Sample Size Calculation for Comparing Two-Stage Treatment Strategies with Censored Data

In two-stage randomization trials subjects are first randomized to an initial treatment, and then if and when a response (or nonresponse) criterium is met, re-randomized to a second-stage treatment. When the primary outcome is a time to event, sample size calculation is challenging because the variances of common estimators depend in a complex manner on the joint distribution of primary time to event outcome and time to response (or nonresponse) to the initial treatment. To circumvent this problem we construct simple upper bounds of the variances; the use of these upper bounds allows us to use the same working assumptions needed to size a single stage trial. The use of the upper bounds necessarily yields conservative sample sizes when all working assumptions are correct, but has the advantage of robustness to incorrect working assumptions. The tests we consider for sample size calculation include a test based on the weighted Kaplan-Meier estimator of survival probabilities at a fixed time point and the weighted log rank test. We also consider several variants of the two-stage randomized design.