Multiple Testings: Multiple Comparisons and Multiple Endpoints*

This paper gives a brief overview of some issues and some general concepts related to multiple testing problems as they are encountered in clinical drug trials. Some recent methods for handling multiple comparisons are discussed. Emphasis is given to the p-value-based procedures and the general closed testing procedure of Marcus, Peritz, and Gabriel (1). Examples are given to illustrate these procedures and to highlight some important issues. Regarding multiple endpoints, the discussion focuses on the need to have a better definition of what primary, coprimary, and secondary endpoints should mean, and suggests that a clinical decision rule defined in terms of primary, coprimary, and relevant secondary endpoints is a clinically relevant way of reducing the dimensionality problem of multiple endpoints. These clinical decision rules, however, often lack a statistical support structure. Further research in this area is needed.