Study design of single‐arm phase II immunotherapy trials with long‐term survivors and random delayed treatment effect

In the traditional study design of a single-arm phase II cancer clinical trial, the one-sample log-rank test has been frequently used. A common practice in sample size calculation is to assume that the event time in the new treatment follows exponential distribution. Such a study design may not be suitable for immunotherapy cancer trials, when both long-term survivors (or even cured patients from the disease) and delayed treatment effect are present, because exponential distribution is not appropriate to describe such data and consequently could lead to severely underpowered trial. In this research, we proposed a piecewise proportional hazards cure rate model with random delayed treatment effect to design single-arm phase II immunotherapy cancer trials. To improve test power, we proposed a new weighted one-sample log-rank test and provided a sample size calculation formula for designing trials. Our simulation study showed that the proposed log-rank test performs well and is robust of misspecified weight and the sample size calculation formula also performs well.