Cumulative statistical power for hierarchical comparisons to evaluate two combination drug doses

According to the regulatory requirements for multiple-dose factorial designs, a combination drug must have confirmatory evidence for being more effective than each component drug alone. An incomplete factorial design may be employed to evaluate some combination drugs because of resource constraints and priorities. In this paper, we compare the powers for four different patterns of sample size allocations in two incomplete factorial designs, with two combination drug doses and fixed total sample size. A hierarchical closed testing procedure is employed for the treatment comparisons of interest as a method to control type I error for multiple comparisons. The overall cumulative powers of contradicting all null hypotheses at a particular stage of the hierarchy and all preceding stages are determined by simulation for the respective stages of the hierarchy. The purpose is to identify the allocation of sample size so as to enable better power in a hierarchical evaluation of comparisons.