ABSTRACT
One view of multiple comparisons is there is an extensive menu of methods to choose from, depending on the problem and perhaps on taste. The perspective given in this chapter instead is, there are basic principles of multiple testing underlying the methods, and these principles can be applied to construct new methods as decision-making processes in clinical trials advance and evolve over time.
Error rates in multiple testing are first defined, then the Partitioning Principle and the Closed Testing principle are stated. Holm's test and Hochberg's test are presented, not as menus items to choose from, but as examples of existing methods that can be de-constructed by the Partitioning Principle.
We then use an example of decision-making in clinical trials with multiple doses and multiple endpoints to demonstrate not only how to construct new methods from basic principles, but also the different choices available in computationally implementing them. An illustration of the Graphical Approach which allows users to customize their own multiple tests is also given.
Availability of targeted therapies has made personalized medicine common practice. To properly respect the logical relationships among efficacy in multiple Subgroups, a new set of principles called Parameter Logic (PL) principles is stated toward the end of the chapter.
