gms | German Medical Science

The one-sample log-rank test (first proposed by Breslow [1]) may be the method of choice if the survival curve of patients under a new treatment is compared to that of a historic control. Such settings arise, for example, in early phase II single-arm cancer trials. Finkelstein et al. [2] and Sun et al. [3] consider single-stage designs with the one-sample log-rank test. They both give a sample size formula based on the number D of events to be observed: In order to achieve an aspired power for allocated significance level and treatment effect, the analysis may be performed as soon as a critical number of events is reached. Here, we study adaptive designs with the one-sample log-rank test.

We show that there are two approaches to planning and analyzing adaptive designs with the one-sample log-rank test based on conditional power. Either the traditional approach based on the number of events D, or an alternative approach based on the sum of cumulative hazards E of the patients. For single-stage designs this aspect has recently been investigated by Schmidt et al. [4]. Here, the focus is on the adaptive setting.

Asymptotically, both approaches are equivalent, but perform differently well for small sample size. This is clearly seen in our simulations. We compare both approaches under a range of scenarios with regard to conditional power performance, type I error control, and study duration. In our simulations, the trial is usually underpowered, and the aspired significance level is not exploited if the traditional stopping criterion based on the number of events is used, whereas a trial based on the new criterion maintains power with the type-I error rate still controlled.