Semiparametric mixed-effects models for clustered failure time data

The Cox proportional hazards model with a random effect has been proposed for the analysis of data which consist of a large number of small clusters of correlated failure time observations. The class of linear transformation models provides many useful alternatives to the Cox model for analyzing univariate failure time data. In this article, we generalize these models by incorporating random effects, which generate the dependence among the failure times within the cluster, to handle correlated data, Inference and prediction procedures for S such random effects models are proposed. They are relatively simple compared with the methods based on the nonparametric maximum likelihood estimators for the Cox frailty model in the literature. Our proposals are illustrated with a data set from a well-known eye study. Extensive numerical studies are conducted to evaluate various robustness properties of the new procedures.