New Methods for Eliminating Inferior Treatments in Clinical Trials
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Multiple comparisons and selection procedures are commonly studied in research and employed in application. Clinical trial is one of popular fields to which the subject of multiple comparisons is extensively applied. Based on the Federal Food, Drug, and Cosmetic Act, drug manufacturers need to not only demonstrate safety of their drug products but also establish effectiveness by substantial evidence in order to obtain marketing approval. However, the problem of error inflation occurs when there are more than two groups to compare with at the same time. How to design a test procedure with high power while controlling type I error becomes an important issue. The treatment with the largest population mean is considered to be the best one in the study. Potentially the best treatments can receive increased resources and further investigation by excluding clearly inferior treatments. Hence, a small number of possibly the best treatments is preferred. This thesis focuses on the problem of eliminating the less effective treatments among three in clinical trials. The goal is to increase the ability to identify any inferior treatment providing that the probability of excluding any best treatment is guaranteed to be less than or equal to alpha. A step-down procedure is applied to solve the problem. The general step-down procedure with fixed thresholds is conservative in our problem. The test is not efficient in rejecting the less effective treatments. We propose two methods with sharper thresholds to improve current procedures and construct a subset containing strictly inferior treatments. The first method, the restricted parameter space approach, is designed for the scenario when prior information about range of treatment means is known. The second method, the step-down procedure with feedback, utilizes observations to modify the threshold and controls error rate for the whole parameter space. The new procedures have greater ability to detect more inferior treatments than the standard procedure. In addition, type I error is also controlled under mild violation of the assumptions demonstrated by simulation.