Journal
PHARMACEUTICAL STATISTICS
Volume 20, Issue 4, Pages 710-720Publisher
WILEY
DOI: 10.1002/pst.2102
Keywords
Bayesian; decision criteria; design prior; pre‐ posterior distribution; trial design; type I error
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For any decision-making study, it is important to consider the trade-off between type I and II error rates, as well as the context and prior beliefs of the study. When resources are limited, optimizing this trade-off becomes crucial, especially in the case of planned Bayesian statistical analysis.
For any decision-making study, there are two sorts of errors that can be made, declaring a positive result when the truth is negative, and declaring a negative result when the truth is positive. Traditionally, the primary analysis of a study is a two-sided hypothesis test, the type I error rate will be set to 5% and the study is designed to give suitably low type II error - typically 10 or 20% - to detect a given effect size. These values are standard, arbitrary and, other than the choice between 10 and 20%, do not reflect the context of the study, such as the relative costs of making type I and II errors and the prior belief the drug will be placebo-like. Several authors have challenged this paradigm, typically for the scenario where the planned analysis is frequentist. When resource is limited, there will always be a trade-off between the type I and II error rates, and this article explores optimising this trade-off for a study with a planned Bayesian statistical analysis. This work provides a scientific basis for a discussion between stakeholders as to what type I and II error rates may be appropriate and some algebraic results for normally distributed data.
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