On the Applications of Fisher's Least Significant Difference (LSD) Procedure in Three-Arm Clinical Trials with Survival Endpoints

Fisher's (protected) least significant difference (LSD) procedure has been suggested in the design and analysis of multiarm clinical trials with survival endpoints. In this article, the power of this procedure is evaluated and compared with that of Bonferroni and Hochberg procedures by Monte Carlo simulations under three scenarios of alternative hypothesis encountered in three arm clinical trials with survival endpoint. The approach of sample size calculation based on the power of a global test in the first step of Fisher's LSD procedure is also evaluated and contrasted with that based on Bonferroni adjustment. It is shown that Bonferroni and Hochberg procedures are more powerful than Fisher's LSD procedure when two specific pair-wise comparisons are of interest, while Fisher's LSD procedure is the most powerful if all three pairwise comparisons are performed. It is recommended that the formula of Makuch and Simon be used in the sample size calculations for all three types of alternative hypothesis considered in this article. However, the Hochberg procedure should be used in the analysis if only two specific pairwise comparisons are of interest and the Fisher's LSD procedure should be used in the analysis when objective of the trial includes all of three pairwise comparisons.