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Optimising the trade‐off between type I and II error rates in the Bayesian context
Author(s) -
Walley Rosalind J.,
Grieve Andrew P.
Publication year - 2021
Publication title -
pharmaceutical statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 38
eISSN - 1539-1612
pISSN - 1539-1604
DOI - 10.1002/pst.2102
Subject(s) - frequentist inference , type i and type ii errors , bayesian probability , context (archaeology) , computer science , word error rate , statistics , econometrics , set (abstract data type) , bayes' theorem , bayesian inference , operations research , mathematics , artificial intelligence , paleontology , biology , programming language
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.