Resampling-based and other multiple testing strategies with application to combination drug trials with factorial designs.

The problem of detecting all effective and superior combinations in a factorial drug efficacy trial is stated in terms of two hypothesis families, full and reduced. The reduced problem formulation allows identification of all simultaneously effective and superior combinations. The full formulation allows individual detection of the efficacy and superiority of combinations resulting in more detailed conclusions. While the full hypothesis family deals with simpler parameters, the true mean effect differences, it has three times as many hypotheses as the reduced family. The reduced family is comprised of hypotheses concerning a gain-parameter, which is defined as the minimum of the true mean differences and leading to a fairly complicated structure. For each problem formulation, Holm's, Hochberg's and two resampling approaches are studied with respect to strong control of overall error rate and several power measures. Holm's and Hochberg's approaches are recommended for the reduced family, while the step-down resampling approach is recommended for the full hypothesis family. Moreover, the correct problem formulation is of great importance, because if the sample size is not sufficient there is a high potential for lack of power associated with the full problem due to a large number of hypotheses.