A key component of drug development is to establish the compound's dose-response relationship, and identify all effective doses of the drug with a general goal of selecting the minimum effective dose (MED). A new closed testing procedure is proposed for identifying the MED for a single component drug. This procedure is based on constructing simultaneous one-sided confidence bands for the response surface of each dose's effect relative to placebo. Our methodology utilizes a stepwise closed testing to test the ordered hypotheses of equality of mean dose-responses. The pattern of the rejected and accepted null hypotheses provides the estimate of the MED, if it exists.In the case of a combination drug, in addition to demonstrating safety and efficacy the FDA requires demonstrating that each component makes a contribution to the claimed effects. A combination which satisfies the last requirement is called an efficacious combination. In the most common case both single drugs are approved ones, and therefore, the efficacious combinations are effective, that is, they produce a therapeutic effect which is superior to placebo.We propose a closed testing procedure for estimating the minimum efficacious combinations (MeD's) in a two-drug study and introduce a notion of the MeD-set.The main advantage of a closed testing procedure is the strong control of the familywise error at level of significance á and allowing testing individual hypotheses at the same significance level á without multiplicity adjustments.The proposed procedure is based on two main steps. In the first step, all possible structures of the population MeD-set are identified and the related closed family of hypotheses is constructed, and the proper step-down testing partial order is established. The second step is the "á-testing" step. Using the closed testing principle, we test the hypotheses by constructing the AVE-test statistic. The pattern of the rejected null hypotheses identifies the MeD-set. In order to assess the performance of our procedure, we define several statistical measures. These notions are used in a large simulation study to examine the goodness of the estimation procedures and to identify the population configurations when the procedure performs the best.
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