Conditional power for arbitrary survival curves to decide whether to extend a clinical trial

This article describes a computer simulation methodology to calculate conditional power for comparing two arbitrary survival curves as an aid in deciding whether or not to extend a clinical trial. The method is a modification of that by Halpern and Brown, which computes unconditional power for comparing arbitrary survival curves at the beginning of a study. The advantage of this method is that it permits conditional power calculations for comparisons of distribution-free survival curves. Power is computed for two commonly used statistical tests, the log-rank test and Gehan's generalization of the Wilcoxon test, and for a modified Kolmogorov-Smirnov test, which is particularly sensitive to crossing survival curves. This method for estimating conditional power should be useful in the situation in which a decision must be made regarding the benefit of continuing a clinical trial. The application of this method is shown using VA Cooperative Study No. 90, "Prognosis and Outcome Following Heart Valve Replacement."