Operating characteristics related to testing and estimation for the normal outcome simulation example. The extreme power loss and extreme sample size gain in a subsequent Phase III trial, are defined as the 80% quantile of the respective distributions induced by the data outcomes. The probability of an indeterminate outcome, the extreme power loss and extreme sample size gain are averaged with respect to the sampling prior |$N(0.25,1/50)$| truncated from below at |$\theta_R=0.15$|. The remaining operating characteristics are averaged with respect to the whole sampling prior distribution. The dashed vertical lines represent the sample sizes identified for cost elicitation with respect to the vague analysis prior, and, independently, for testing (upper panels, |$n^{\rm SATE}=160$|) and estimation (lower panels, |$n^{\rm AMSE}=180$|). Such sample sizes allow to maintain an average type I and type II error rate below 0.05 and 0.2, respectively, as well as an average probability of an indeterminate outcome, average extreme power loss and average extreme sample size gain below 0.1, 0.3, and approximately 50, respectively. Note that the informative prior results exactly overlap with the sampling prior ones.
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