The superiority of a drug combination over each of its components

The requirement for approval of a combination drug treatment AB is its demonstrated superiority over each of its components A and B at their most appropriate dose levels. This has led to frequent use of a three-group experimental design that permits separate testing of H0:AB less than or equal to A and H0:AB greater than or equal to B. A type I error can occur if no true treatment effect is present in either or both of the contrasts. The sampling distribution for the larger of the two observed p-values, however, depends on whether a non-null treatment effect is or is not present in one of the contrasts. We propose a strategy in which a conservative experiment-wide type I error is achieved by defining the criterion for significance of the smaller observed treatment effect contingent on the magnitude of the larger observed treatment effect. We also discuss sample size requirements for the three-group design.