ABSTRACT
The Partitioning Principle (PP) is a fundamental principle in multiple comparisons. This chapter discusses three applications of PP corresponding to the following motivations.
Some scientific problems naturally partition. For example, in comparing four treatments for a disease, if treatment one is the best, then treatment two is not; if treatment three is the best, then treatment four is not.
While both the Partitioning Principle and the Closed Testing Principle can control the familywise error rate (FWER) in testing multiple hypotheses while keeping multiplicity adjustment only to the extent needed, PP is more able to derive associated confidence sets, which, in turn, guarantees control of the directional error rate in making decisions.
Some decision-making processes have paths. For example, in some (but not all) therapeutic areas, it is natural to test doses from high to low in that order. As another example, the efficacy in the primary endpoint would be tested before the secondary endpoint because efficacy in the secondary endpoint is relevant only if there is efficacy in the primary endpoint. The PP can formulate multiple testing problems that automatically channel the decision-making process onto desirable decision paths (without rigid rules) by transparently partitioning the parameter space.
