Title: Assistant Professor, Division of Biostatistics
Institution: Medical College of Wisconsin
Street: 8701 Watertown Plank Rd.
City: Milwaukee, WI
Authors: Brent R. Logan
Title: A cone order monotone version of the likelihood ratio test for comparing two treatments on multiple endpoints
Abstract: When comparing two treatments on multiple endpoints, oftentimes the researcher expects a one-sided treatment effect. Many likelihood ratio (LR) tests have been constructed to test the null hypothesis that a normal mean vector equals a null vector against the alternative that at least one of its components is positive. However, these tests have some unappealing properties, such as a non-monotone rejection region and potential lack of type I error rate control when there are negative treatment effects on some endpoints. A modification to the one-sided LR test for multiple endpoints is proposed that is cone order monotone (COM) with respect to the positive orthant alternative. This test has a monotone rejection region and maintains control of the type I error rate under all null configurations. It can be implemented within a closed test procedure to make inferences about individual endpoints while controlling the familywise error rate. The properties of this test are studied and compared to those of other competing tests of multiple endpoints, and an example is given to illustrate the use of the test. The COM test is then extended to the two-sided testing situation, where it maintains high power when the treatment has the same directional effect on each endpoint.