Power analysis, sample size calculation for testing the largest binomial probability

Abstract

A procedure is developed for power analysis and sample size calculation for a class of complex testing problems regarding the largest binomial probability under a combination of treatments. It is shown that the asymptotic null distribution of the likelihood-ratio statistic is not parameter-free, but $\chi _{1}^{2} $ is a conservative asymptotic null distribution. A nonlinear Gauss-Seidel algorithm is proposed to uniquely determine the alternative for the power and sample size calculation given the baseline binomial probability. An example from an animal clinical trial is discussed.

Keywords

• asymptotic null distribution
• binomial probability
• complex hypotheses
• gauss-seidel
• logistic regression
• power
• sample size
• tests