Model selection and diagnostics for joint modeling of survival and longitudinal data with crossing hazard rate functions.

Comparison of two hazard rate functions is important for evaluating treatment effect in studies concerning times to some important events. In practice, it may happen that the two hazard rate functions cross each other at one or more unknown time points, representing temporal changes of the treatment effect. Also, besides survival data, there could be longitudinal data available regarding some time-dependent covariates. When jointly modeling the survival and longitudinal data in such cases, model selection and model diagnostics are especially important to provide reliable statistical analysis of the data, which are lacking in the literature. In this paper, we discuss several criteria for assessing model fit that have been used for model selection and apply them to the joint modeling of survival and longitudinal data for comparing two crossing hazard rate functions. We also propose hypothesis testing and graphical methods for model diagnostics of the proposed joint modeling approach. Our proposed methods are illustrated by a simulation study and by a real-data example concerning two early breast cancer treatments.