Abstract
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.
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References
Meier U. A note on the power of Fisher’s least significant difference procedure. Pharm Stat. 2006; 5:253–263.
Makuch RW, Simon RM. Sample size requirements for comparing time-to-failure among k treatment groups. J Chron Dis. 1982;35:861–867.
Liu PY. Dahlberg S. Design and analysis of multiarm clinical trials with survival endpoints. Control Clin Trials. 1995;16:119–130.
Ahnn S. Anderson SJ. Sample size determination for comparing more than two survival distributions. Stat Med. 1995;14:2273–2282.
Ahnn S, Anderson SJ. Sample size determination in complex clinical trials comparing more than two groups for survival endpoints. Stat Med.. 1998;17:2525–2534.
Halabi S. Singh B. Sample size determination for comparing several survival curves with unequal allocations. Stat Med. 2004;23:1793–1815.
Barthel FMS, Babiker A, Royston P, Parmar MKB. Evaluation of sample size and power for multiarm survival trials allowing for non-uniform accrual, non-proportional hazards, loss to follow-up and cross-over. Stat Med. 2006;25:2521–2542.
Weslfall PH, Tobias RD, Rom D, Wolfinger RD, Hochberg Y. Multiple Comparisons and Multiple Tests Using SAS®. Cary, NC: SAS Institute Inc.; 1999.
Hochberg Y. A sharper Bonferroni procedure for multiple tests of significance. Biometrika. 1988;75:800–802.
Rubinstein LV, Gail MH, Santner TJ. Planning the duration of a comparative clinical trial with loss to follow-up and a period of continued observation. J Chron Dis. 1981;34:469–479.
Casella G, Berger RL. Statistical Inference. Belmont. CA: Wadsworth Inc.; 1990.
George SL, Desu MM. Planning the size and duration of a clinical trial studying the time to some critical event. J Chron Dis. 1974;27:15–29.
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Liu, S., Tu, D. On the Applications of Fisher’s Least Significant Difference (LSD) Procedure in Three-Arm Clinical Trials with Survival Endpoints. Ther Innov Regul Sci 42, 81–91 (2008). https://doi.org/10.1177/009286150804200112
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DOI: https://doi.org/10.1177/009286150804200112