The undergraduate curriculum in statistics and data science is undergoing changes to accommodate new methods, newly interested students, and the changing role of statistics in society. Because of this, it is more important than ever that students understand the role of study design and how to formulate meaningful scientific and statistical research questions. While the traditional Design of Experiments

Meta-analysis is a well-established method for integrating results from several independent studies to estimate a common quantity of interest. However, meta-analysis is prone to selection bias, notably when particular studies are systematically excluded. This can lead to bias in estimating the quantity of interest. Motivated by a meta-analysis to estimate the rate of completed-suicide after bariatric

In this tutorial we present the use of R package mgcv to implement Distributed Lag Non-Linear Models (DLNMs) in a flexible way. Interpretation of smoothing splines as random quantities enables approximate Bayesian inference, which in turn allows uncertainty quantification and comprehensive model checking. We illustrate various modeling situations using open-access epidemiological data in conjunction

A longstanding question in the judgment and decision making literature is whether experts, even in high-stakes environments, exhibit the same cognitive biases observed in controlled experiments with inexperienced participants. Massey and Thaler (2013) claim to have found an example of bias and irrationality in expert decision making: general managers’ behavior in the National Football League draft

In his 1996 paper, Talagrand highlighted that the Law of Large Numbers (LLN) for independent random variables can be viewed as a geometric property of multidimensional product spaces. This phenomenon is known as the concentration of measure. To illustrate this profound connection between geometry and probability theory, we consider a seemingly intractable geometric problem in multidimensional Euclidean

Bayes’ theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of expected values of state variables modify posterior probabilities by constraining prior probabilities to be consistent with the information. Constraints on the prior

Chi-square tests are often employed to examine the association of categorical variables, the homogeneity of proportions between two or more samples, and the goodness-of-fit for a specified distribution. To account for the complex design of survey data, variants of chi-square tests as well as software packages that implement these tests have been developed. Nevertheless, from a survey practitioner’s

The standard mathematical approach to fourth-down decision-making in American football is to make the decision that maximizes estimated win probability. Win probability estimates arise from machine learning models fit from historical data. These models attempt to capture a nuanced relationship between a noisy binary outcome variable and game-state variables replete with interactions and non-linearities

This paper introduces a volleyball point-by-point win probability model that updates the probability of winning a set after each play in the set. The covariate informed product partition model (PPMx) is well suited to flexibly include in-set team performance information when making predictions. However, making predictions in real time would be too expensive computationally as it would require refitting

Tom Alby. Boca Raton, FL: Chapman & Hall/CRC Press, 2024, xvi + 301 pp., $200.00(H), ISBN: 978-1-032-50524-4.This book is a comprehensive introduction to data science, with a focus on how it is use...

Pedro J. Aphalo. Boca Raton, FL: Chapman & Hall/CRC Press, 2024, xvii + 447 pp., $220.00(H), ISBN: 978-1-032-51843-5.R programming has become an essential tool for data analysis and statistical com...

Recently, the International Conference on Harmonisation finalized an estimand framework for randomized trials that was adopted by regulatory bodies worldwide. The framework introduced five strategies for handling post-randomization events; namely the treatment policy, composite variable, while on treatment, hypothetical and principal stratum estimands. We describe an illustrative example to elucidate

A control group versus treatment group design is considered where the responses in the treatment group are modeled as a two-component mixture model that accounts for the possibility that only a fraction of the patients in the treated group will respond to the treatment. In this setting, the treatment effect is generalized to include both the fraction of treated patients that respond to the treatment

Consider a study whose primary results are “not statistically significant”. How often does it lead to the following published conclusion that “there is no effect of the treatment/exposure on the outcome”? We believe too often and that the requirement to report counternull values could help to avoid this! In statistical parlance, the null value of an estimand is a value that is distinguished in some

Foundations of Data Science with Python, by John M. Shea, provides a comprehensive and modern introduction of data science. The book illustrates different aspects of working with data computational...

This book is available in hardcover and as downloadable chapters on the internet. The author states he wants “to provide you with the tools to both select and create graphs that present data as cle...

Machine learning has become an important tool in scientific research and industry, driven in part by the availability of user-friendly software for model development. While most of the notable soft...

In this paper, we develop a new general class of discrete bivariate distributions that can model the effect of the so-called ‘load-sharing configuration’. Under such load-sharing configuration, after the failure of one component, the surviving component has to shoulder extra load, which eventually results in its failure at an earlier time than what is expected under the case of independence. To model

Probability surveys are a major source of population representative data for policy research and program evaluation. However, the data come with the added complications of being observational and selected with unequal probabilities. Propensity score adjustments have become increasingly popular for inferring causal relationships in non-randomized studies, but when using survey data, estimates of the

Accurate model performance assessment in survival analysis is imperative for robust predictions and informed decision-making. Traditional residual diagnostic tools like martingale and deviance residuals lack a well-characterized reference distribution for censored regression, making numerical statistical tests based on these residuals challenging. Recently, the introduction of Z-residuals for diagnosing

The Network Scale-up Methods (NSUM) are methods to estimate unknown populations based on indirect surveys in which the participants provide information about aggregated data of their acquaintances. This preserves the privacy and may lead to higher participation. During the last thirty years, new NSUM estimators have emerged. However, conditions related to the design of the experiments and the robustness

We propose a mean functional that exists for arbitrary probability distributions and characterizes the Pareto distribution within the set of distributions with finite left endpoint. This is in sharp contrast to the mean excess plot, which is meaningless for distributions without an existing mean and has nonstandard behavior when the mean is finite, but the second moment does not exist. The construction

For grouped covariates, we propose a framework for boosting that allows for sparsity within and between groups. By using component-wise and group-wise gradient ridge boosting simultaneously with adjusted degrees of freedom or penalty parameters, a model with similar properties as the sparse-group lasso can be fitted through boosting. We show that within-group and between-group sparsity can be controlled

With the rapid development of data acquisition and storage space, massive datasets exhibited with large sample size emerge increasingly and make more advanced statistical tools urgently need. To accommodate such big volume in the analysis, a variety of methods have been proposed in the circumstances of complete or right censored survival data. However, existing development of big data methodology has

Wheelchair basketball, regulated by the International Wheelchair Basketball Federation, is a sport designed for individuals with physical disabilities. This article presents a data-driven tool that effectively determines optimal team lineups based on past performance data and metrics for player effectiveness. Our proposed methodology involves combining a Bayesian longitudinal model with an integer

Heavy tails (HT) arise in many applications and their presence can disrupt statistical inference, yet the HT statistical literature requires a theoretical background most practicing statisticians lack. We provide an overview of the influence of HT on the performance of basic statistical methods and useful theorems aimed at the practitioner encountering HT in an applied setting. Higher or even lower

A dose–response curve is essential for determining the safe dosage of a drug and is widely used in bioassay and in phase 1 clinical trials. It is generally accepted that the probability of death or the probability of dose-limiting toxicity is a nondecreasing function of the dose. This article proposes and develops an effective point-wise confidence interval for an isotonic dose–response curve, a problem

Continuous processes in most applications are measured discretely with error. This complicates the task of detecting intersections and the number of intersections between two continuous processes (i.e., when the processes have the same value). Intersections of continuous processes are scientifically important, but challenging to estimate from data. For example, in the field of animal ecology, intersections

Various generalizations of single-index models and associated estimation methods have been developed. However, implementing these developed methods requires much effort to program, case by case, due to the lack of a common and flexible vehicle to cover them. We suggest an efficient computation strategy for easily estimating parameters and nonparametric functions in generalized single-index models and

Determining an appropriate sample size is a critical element of study design, and the method used to determine it should be consistent with the planned analysis. When the planned analysis involves Bayes factor hypothesis testing, the sample size is usually desired to ensure a sufficiently high probability of obtaining a Bayes factor indicating compelling evidence for a hypothesis, given that the hypothesis

John Kloke and Joseph McKean. Boca Raton, FL: Chapman & Hall/CRC Press, 2024, xvii + 447 pp., $91.99(H), ISBN: 978-0-367-65135-0.The second edition of Nonparametric Statistical Methods Using R subs...

Multiplex immunofluorescence (mIF) imaging technology facilitates the study of the tumor microenvironment in cancer patients. Due to the capabilities of this emerging bioimaging technique, it is possible to statistically analyze, for example, the co-varying location and functions of multiple different types of immune cells. Complex spatial relationships between different immune cells have been shown

There are many connections between probability, other mathematics courses, and statistics. Understanding these connections provides insights that might not be fully appreciated when considering each discipline in isolation. While the typical instruction of statistics courses relies on elucidating its foundational principles from mathematical and probability theory, it is generally less appreciated

Measures of regression association aiming at predictability of a dependent variable Y from an independent variable X have received considerable attention recently. In this article, we provide a unified discussion of some existing measures, including their rationale, properties, and estimation. Motivated by these measures, we consider a general class of regression association measures which views the

We present an alternative approach to estimating the cumulative incidence function that uses nonparametric multiple imputation to reduce the problem to that of estimating a binomial proportion. In the standard competing risks setting, we show mathematically and empirically that our imputation-based estimator is equivalent to the Aalen-Johansen estimator of the cumulative incidence given a sufficient

The classic formula for estimating the binomial probability as the proportion of successes contradicts common sense for extreme probabilities when the event never occurs or occurs every time. Laplace’s law of succession estimator, one of the first applications of Bayesian statistics, has been around for over 250 years and resolves the paradoxes, although rarely discussed in modern statistics texts

An observational block design has I blocks matched for covariates and J individuals per block, but treatments were not randomly assigned to individuals within blocks, as would have been done in an ...

Asymptotic goodness-of-fit methods in contingency table analysis can struggle with sparse data, especially in multi-way tables where it can be infeasible to meet sample size requirements for a robu...

Distance covariance (Székely et al. 2007) is a fascinating recent notion, which is popular as a test for dependence of any type between random variables X and Y. This approach deserves to be touche...

Despite the fact that most police departments in the U.S. serve jurisdictions with fewer than 10,000 residents, policing practices in small towns are understudied. This is due in part to data limit...

“The use of health care claims datasets often encounters criticism due to the pervasive issues of omitted variables and inaccuracies or mis-measurements in available confounders. Ultimately, the tr...

A full parametric and linear specification may be insufficient to capture complicated patterns in studies exploring complex features, such as those investigating age-related changes in brain functi...

The Kolmogorov–Smirnov (KS) test is widely employed to assess the goodness-of-fit of a hypothesized continuous distribution to a sample. Despite its popularity, the test is frequently misused in th...

In recent years, there has been an explosion in the growth of undergraduate statistics and data science programs across the US. Simultaneously, there has been clear guidance written on curriculum d...

Squared 2 × 2 tables with binary data from matched pairs are typically analyzed using Cochran-Mantel-Haenszel methodology, conditional logistic regression, or random intercepts logistic regression....

The Second Generation P-Value (SGPV) measures the overlap between an estimated interval and a composite hypothesis of parameter values. We develop a sequential monitoring scheme of the SGPV (SeqSGP...

Confidence interval performance is typically assessed in terms of two criteria: coverage probability and interval width (or margin of error). In this article, we assess the performance of four comm...

In Bayesian analysis, the selection of a prior distribution is typically done by considering each parameter in the model. While this can be convenient, in many scenarios it may be desirable to plac...

Probability predictions are essential to inform decision making across many fields. Ideally, probability predictions are (i) well calibrated, (ii) accurate, and (iii) bold, that is, spread out enou...

The best time to play the lottery is when the jackpot has rolled over several times and grown large, but not so large that you must share the prize if you win. We examine maximizing the expected va...

This article describes a simple and fast algorithm for generating correlation matrices ( R) with a known average correlation. The algorithm should be useful for researchers desiring plausible R m...

In this article, I propose a tractable approach to Bayesian inference in a simple linear regression model for which the standard exogeneity assumption does not hold. By specifying a beta prior for ...

Published in The American Statistician (Vol. 78, No. 4, 2024)

Published in The American Statistician (Vol. 78, No. 2, 2024)

Published in The American Statistician (Vol. 78, No. 2, 2024)

Let X1,…,Xn be a random sample from the gamma distribution with density f(x)=λαxα−1e−λx/Γ(α), x > 0, where both α>0 (the shape parameter) and λ>0 (the reciprocal scale parameter) are unknown. The m...

Published in The American Statistician (Vol. 78, No. 3, 2024)

Published in The American Statistician (Vol. 78, No. 3, 2024)

I present the moments of the nonnegative adjusted estimator of the squared multiple correlation ρ2, the coefficient of determination for random-predictor regression. This estimator, first proposed ...

A gap remains between developing risk prediction models and deploying models to support real-world decision making, especially in high-stakes situations. Human-experts’ reasoning abilities remain c...