An improved one-sample log-rank test

The one-sample log-rank test allows to compare the survival of a single sample with a prefixed reference survival curve. It naturally applies in single-arm phase IIa trials with time-to-event endpoint. Several authors have described that the original one-sample log-rank test is conservative when sample size is small and have proposed strategies to correct the conservativeness. Here, we propose an alternative approach to improve the one-sample log-rank test. Our new one-sample log-rank statistic is based on the unique transformation of the underlying counting process martingale such that the moments of the limiting normal distribution have no shared parameters. Simulation results show that the new one-sample log-rank test gives type I error rate and power close to the nominal levels also when sample size is small, while relevantly reducing the required sample size to achieve the desired power as compared to current approaches to design studies to compare the survival outcome of a sample with a reference.