Testing for decreasing heterogeneity in a new time-varying frailty model

Abstract

Frailty models adjust for between-cluster variability in survival data by including a cluster-specific random factor, the frailty term, in the Cox model. The frailty term is assumed to be constant over time. This assumption is questionable in some particular settings, e.g., in cancer clinical trials on chronic myeloid leukaemia. We therefore relax the time-constant heterogeneity assumption and consider frailty models with a time-varying frailty term. Instead of working with hazard models, we rather model the log cumulative hazard function, making use of the mixed model framework, and introduce a time-varying random effect at that level. Simulations demonstrate that the proposed method has acceptable size and power to detect time-dependent clustering. The method is applied to data from a large-scale multicentre clinical trial in patients with chronic myeloid leukaemia.