Design and analysis of multiarm clinical trials with survival endpoints

The clinical trials literature has paid relatively little attention to the design and analysis of K-sample trials with survival endpoints where K is 3 or greater. Following the least-significant-difference approach proposed by Makuch and Simon [1], we derive sample size formulas by working with the logrank test and proportional hazards model directly. This approach ensures the type I error rate to be the nominal value when the global null hypothesis is true. For power considerations, planning the study based on the least favorable alternative is recommended. The resulting sample size requirements are presented in graphic form for K = 3 and 4. Assuming that there is a control group and considering only the alternative that the survival of the experimental treatments is at least as good as that of the control group, power investigations indicate that the proposed strategy has good power for detecting the difference between the control and the best treatment. The "overall power," defined as the chance of the global test and subsequent pairwise comparisons all being correct, is good when all treatments are similar to either the control or the best treatment. Overall power is poor when the hazards are more evenly spread out between the control and the best group because the sample size is inadequate to detect such differences.