Sample Size Determination in Two-Sided Distribution-Free Treatment vs. Control Multiple Comparisons

• Activity Number: 407
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Chunpeng Fan*+ and Donghui Zhang
• Companies: sanofi-aventis and sanofi-aventis
• Keywords: FWER ; Power ; Nonparametric ; Joint Ranking ; Pairwise Ranking

Abstract

The problem of power and sample size determination for distribution-free multiple comparison tests of $K$ treatments versus a control group is addressed. We define the power as the probability of correctly rejecting $M$ specified hypotheses, where $M$ can be any positive integer up to $K$. The power formulae are derived for both joint ranking and pairwise ranking mechanism for general multiple comparison problems, followed by explicit form of these formulae when the single-step, step-down, or step-up adjustments are applied. Numerical methods via quasi-Monte Carlo integration and Monte Carlo integration are assessed. Our simulation studies show the accuracy of the power and sample size calculation formulae. We recommend the Monte Carlo integration as the calculation algorithm. An example from a mouse peritoneal cavity study is used to demonstrate the application of the methods.