One-sided multiple endpoint testing in two-sample comparisons

This article reviews several methods for comparing two treatments with multiple endpoints that take into account the dependence structure among the endpoints and that are sensitive to the multivariate one-sided alternative. The methods are classified into procedures that adjust single endpoint P-values separately, into bootstrap procedures that adjust single endpoint P-values through resampling from the whole data, and into procedures that summarize the data into a global test statistic. In this context, we describe step-down procedures leading to conclusions about the single endpoints. Applying the closed test principle, James (1991, Statistics in Medicine 10, 1123-1135)-based, O'Brien (1984, Biometrics 40, 1079-1087)-based, Tang, Gnecco, and Gellar (1989, Biometrika 76, 577-583)-based, and Westfall and Young (1989, Journal of the American Statistical Association 84, 780-786)-based procedures are investigated and compared to standard techniques. Monte Carlo simulations for small to moderate sample sizes are performed to give some recommendations for practical use.