We consider a multi-arm trial with two or more active treatments plus a control where it is reasonable to assume an order for the treatment effects of the active arms compared to control. For example, the arms could be a high dose and low dose of a new drug and a placebo. The objective of the trial is to compare each active arm to control while maintaining strong control of the type 1 error rate. We show that when the study is powered to identify all promising treatments, a design that uses the order of the treatment effects to calculate the test statistic and to set the order of testing requires a smaller sample size than a design where each active arm is tested against the control arm independently. Under the considered settings, the sample size for a single-stage trial and a two-stage trial was reduced by at least 20%.
Keywords: Williams' test; isotonic estimation; multi-arm multi-stage; order restricted inference.
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