Institution: The Ohio State University
Street: 1958 Neil Avenue
City: Columbus, OH
Phone: (614) 292-7663
Fax: (614) 292-2096
Authors: Jason C. Hsu
Title: The Closed Testing Principle and the Partitioning Principle
Abstract: The closed testing principle of Marcus, Peritz, and Gabreil (1976) has been a cornerstone of multiple hypotheses testing for decades. Separately, Stefansson, Kim, and Hsu (1988) originated what is now called the partitioning principle to derive confidence sets in a variety of problems, such as multiple comparisons with the best, stepwise testing, and bioequivalence. It turns out the partitioning principle is useful in multiple testing itself. We will explain, in an elementary way, why every closed testing inference can at least be matched by partitioning testing. Finner and Strassburger (2002) in fact show partitioning can obtain more powerful tests than closed testing in some situations. In this talk, we will use the examples of efficacy testing in Phase II dose-response clinical trials and multiple endpoints testing in Phase III pivotal trials to compare the partitioning principle with the closed testing principle.
References: Marcus, Peritz, and Gabreil (1976). On closed testing procedures with special reference to ordered analysis of variance. Biometrika 63, 655-660. Stefansson, Kim, and Hsu (1988). On confidence sets in multiple comparisons. Statistical Decision Theory and Related Topics IV, Gupta and Berger editors. Springer-Verlag, New York. Finner and Strassburger (2002). The partitioning principle: a powerful tool in multiple decision theory. To appear in Annals of Statistics.