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 behaviors, 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 develop a new model for repeated events processes that accurately 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 these models and others that are commonly used in applied work using Monte Carlo simulations, and apply the findings to data on chronic granulomatous disease and cystic.