Repeated events survival models: the conditional frailty model

Repeated events processes are ubiquitous across a great range of important health, medical, and public policy applications, but models for these processes have serious limitations. Alternative estimators often produce different inferences concerning treatment effects due to bias and inefficiency. We recommend a robust strategy for the estimation of effects in medical treatments, social conditions, individual behaviours, and public policy programs in repeated events survival models under three common conditions: heterogeneity across individuals, dependence across the number of events, and both heterogeneity and event dependence. We compare several models for analysing recurrent event data that exhibit both heterogeneity and event dependence. The conditional frailty model best accounts for the various conditions of heterogeneity and event dependence by using a frailty term, stratification, and gap time formulation of the risk set. We examine the performance of recurrent event models that are commonly used in applied work using Monte Carlo simulations, and apply the findings to data on chronic granulomatous disease and cystic fibrosis.