We present a theoretical basis for testing related endpoints. Typically, it is known how to construct tests of the individual hypotheses, and the problem is how to combine them into a multiple test procedure that controls the familywise error rate. Using the closure method, we emphasize the role of consonant procedures, from an interpretive as well as a theoretical viewpoint, and introduce a new procedure, which is consonant and has a maximin property under the normal model. The results are then applied to PROactive, a clinical trial designed
to investigate the effectiveness of a glucose-lowering drug on macrovascular outcomes among patients with type 2 diabetes.