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

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 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.