Goodness-of-fit tests for semiparametric models with multiple event-time data

A counting process approach to multiple event times modeled by an Andersen- Gill-type extension of the Cox proportional hazards regression model is con sidered. Tests for checking the validity of such a model against a general frailty model are proposed. These tests axe derived from a class of statist ics that are connected to Robbins' empirical Bayes estimation of Poisson me ans. We show that these tests axe consistent against any alternative as spe cified by a nondegenerate frailty. A simple graphical method is introduced to visually check the appropriateness of model assumptions. Simulation stud ies axe reported and a real life example is presented. A similar test for c hecking the gamma frailty assumption is also introduced.