Testing for Decreasing Heterogeneity Between Hospitals in Time to Death from Chronic Myeloid Leukemia

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 acts on the hazard rate in a multiplicative way and is assumed to be constant over time. This assumption is questionable in some particular settings, e.g., in cancer clinical trials on chronic myeloid leukemia. We therefore relax this assumption and consider frailty models with time-varying frailties. 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 multicentre clinical trial in patients with chronic myeloid leukemia.