Abstract: A counting process approach to multiple event times modeled by an Andersen-Gill-type extension of the Cox proportional hazards regression model is considered. Tests for checking the validity of such a model against a general frailty model are proposed. These tests are derived from a class of statistics that are connected to Robbins' empirical Bayes estimation of Poisson means. We show that these tests are consistent against any alternative as specified by a nondegenerate frailty. A simple graphical method is introduced to visually check the appropriateness of model assumptions. Simulation studies are reported and a real life example is presented. A similar test for checking the gamma frailty assumption is also introduced.
Key words and phrases: Counting process, Cox regression, empirical Bayes, goodness of fit, martingale, multiple event times, Poisson process, random effect.