical Letters, 49, 445–457.10.1080/00032719.2015.1075131Search in Google Scholar

Van Leeuwen, J., Vandeginste, B., Kateman, G., Mulholland, M. & Cleland, A. (1990). An expert system for the choice of factors for a ruggedness test in liquid chromatography. Analytica Chimica Acta, 228, 145–153.10.1016/S0003-2670(00)80490-0Search in Google Scholar

Van Leeuwen, J., Buydens, L., Vandeginste, B., Kateman, G., Schoenmakers, P. & Mulholland, M. (1991). RES, an expert system for the set-up and interpretation of a ruggedness test in HPLC method validation: Part 1: The ruggedness test in HPLC method validation. Chemometrics and Intelligent Laboratory Systems, 10, 337–347.10.1016/0169-7439(91)80098-BSearch in Google Scholar

Vander Heyden, Y. & Massart, D. (1996). Review of the use of robustness and ruggedness in analytical, robustness of analytical chemical methods and pharmaceutical technological products. Data Handling in Science and Technology, 19, 79–147.10.1016/S0922-3487(96)80016-5Search in Google Scholar

Vander Heyden, Y., Questier, F. & Massart, L. (1998). Ruggedness testing of chromatographic methods: selection of factors and levels. Journal of Pharmaceutical and Biomedical Analysis, 18, 43–56.10.1016/S0731-7085(98)00174-5Search in Google Scholar

Vander Heyden, Y., Nijhuis, A., Smeyers-Verbeke, J., Vandeginste, B. & Massart, D. (2001). Guidance for robustness/ruggedness tests in method validation. Journal of Pharmaceutical and Biomedical Analysis, 24, 723–753.10.1016/S0731-7085(00)00529-XSearch in Google Scholar

Vannecke, C., Bloomfield, M., Vander Heyden, Y. & Massart, D. (2002). Development of a generic flow-injection analysis method for compounds with a secondary amine or amide function, using an experimental design approach: Part II. Selection and evaluation of the chemical reaction parameters. Analytica Chimica Acta, 455, 117–130.10.1016/S0003-2670(01)01585-9Search in Google Scholar

Vasselle, B., Gousset, G. & Bounine, J.-P. (1999). Development and validation of a high-performance liquid chromatographic stability-indicating method for the analysis of Synercid® in quality control, stability and compatibility studies. Journal of Pharmaceutical and Biomedical Analysis, 19, 641–657.10.1016/S0731-7085(98)00242-8Search in Google Scholar

Vemić, A., Stojanović, B. J., Stamenković, I. & Malenović, A. (2013). Chaotropic agents in liquid chromatographic method development for the simultaneous analysis of levodopa, carbidopa, entacapone and their impurities. Journal of Pharmaceutical and Biomedical Analysis, 77, 9–15.10.1016/j.jpba.2013.01.007Search in Google Scholar

Verma, A., Hartonen, K. & Riekkola, M. L. (2008). Optimisation of supercritical fluid extraction of indole alkaloids from Catharanthus roseus using experimental design methodology—comparison with other extraction techniques. Phytochemical Analysis, 19, 52–63.10.1002/pca.1015Search in Google Scholar

Vučićević, K., Popović, G., Nikolic, K., Vovk, I. & Agbaba, D. (2009). An experimental design approach to selecting the optimum HPLC conditions for the determination of 2-arylimidazoline derivatives. Journal of Liquid Chromatography and Related Technologies, 32, 656–667.10.1080/10826070802711113Search in Google Scholar

Vuolo-Schuessler, L., Newton, M. E., Smith, P., Burgess, C. & McDowall, R. (2014). Harmonizing USP <1058> and GAMP for analytical instrument qualification. Pharmaceutical Engineering, 34(1), 1–8. http:// www.ispe.org/pharmaceutical_engineering/ january2014.Search in Google Scholar

Waters, R. B. & Dovletoglou, A. (2003). Evaluating HPLC assay robustness with experimental design. Journal of Liquid Chromatography and Related Technologies, 26, 2975–2985.10.1081/JLC-120025411Search in Google Scholar

Weld, H. (1982). Systems Under Indirect Observations. Amsterdam: North-Holand.Search in Google Scholar

Wheeler, D. J. (1989). Tables of Screening Designs. Knoxville, TN: SPC Press.Search in Google Scholar

Wieling, J., Hendriks, G., Tamminga, W., Hempenius, J., Mensink, C., Oosterhuis, B. & Jonkman, J. (1996). Rational experimental design for bioanalytical methods validation illustration using an assay method for total captopril in plasma. Journal of Chromatography A, 730, 381–394.10.1016/0021-9673(96)00006-4Search in Google Scholar

Wold, S. (1995). Chemometrics: what do we mean with it, and what do we want from it. Chemometrics and Intelligent Laboratory Systems, 30, 109–115.10.1016/0169-7439(95)00042-9Search in Google Scholar

Yadav, N. K., Raghuvanshi, A., Sharma, G., Beg, S., Katare, O. P. & Nanda, S. (2015). QbD-Based development and validation of a stability-indicating HPLC method for estimating ketoprofen in bulk drug and proniosomal vesicular system. Journal of Chromatographic Science, bmv151–bmv151. DOI:10.1093/chromsci/bmv151.Search in Google Scholar

Yates, F. & Mather, K. (1963). Ronald Aylmer Fisher. 1890–1962. Biographical Memoirs of Fellows of the Royal Society of London, 9, 91–129.10.1098/rsbm.1963.0006Search in Google Scholar

Ye, C., Liu, J., Ren, F. & Okafo, N. (2000). Design of experiment and data analysis by JMP® (SAS institute) in analytical method validation. Journal of Pharmaceutical and Biomedical Analysis, 23, 581–589.10.1016/S0731-7085(00)00335-6Search in Google Scholar

Yekkala, R. S., Vandenwayenberg, S., Hoogmartens, J. & Adams, E. (2006). Evaluation of an International Pharmacopoeia method for the analysis of nelfinavir mesilate by liquid chromatography. Journal of Chromatography A, 1134, 56–65.10.1016/j.chroma.2006.08.054Search in Google Scholar PubMed

Received: 2016-7-8
Accepted: 2016-12-23
Published Online: 2017-7-27

©2017 Walter de Gruyter GmbH, Berlin/Boston

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Downloaded on 28.3.2024 from https://www.degruyter.com/document/doi/10.1515/revac-2016-0025/html
Scroll to top button