Extended MaxT Tests of One-Sided Hypotheses

Abstract

In many statistical applications of one-sided tests of multiple hypotheses researchers are often concerned not only with global tests of the intersection of individual hypotheses, but also with multiple tests of individual hypotheses. For example, in clinical trial studies researchers often need to find out the efficacy of a treatment, as well as the significance of each outcome measurement (endpoint) of the treatment. This article proposes MaxT type tests aiming at improving the global power of existing MaxT tests. Our extended MaxT tests are constructed by adding an extra component to the maximand set of existing MaxT tests. The added component is a weighted sum of other components. Some power properties relating to choices of weight are studied. Our simulation study shows that the proposed tests can considerably improve the global power of existing MaxT tests and can also outperform many other global tests under some alternatives and/or some nonnormal distributions. Furthermore, it is shown that such global power improvement may involve little loss of power on multiple testing. Two real data examples on clinical trial studies reported in the literature are reexamined. The results of our tests suggest stronger evidence on treatment effects over MaxT tests and likelihood ratio tests while changing little on the evidence concerning endpoint testing. Supplementary materials for this article are available online.

• Global one-sided test
• Maximin test
• Multiple one-sided test
• Unbiasedness.