An Empirical Likelihood Based EM Algorithm for the Inference of Proportional Hazard Models with Multivariate Random Effects

• Activity Number: 558
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Jiayin Zheng*+ and Junshan Shen and Shuyuan He and Xiao-Hua Andrew Zhou
• Companies: Peking University/University of Washington and Peking University and Capital Normal University and University of Washington
• Keywords: EM algorithm ; Empirical Likelihood ; Multiplicative shared frailty model ; Partial likelihood ; Proportional hazards model ; Survival analysis

Abstract

There exists a growing literature on the estimation of Semi-parametric multiplicative shared frailty models. But they often assume frailties follow some specific distributions which may not well agree with the reality. To get rid of such restrictions, we propose an Empirical Likelihood based EM algorithm given some working discrete supports of random effects. In each iteration of the EM algorithm, the Empirical Likelihood method is used to reassign weights to such support points. The performance of our method is assessed based on simulation studies comparing our method with other existing ones such as normal frailty model and gamma frailty model. The results show that with enough number of groups corresponding to random effects, our method performs better in estimating the coefficients of fixed effects and random effects' distribution, while other methods appear to be affected by violation of their corresponding assumptions. We also discuss how to choose working discrete supports and simulation studies show that results seem to converge as the range of the support becomes larger and the grids of it get more refined. The method is also exemplified on a real data set.