Power and Sample Size Calculations in Clinical Trials with Multiple Primary Variables

This article proposes a method of power and sample size calculation for confirmatory clinical trials, with the objective of showing superiority for all multiple primary variables, assuming normality of the variables. Since one sided t-statistics are used to evaluate statistical significance, the power is calculated based on a Wishart distribution. A Monte Carlo integration is used to calculate the expectation of conditional power, conditioned on Wishart variables, where random numbers are generated using the Bartlett's decomposition. Numerical examples revealed that the required sample size decreases with increases in the correlation coefficient, although the dependency is not large when the correlation coefficient is negative or when the effect sizes, on which power is calculated, are far different between variables. A SAS program (version 9.1) for the proposed method is provided in the Appendix.