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Multilevel Models for Survival Analysis with Random Effects

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  • Kelvin K. W. Yau

Abstract

Summary. A method for modeling survival data with multilevel clustering is described. The Cox partial likelihood is incorporated into the generalized linear mixed model (GLMM) methodology. Parameter estimation is achieved by maximizing a log likelihood analogous to the likelihood associated with the best linear unbiased prediction (BLUP) at the initial step of estimation and is extended to obtain residual maximum likelihood (REML) estimators of the variance component. Estimating equations for a three‐level hierarchical survival model are developed in detail, and such a model is applied to analyze a set of chronic granulomatous disease (CGD) data on recurrent infections as an illustration with both hospital and patient effects being considered as random. Only the latter gives a significant contribution. A simulation study is carried out to evaluate the performance of the REML estimators. Further extension of the estimation procedure to models with an arbitrary number of levels is also discussed.

Suggested Citation

  • Kelvin K. W. Yau, 2001. "Multilevel Models for Survival Analysis with Random Effects," Biometrics, The International Biometric Society, vol. 57(1), pages 96-102, March.
    • Handle: RePEc:bla:biomet:v:57:y:2001:i:1:p:96-102
    DOI: 10.1111/j.0006-341X.2001.00096.x
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    Cited by:

    1. Xiang, Liming & Yau, Kelvin K.W. & Tse, S.K. & Lee, Andy H., 2007. "Influence diagnostics for random effect survival models: Application to a recurrent infection study for kidney patients on portable dialysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5977-5993, August.
    2. Sharif Mahmood & Begum Zainab & A.H.M. Mahbub Latif, 2013. "Frailty modeling for clustered survival data: an application to birth interval in Bangladesh," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(12), pages 2670-2680, December.
    3. Guillaume Horny & Dragana Djurdjevic & Bernhard Boockmann & François Laisney, 2008. "Bayesian Estimation of Cox Models with Non-nested Random Effects: an Application to the Ratification Of ILO Conventions by Developing Countries," Annals of Economics and Statistics, GENES, issue 89, pages 193-214.
    4. James W. Vaupel & Trifon Missov, 2014. "Unobserved population heterogeneity," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 31(22), pages 659-686.
    5. Guillaume Horny, 2009. "Inference in mixed proportional hazard models with K random effects," Statistical Papers, Springer, vol. 50(3), pages 481-499, June.
    6. Kelvin Yau & Karen Yip & H. K. Yuen, 2003. "Modelling repeated insurance claim frequency data using the generalized linear mixed model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(8), pages 857-865.
    7. Eric C. Brown & John W. Graham & J. David Hawkins & Michael W. Arthur & Megan M. Baldwin & Sabrina Oesterle & John S. Briney & Richard F. Catalano & Robert D. Abbott, 2009. "Design and Analysis of the Community Youth Development Study Longitudinal Cohort Sample," Evaluation Review, , vol. 33(4), pages 311-334, August.
    8. Guillaume Horny, 2006. "Partial Likelihood Estimation of a Cox Model with Random Effects: an EM Algorithm based on Penalized Likelihood," Working Papers of BETA 2006-10, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    9. Richard Tawiah & Geoffrey J. McLachlan & Shu Kay Ng, 2020. "A bivariate joint frailty model with mixture framework for survival analysis of recurrent events with dependent censoring and cure fraction," Biometrics, The International Biometric Society, vol. 76(3), pages 753-766, September.
    10. repec:jss:jstsof:08:i09 is not listed on IDEAS

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