›› 2014, Vol. 53 ›› Issue (5): 39-46.

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The Estimation and Application for Cox Model with Weibull Frailty Via Hierarchical-likelihood

WANG Ningning1, XU Shuyi 2   

  1. 1. Public Health School, Guangzhou Medical University, Guangzhou 510182, China;
    2. Lingnan (University) College, Sun Yat-sen University, Guangzhou 510275, China
  • Received:2013-11-08 Online:2014-09-25 Published:2014-09-25

Abstract: The proportional hazard model with Weibull frailty is used for analyzing right-censoring longitudinal survival data. Complex marginal integrals are avoided by using Hierarchal-likelihood to estimate covariate coefficients and prediction of random effects, the adjusted profile hierarchical-likelihood is taken to estimate the parameters of random factors'distribution. Simulation studies of comparing with other frailties including lognormal frailty and Gamma frailty are provided and the result indicates that the Weibull frailty performs very well. The examples for analyzing two real data sets are also presented, and the results indicate that the Weibull frailty model is at least as good as lognormal and Gamma frailty model, and the Weibull frailty model is more helpful to diagnose the heterogeneity.

Key words: frailty model, Weibull distribution, hierarchal-likelihood, proportional hazard, right censor

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