The Application Of Edgeworth Expansion In Optimal Clinical Trial Sample Sizes

Abstract

Consider designing an r-stage clinical trial. There are two available treatments and N exchangeable patients to be treated as effectively as possible. The stages may be viewed as separate trials. Responses are dichotomous. The problem is to decide how large each stage should be and how many patients should be assigned to each treatment during each stage. Information is updated during after each stage using Bayes' theorem. In planning stage j, responses from selections in stages 1 to j-1 are available but responses in stage j are not. We consider r=2 for two situations, when one arm is known and when both arms are unknown. The dominant term for the length of the first stage in an optimal design for general Nis found explicitly. In both situations the order of magnitude of the length of the first stage is square root of N.