Phase II cancer clinical trials with a one-sample log-rank test and its corrections based on the Edgeworth expansion

The response rate has been frequently used as the primary endpoint of phase II cancer clinical trials. It may not be an appropriate endpoint when a new treatment is not expected to produce any tumour shrinkage. When a large database for a historical control is available, the direct comparison of survival curves between a new treatment and the historical control may be made in phase II cancer clinical trials. In this paper, a one-sample log-rank test is introduced for the design and analysis of phase II cancer clinical trials with time-to-event endpoints. Corrections to the one-sample log-rank test are also derived based on the Edgeworth expansion. Simulations showed that the original one-sample log-rank test may be preferred if strictly controlling for type I error is important or when the sample size of a phase II trial is as large as 50, and a corrected one-sample log-rank test is used if the sample size of a phase II trial is small. A data set from a clinical trial conducted by the NCIC Clinical Trials Group is used to illustrate the proposed procedures.