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Abstract:
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In a previous paper, I proposed a decision model to explicitly harness loss in clinical trial design (e.g., in choosing the optimal minimum detectable difference d for superiority or noninferiority). This approach requires knowledge of P(H0), or a P(H0) that can be described in terms of d, since P(H0) is otherwise meaningless in a frequentist sense. Bayesian inference relies on P(H0) and P(H1); a loss-based decision approach is therefore a natural fit in Bayesian study design. This paper considers a loss based decision model for Bayesian clinical study design. In this model, action (i.e., rejecting or accepting H0) is taken based on Bayesian inference and the losses incurred from the decision. Simple cases with parameters having conjugated priors are studied in deriving optimal decisions in hypothesis testing. Actions based on posterior probability and Bayes factor are also examined.
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