Analysis of Tumor Recurrence Data Using AR(1) Frailty Model

Frailty models have been widely used for analyzing multivariate survival data such as recurrent or multiple event data. We analyze the tumor recurrence data(Gail et al., 1980), which show the gap times between successive mammary tumor occurrences in a subject, using a serially correlated AR(1) frailty model. Here, the frailty of each subject is not constant, but changes stochastically over the gap times. Inferences are based on hierarchical-likelihood, which provides a simple unified framework for various random-effect models. In particular, we demonstrate that an AIC(Akaike information criterion) based on hierarchical-likelihood selects the AR(1) frailty model as an appropriate model for the tumor data.