Article
An approach to robustification of Bayesian test decisions though test error cost elicitation
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Authors
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Silvia Calderazzo
- German Cancer Research Center, Heidelberg, Germany
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Manuel Wiesenfarth
- German Cancer Research Center, Heidelberg, Germany
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Annette Kopp-Schneider
- German Cancer Research Center, Heidelberg, Germany
| Published: | February 26, 2021 |
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Outline
Text
Background: Bayesian clinical trials allow making use of external information through the elicitation of prior distributions. The impact of prior specification on frequentist (conditional) test error rates is generally investigated at the trial design stage. However, as power gains are typically not possible when requiring strict type I error rate control, even in case dynamic borrowing mechanisms are adopted [1], it is of interest to investigate principled approaches to relax such requirement when borrowing is desired.
Methods: The objective of this work is to investigate rationales for inflation of conditional type I error rate from a decision-theoretic standpoint. In particular, we aim to robustly incorporate prior beliefs, e.g. from a historical trial, about the plausibility of the null and alternative hypotheses, while also explicitly controlling for an (inflated) type I error rate.
Results: We build on the known duality between test error costs and prior probabilities [2], [3] to this aim. A compromise between frequentist test decisions at a canonical type I error rate level and decisions under an informative prior distribution, is obtained by progressively incorporating prior knowledge in the definition of the posterior test decision threshold when performing the analysis under a minimally informative prior. We analytically highlight the strict connection between the proposed method, the restricted Bayes approach [3], and the robust mixture prior approach [4], and when equivalence is achieved. This is also graphically illustrated via simulations for normal and binomial outcomes.
Conclusion: We obtain a closed-form relationship between a pre-specified (inflated) target conditional type I error rate and the weight assigned to prior information, which can be straightforwardly exploited to robustly incorporate prior information in test decisions. The approach can also be applied to perform sample size selection and sensitivity analyses.
The authors declare that they have no competing interests.
The authors declare that an ethics committee vote is not required.
References
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- Kopp-Schneider A, Calderazzo S, Wiesenfarth M. Power gains by using external information in clinical trials are typically not possible when requiring strict type I error control. Biometrical Journal. 2020 Mar;62(2):361-374.
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- Berger J, Berliner LM. Robust Bayes and Empirical Bayes Analysis with ε-Contaminated Priors. Ann Statist. 1986;14(2):461-486.
