Anscombe's Model for Sequential Clinical Trials Revisited
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In Anscombe's classical model, the objective is to find the optimal sequential rule for learning about the difference between two alternative treatments and subsequently selecting the superior one. The population for which the procedure is optimised has size N and includes both the patients in the trial and those which are treated with the chosen alternative after the trial. We review earlier work on this problem and give a detailed treatment of the problem itself. In particular, while previous work has mainly focused on the case of conjugate normal priors for the incremental effect, we demonstrate how to handle the problem for priors of a general form. We also discuss methods for numerical solutions and the practical implications of the results for the regulation of clinical trials. Two extensions of the model are proposed and analysed. The first breaks the symmetry of the treatments, giving one the role of the current standard being administered in parallel with the trial. We show how certain asymptotic results due to Chernoff can be adapted to this asymmetric case. The other extension assumes that N is a random variable instead of a known constant.
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