Skip to main content
SpringerLink
Log in

A review on recent advances and applications of h-likelihood method

  • Review Article
  • Published:
Journal of the Korean Statistical Society Aims and scope Submit manuscript

Abstract

Having spent almost 30 years since Lee and Nelder introduced the h-likelihood at the discussion meeting held in Royal Statistical Society in 1994, Lee and his colleagues and students have studied how to define the h-likelihood for complex statistical models and conduct inference about unobservables and fixed unknown parameters in them. In this paper we review several important research areas with a focus on how the h-likelihood method has been applied. This review covers areas including analysis of clustered survival data, competing risk models with frailty, joint models for longitudinal and survival outcomes, sparse high-dimensional multivariate analysis, spatial analysis and multiple testing.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  • Balan, T. A., & Putter, H. (2020). A tutorial on frailty models. Statistical Methods in Medical Research, 29, 3424–3454.

    MathSciNet  Google Scholar 

  • Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society: Series B, 57, 289–300.

    MathSciNet  MATH  Google Scholar 

  • Berger, J.O. & Wolpert, R.L. (1988). The likelihood principle, IMS Lecture Notes Monogr. Ser., 6.

  • Besag, J. (1974). Spatial Interaction and the Statistical Analysis of Lattice Systems (with discussion). J R Statist Soc B, 36, 192–236.

    MathSciNet  MATH  Google Scholar 

  • Besag, J., & Kempton, R. (1986). Statistical analysis of field experiments using neighbouring plots. Biometrics, 42, 231–251.

    MATH  Google Scholar 

  • Besag, J., & Kooperberg, C. (1995). On conditional and intrinsic autoregressions. Biometrika, 82, 733–746.

    MathSciNet  MATH  Google Scholar 

  • Bjørnstad, J. F. (1996). On the Generalization of the Likelihood Function and the Likelihood Principle. Journal of the American Statistical Association, 91, 791–806.

    MathSciNet  MATH  Google Scholar 

  • Breslow, N. E. (1972). Discussion of the paper by D. R. Cox. Journal of the Royal Statistical Society: Series B, 34, 216–217.

    MathSciNet  Google Scholar 

  • Christian, N. J., Ha, I. D., & Jeong, J. H. (2016). Hierarchical likelihood inference on clustered competing risks data. Statistics in Medicine, 35, 251–267.

    MathSciNet  Google Scholar 

  • Duchateau, L., & Janssen, P. (2008). The frailty model. Springer.

    MATH  Google Scholar 

  • Durbin, J., & Koopman, S. J. (2001). Time series analysis by state space methods. Oxford University Press.

    MATH  Google Scholar 

  • Diggle, P. J., Liang, K. Y., & Zeger, S. L. (1994). Analysis of Longitudinal Data. Oxford University Press.

    MATH  Google Scholar 

  • Diggle, P. J., Tawn, J. A., & Moyeed, R. A. (1998). Model-based geostatistics (with discussion). Applied Statistics, 47, 299–350.

    MathSciNet  MATH  Google Scholar 

  • Efron, B. (2004). Large-scale simultaneous hypothesis testing: The choice of a null hypothesis. Journal of the American Statistical Association, 99, 96–104.

    MathSciNet  MATH  Google Scholar 

  • Elliot, H., Derin, H., Christi, R., & Geman, D. (1984). Application of the Gibbs distribution to image segmentation. In: Proceedings of the International Conference on Acoustics, Speech and Signal Processing, San Diego, IEEE.

  • Fan, J., & Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal American Statistical Association, 96, 1348–1360.

    MathSciNet  MATH  Google Scholar 

  • Fine, J. P., & Gray, R. J. (1999). A proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association, 94, 496–509.

    MathSciNet  MATH  Google Scholar 

  • Fisher, R. A. (1921). On the ‘probable error’ of a coefficient of correlation deduced from a small sample. Metron, 1, 1–32.

    Google Scholar 

  • Golub, G. H., & Reinsch, C. (1971). Singular value decomposition and least squares solutions. Numerische Mathematik, 14, 403–420.

    MATH  Google Scholar 

  • Green, P. J., & Silverman, B. W. (1984). Nonparametric regression and generalized linear models: a roughness penalty approach. Chapman & Hall.

    MATH  Google Scholar 

  • Green, P., Christopher, J., & Seheult, A. (1985). Analysis of field experiments by least squares smoothing. Journal of the Royal Statistical Society: Series B, 47, 299–315.

    MathSciNet  Google Scholar 

  • Ha, I. D., Lee, Y., & Song, J. K. (2001). Hierarchical likelihood approach for frailty models. Biometrika, 88, 233–243.

    MathSciNet  MATH  Google Scholar 

  • Ha, I. D., & Lee, Y. (2003). Estimating frailty models via Poisson hierarchical generalized linear models. Journal of Computational and Graphical Statistics, 12, 663–681.

    MathSciNet  Google Scholar 

  • Ha, I. D., Lee, Y., & MacKenzie, G. (2007). Model selection for multi-component frailty models. Statistics in Medicine, 26, 4790–4807.

    MathSciNet  Google Scholar 

  • Ha, I. D., Noh, M., & Lee, Y. (2010). Bias reduction of likelihood estimators in semi-parametric frailty models. Scandinavian Journal of Statistics, 37, 307–320.

    MathSciNet  MATH  Google Scholar 

  • Ha, I. D., Sylvester, R., Legrand, C., & MacKenzie, G. (2011). Frailty modelling for survival data from multi-centre clinical trials. Statistics in Medicine, 30, 2144–2159.

    MathSciNet  Google Scholar 

  • Ha, I. D., Noh, M., & Lee, Y. (2012). frailtyHL: A package for fitting frailty models with h-likelihood. R Journal, 4, 307–320.

    Google Scholar 

  • Ha, I. D., Pan, J., Oh, S., & Lee, Y. (2014). Variable selection in general frailty models using penalized h-likelihood. Journal of Computational and Graphical Statistics, 23, 1044–1060.

    MathSciNet  Google Scholar 

  • Ha, I. D., Lee, M., Oh, S., Jeong, J. H., Sylvester, R., & Lee, Y. (2014). Variable selection in subdistribution hazard frailty models with competing risks data. Statistics in Medicine, 33, 4590–4604.

    MathSciNet  Google Scholar 

  • Ha, I. D., Christian, N. J., Jeong, J. H., Park, J., & Lee, Y. (2016). Analysis of clustered competing risks data using subdistribution hazard models with multivariate frailties. Statistical Methods in Medical Research, 25, 2488–2505.

    MathSciNet  Google Scholar 

  • Ha, I. D., Vaida, F., & Lee, Y. (2016). Interval estimation of random effects in proportional hazards models with frailties. Statistical Methods in Medical Research, 25, 936–953.

    MathSciNet  Google Scholar 

  • Ha, I. D., Jeong, J. H., & Lee, Y. (2017). Statistical modelling of survival data with random effects: h-likelihood approach. Springer.

    MATH  Google Scholar 

  • Ha, I. D., Noh, M., & Lee, Y. (2017). H-likelihood approach for joint modelling of longitudinal outcomes and time-to-event data. Biometrical Journal, 59, 1122–1143.

    MathSciNet  MATH  Google Scholar 

  • Ha, I.D., Noh, M., Kim, J. & Lee, Y. (2018). frailtyHL: Frailty models using h-likelihood. http://CRAN.Rproject.org/package=frailtyHL. R package version 2.1.

  • Ha, I. D., Lee, Y., Xiang, L., Peng, M., & Jeong, J. H. (2020). Frailty modelling approaches for semi-parametric risks data. Lifetime Data Analysis, 26, 109–133.

    MathSciNet  MATH  Google Scholar 

  • Hougaard, P. (2000). Analysis of multivariate survival data. Springer.

    MATH  Google Scholar 

  • Huang, R., Xiang, L., & Ha, I. D. (2019). Frailty proportional mean residual life regression for clustered survival data: A hierarchical quasi-likelihood method. Statistics in Medicine, 38, 4854–4870.

    MathSciNet  Google Scholar 

  • Jin, S., & Lee, Y. (2020). A review of h-likelihood and hierarchical generalized linear model. WIREs Computational Statistics,. https://doi.org/10.1002/wics.1527.

    Article  Google Scholar 

  • Kalbfleisch, J. D., & Prentice, R. (1982). The statistical analysis of failure time data. Wiley.

    MATH  Google Scholar 

  • Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38, 963–974.

    MATH  Google Scholar 

  • Lee, D., Lee, W., Lee, Y., & Pawitan, Y. (2010). Super sparse principal component analysis for high-throughput genomic data. BMC Bioinformatics, 11, 296.

    Google Scholar 

  • Lee, D., Lee, W., Lee, Y., & Pawitan, Y. (2011). Sparse partial least-squares regression and its applications to high-throughput data analysis. Chemometrics and Intelligent Lab Systems, 109, 1–8.

    Google Scholar 

  • Lee, D., Kang, H., Kim, E., et al. (2015). Optimal likelihood-ratio multiple testing with application to Alzheimer’s disease and questionable dementia. BMC Medical Research Methodology, 15, 9.

    Google Scholar 

  • Lee, D., & Lee, Y. (2016). Extended likelihood approach to multiple testing with directional error control under a hidden Markov random field model. Journal of Multivariate Analysis, 151, 1–13.

    MathSciNet  MATH  Google Scholar 

  • Lee, D., Choi, D., & Lee, Y. (2020). Clustering with varying risks of false assignments in discrete latent variable model. Statistical Methods in Medical Research, 29(10), 2932–2944.

    MathSciNet  Google Scholar 

  • Lee, W., Lee, D., Lee, Y., & Pawitan, Y. (2011). Sparse canonical covariance analysis for high-throughput data. Statistical Applications in Genetics and Molecular Biology, 10(1), Article 30.

    MathSciNet  MATH  Google Scholar 

  • Lee, W., Lim, J., Lee, Y., & Castillo, J. D. (2011). The hierarchical-likelihood approach to autoregressive stochastic volatility models. Computational Statistics & Data Analysis, 55, 248–260.

    MathSciNet  MATH  Google Scholar 

  • Lee, W., & Lee, Y. (2013). Random-effect models with singular precision. Journal of Statistical Planning and Inference, 143, 2128–2141.

    MathSciNet  MATH  Google Scholar 

  • Lee, Y., & Nelder, J. A. (1996). Hierarchical generalized linear models (with discussion). Journal of the Royal Statistical Society: Series B, 58, 619–678.

    MathSciNet  MATH  Google Scholar 

  • Lee, Y., & Nelder, J. A. (2001). Hierarchical generalised linear models: A synthesis of generalised linear models, random-effect model and structured dispersion. Biometrika, 88, 987–1006.

    MathSciNet  MATH  Google Scholar 

  • Lee, Y., & Nelder, J. A. (2006). Double hierarchical generalized linear models (with discussion). Applied Statistics, 55, 139–185.

    MathSciNet  MATH  Google Scholar 

  • Lee, Y., Nelder, J. A., & Pawitan, Y. (2006). Generalized linear models with random effects: Unified analysis via H-likelihood. Chapman and Hall.

    MATH  Google Scholar 

  • Lee, Y., & Nelder, J. A. (2009). Likelihood inference for models with unobservables: Another view (with discussion). Statistical Science, 24, 255–293.

    MathSciNet  MATH  Google Scholar 

  • Lee, Y., & Bjø rnstad, J. F. (2013). Extended likelihood approach to large-scale multiple testing. Journal of the Royal Statistical Society: Series B, 75, 553–575.

    MathSciNet  Google Scholar 

  • Lee, Y., & Oh, H.-S. (2014). A new sparse variable selection via random-effect model. Journal of Multivariate Analysis, 125, 89–99.

    MathSciNet  MATH  Google Scholar 

  • Lee, Y., Nelder, J. A., & Pawitan, Y. (2017). Generalized linear models with random effects: Unified analysis via H-likelihood (2nd ed.). Chapman and Hall.

    MATH  Google Scholar 

  • Lee, Y., Rönnegȧrd, L., & Noh, M. (2017). Data Analysis Using Hierarchical Generalized Linear Models with R. CRC Press.

    Google Scholar 

  • Lee, Y., & Kim, G. (2019). Properties of H-likelihood estimators in clustered data. International Statistical Review, 88, 380–395.

    MathSciNet  Google Scholar 

  • Meng, X. (2009). Decoding the H-likelihood. Statistical Science, 24, 280–293.

    MathSciNet  MATH  Google Scholar 

  • Park, E., & Ha, I. D. (2019). Penalized variable selection for accelerated failure time models with random effects. Statistics in Medicine, 38, 878–892.

    MathSciNet  Google Scholar 

  • Pawitan, Y., & Lee, Y. (2017). Wallet game: Probability, likelihood, and extended likelihood. The American Statistician, 71(2), 120–122.

    MathSciNet  Google Scholar 

  • Pawitan, Y., & Lee, Y. (2021). Confidence as likelihood. Statistical Science (to appear).

  • Pawitan, Y., Lee, H., & Lee, Y. (2021). Epistemic confidence, the Ducth book and relevant subsets. (Manuscript prepared for publication).

  • Rizopoulos, D. (2012). Joint models for longitudinal and time-to-event data, with applications in R. Chapman and Hall.

    MATH  Google Scholar 

  • Sun, W., & Cai, T. T. (2007). Oracle and adaptive compound decision rules for false discovery rate control. Journal of the American Statistical Association, 102, 901–912.

    MathSciNet  MATH  Google Scholar 

  • Ter Braak, C. J. F., & de Jong, S. (1998). The objective function of partial least squares regression. Journal of Chemometrics, 12, 41–54.

    Google Scholar 

  • Therneau, T. M., & Grambsch, P. M. (2000). Modeling survival data: Extending the Cox model. Springer.

    MATH  Google Scholar 

  • Tibshirani, R. (1996). Regression Shrinkage and Selection via the Lasso. Journal of the Royal Statistical Society: Series B, 58, 267–288.

    MathSciNet  MATH  Google Scholar 

  • Zou, H., & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B, 67, 301–320.

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

Woojoo Lee was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1A2C1014409). Youngjo Lee was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2019R1A2C1002408). Donghwan Lee was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2021R1A2C1012865).

Author information

Authors and Affiliations

  1. Department of Public Health Sciences, Graduate School of Public Health, Seoul National University, 1 Kwanak-ro Kwanak-gu, Seoul, 151-742, South Korea

    Woojoo Lee

  2. Department of Statistics, Pukyong National University, Busan, 608-737, South Korea

    Il Do Ha & Maengseok Noh

  3. Department of Statistics, Ewha Womans University, 52 Ewhayeodae-gil, Seodaemun-gu , Seoul, 03760, Republic of Korea

    Donghwan Lee

  4. Department of Data Knowledge Service Engineering, Graduate School, Dankook University, Yongin, South Korea

    Youngjo Lee

Authors
  1. Woojoo Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Il Do Ha
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maengseok Noh
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Donghwan Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Youngjo Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Youngjo Lee.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lee, W., Do Ha, I., Noh, M. et al. A review on recent advances and applications of h-likelihood method. J. Korean Stat. Soc. 50, 681–702 (2021). https://doi.org/10.1007/s42952-021-00130-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42952-021-00130-8

Keywords

Search

Navigation