Sample Size Determination in Heterogeneous Populations for Multivariate Time-to-event Data

Most of randomized clinical trials (RCT) using time-to-event criteria as the primary endpoint are designed, powered and analyzed based on an hypothetical hazard ratio (HR) corresponding to the targeted effect size between experimental and control arms. Usually, one assumes that populations are homogeneous within each treatment arm, that is, within each arm, (i) the baseline risk is identical for all patients, and (ii) the treatment effect is identical for all patients. This assumption however may not hold in all circumstances. This project aims at providing a statistical method for the estimation of sample size in RCT, in the presence of heterogenous populations, such as assuming populations with distinct underlying baseline risks or assuming different treatment effects.