In this talk we describe our recent work on random effects models for right-censored data. Vaida and Xu (2000) provided a general framework for handling random effects in proportional hazards regression, in a way similar to the linear, non-linear and generalized linear mixed effects models that allow random effects of arbitrary covariates. This general framework includes the frailty models as a special case. Maximum likelihood estimates of the regression parameters, the variance components and the baseline hazard, and empirical Bayes estimates of the random effects can be obtained via an MCEM algoritm. Variances of the parameter estimates are approximated using Louis' formula.

We show interesting applications of the random effects Cox model to a US Vietnam Era Twin Registry study on alcohol abuse, with the primary goal of identifying genetic contributions to such events. The twin pairs in the registry consist of monozygotic and dizygotic twins. After model fitting and for interpretation purposes, the proportional hazards formulation is converted to a linear transformation model before the results on genetic contributions are reported. The model also allows examination of gene and covariate interactions, as well as the modelling of multivariate outcomes (comorbidities).

Time permitting we will discuss methods for model selection. These include likelihood ratio tests for the variance components, and information criteria under the random effects models.