Design and analysis of clinical trials in the presence of delayed treatment effect

In clinical trials with survival endpoint, it is common to observe an overlap between two Kaplan-Meier curves of treatment and control groups during the early stage of the trials, indicating a potential delayed treatment effect. Formulas have been derived for the asymptotic power of the log-rank test in the presence of delayed treatment effect and its accompanying sample size calculation. In this paper, we first reformulate the alternative hypothesis with the delayed treatment effect in a rescaled time domain, which can yield a simplified sample size formula for the log-rank test in this context. We further propose an intersection-union test to examine the efficacy of treatment with delayed effect and show it to be more powerful than the log-rank test. Simulation studies are conducted to demonstrate the proposed methods.