Sample size calculation for small sample single-arm trials for time-to-event data: Logrank test with normal approximation or test statistic based on exact chi-square distribution?

Background: Sample size calculations are critical to the planning of a clinical trial. For single-arm trials with time-to-event endpoint, standard software provides only limited options. The most popular option is the log-rank test. A second option assuming exponential distribution is available on some online websites. Both these approaches rely on asymptotic normality for the test statistic and perform well for moderate-to-large sample sizes. Methods: As many new treatments in the field of oncology are cost-prohibitive and have slow accrual rates, researchers are often faced with the restriction of conducting single arm trials with potentially small-to-moderate sample sizes. As a practical solution, therefore, we consider the option of performing the sample size calculations using an exact parametric test with the test statistic following a chi-square distribution. Analytic results of sample size calculations from the two methods with Weibull distributed survival times are briefly compared using an example of a clinical trial on cholangiocarcinoma and are verified through simulations. Results: Our simulations suggest that in the case of small sample phase II studies, there can be some practical benefits in using the exact test that could affect the feasibility, timeliness, financial support, and 'clinical novelty' factor in conducting a study. The exact test is a good option for designing small-to-moderate sample trials when accrual and follow-up time are adequate. Conclusions: Based on our simulations for small sample studies, we conclude that a statistician should assess sensitivity of his calculations obtained through different methods before recommending a sample size to their collaborators.