Abstract
In some clinical trials, more than one primary endpoints are used for efficacy evaluation, and the drug is considered efficacious as long as a large enough subset of the endpoints meet some 'success' criteria. In this paper, we study the type I error rate and power under this subset decision rule. We demonstrate that the type I error rate can be inflated when each endpoint is tested at the nominal level. Particularly, when the endpoints are conditionally unbiased, this inflation is maximized when the number of endpoints that truly carry the drug effect is exactly one less than that in the subset. We study two methods in adjusting the type I error rate: modified Bonferroni method and Hochberg method. With mutually independent endpoints, when the number of endpoints in the subset is pre-fixed (due to the requirement of regulatory agency or a established criteria), we recommend that the total number of endpoints specified should be as close as possible to that of the subset to avoid excessive loss in power with adjustment procedures. Discussion for the situation of correlated endpoints and improvement for decision rule are also provided.