Comparison of several testing strategies for combination drug efficacy trials based on the closure principle

The author discusses three multiple testing procedures for identifying the minimum efficacious doses in a balanced factorial combination drug trial. All of these procedures utilize the closed testing principle, and hence strongly control the overall error rate and satisfy the coherence property, that is, if a hypothesis is retained then any hypothesis implied by it is also retained. While coherence is an essential requirement for any multiple testing procedure, consonance is a highly desirable characteristic. In the considered settings if a testing procedure is consonant then it always provides a set of all minimum efficacious combinations as a result, otherwise, it may lead to ambiguity. Although the coherence property is satisfied for any closed testing procedure and thus, does not depend on the test used for an individual hypothesis, whether the considered procedures satisfy the consonance property depends entirely on the nature of the test statistic. The author identifies the consonant and non-consonant procedures among the presented procedures and discusses possible drawbacks of non-consonant procedures with respect to combination drug efficacy trials. Additional properties of these procedures are assessed by simulations.