Assessment of effect size and power for survival analysis through a binary surrogate endpoint in clinical trials

A strategy for early-stage breast cancer trials in recent years consists of a neoadjuvant trial with pathological complete response (pCR) at time of surgery as the efficacy endpoint, followed by the collection of long-term data to show efficacy in survival. To calculate an appropriate sample size to detect a survival difference based upon pCR data, it is necessary to relate the effect size in pCR with the effect size in survival. Here, we propose an exponential mixture model for survival time with parameters for the neoadjuvant pCR rates and an estimated benefit of achieving pCR to determine the treatment effect size. Through simulation studies, we demonstrated how to estimate the empirical power for detecting the survival efficacy under a parameter setting. We also showed a more efficient way to estimate the power for detecting the survival efficacy through estimated average hazard ratios and the Schoenfeld formula. Our method can be used to power future confirmatory adjuvant trials based on the preliminary data obtained from the neoadjuvant component.