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Power priors for replication studies


Pawel, Samuel; Aust, Frederik; Held, Leonhard; Wagenmakers, Eric-Jan (2024). Power priors for replication studies. Test, 33(1):127-154.

Abstract

The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study’s data is raised to the power of $\alpha $, and then used as the prior distribution in the analysis of the replication data. Posterior distribution and Bayes factor hypothesis tests related to the power parameter $\alpha $ quantify the degree of compatibility between the original and replication study. Inferences for other parameters, such as effect sizes, dynamically borrow information from the original study. The degree of borrowing depends on the conflict between the two studies. The practical value of the approach is illustrated on data from three replication studies, and the connection to hierarchical modeling approaches explored. We generalize the known connection between normal power priors and normal hierarchical models for fixed parameters and show that normal power prior inferences with a beta prior on the power parameter $\alpha $ align with normal hierarchical model inferences using a generalized beta prior on the relative heterogeneity variance $I^2$. The connection illustrates that power prior modeling is unnatural from the perspective of hierarchical modeling since it corresponds to specifying priors on a relative rather than an absolute heterogeneity scale.

Abstract

The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study’s data is raised to the power of $\alpha $, and then used as the prior distribution in the analysis of the replication data. Posterior distribution and Bayes factor hypothesis tests related to the power parameter $\alpha $ quantify the degree of compatibility between the original and replication study. Inferences for other parameters, such as effect sizes, dynamically borrow information from the original study. The degree of borrowing depends on the conflict between the two studies. The practical value of the approach is illustrated on data from three replication studies, and the connection to hierarchical modeling approaches explored. We generalize the known connection between normal power priors and normal hierarchical models for fixed parameters and show that normal power prior inferences with a beta prior on the power parameter $\alpha $ align with normal hierarchical model inferences using a generalized beta prior on the relative heterogeneity variance $I^2$. The connection illustrates that power prior modeling is unnatural from the perspective of hierarchical modeling since it corresponds to specifying priors on a relative rather than an absolute heterogeneity scale.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:04 Faculty of Medicine > Epidemiology, Biostatistics and Prevention Institute (EBPI)
Dewey Decimal Classification:610 Medicine & health
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Uncontrolled Keywords:Statistics, Probability and Uncertainty, Statistics and Probability
Language:English
Date:1 March 2024
Deposited On:16 Jan 2024 12:13
Last Modified:30 Jun 2024 01:37
Publisher:Springer
ISSN:1133-0686
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/s11749-023-00888-5
Project Information:
  • : FunderSNSF
  • : Grant ID189295
  • : Project TitleReverse-Bayes Design and Analysis of Replication Studies
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)