The shared frailty model and the power for heterogeneity tests in multicenter trials

Heterogeneity between centers in multicenter trials with time to event outcome can be modeled by the frailty proportional hazards model. The majority of the different approaches that have been used to fit frailty models assume either the gamma or the lognormal frailty density and are based on similar log likelihood expressions. These approaches are briefly reviewed and their specific features described; simulations further demonstrate that the different techniques lead to virtually the same estimates for the heterogeneity parameter. An important issue is the relationship between the size of a multicenter trial, in terms of number of centers and number of patients per center, and the bias and the spread of estimates of the heterogeneity parameter around its true value. Based on simulation results (restricted to constant hazard rate and the gamma frailty density), it becomes clear how the number of centers and the number of patients per center influence the quality of the estimates in the particular setting of breast cancer clinical trials. This insight is important in treatment outcome research, where one tries to relate differences with respect to clinical practice to differences in outcome in the various centers.