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Sensitivity and identification quantification by a relative latent model complexity perturbation in Bayesian meta‐analysis


Roos, Malgorzata; Hunanyan, Sona; Bakka, Haakon; Rue, Håvard (2021). Sensitivity and identification quantification by a relative latent model complexity perturbation in Bayesian meta‐analysis. Biometrical Journal, 63(8):1555-1574.

Abstract

In recent years, Bayesian meta-analysis expressed by a normal-normal hierarchical model (NNHM) has been widely used for combining evidence from multiple studies. Data provided for the NNHM are frequently based on a small number of studies and on uncertain within-study standard deviation values. Despite the widespread use of Bayesian NNHM, it has always been unclear to what extent the posterior inference is impacted by the heterogeneity prior (sensitivity S ) and by the uncertainty in the within-study standard deviation values (identification I ). Thus, to answer this question, we developed a unified method to simultaneously quantify both sensitivity and identification ( S - I ) for all model parameters in a Bayesian NNHM, based on derivatives of the Bhattacharyya coefficient with respect to relative latent model complexity (RLMC) perturbations. Three case studies exemplify the applicability of the method proposed: historical data for a conventional therapy, data from which one large study is first included and then excluded, and two subgroup meta-analyses specified by their randomization status. We analyzed six scenarios, crossing three RLMC targets with two heterogeneity priors (half-normal, half-Cauchy). The results show that S - I explicitly reveals which parameters are affected by the heterogeneity prior and by the uncertainty in the within-study standard deviation values. In addition, we compare the impact of both heterogeneity priors and quantify how S - I values are affected by omitting one large study and by the randomization status. Finally, the range of applicability of S - I is extended to Bayesian NtHM. A dedicated R package facilitates automatic S - I quantification in applied Bayesian meta-analyses.

Keywords: Bayesian meta-analysis; formal sensitivity and identification diagnostics; normal-normal hierarchical model; normal-t hierarchical model; relative latent model complexity

Abstract

In recent years, Bayesian meta-analysis expressed by a normal-normal hierarchical model (NNHM) has been widely used for combining evidence from multiple studies. Data provided for the NNHM are frequently based on a small number of studies and on uncertain within-study standard deviation values. Despite the widespread use of Bayesian NNHM, it has always been unclear to what extent the posterior inference is impacted by the heterogeneity prior (sensitivity S ) and by the uncertainty in the within-study standard deviation values (identification I ). Thus, to answer this question, we developed a unified method to simultaneously quantify both sensitivity and identification ( S - I ) for all model parameters in a Bayesian NNHM, based on derivatives of the Bhattacharyya coefficient with respect to relative latent model complexity (RLMC) perturbations. Three case studies exemplify the applicability of the method proposed: historical data for a conventional therapy, data from which one large study is first included and then excluded, and two subgroup meta-analyses specified by their randomization status. We analyzed six scenarios, crossing three RLMC targets with two heterogeneity priors (half-normal, half-Cauchy). The results show that S - I explicitly reveals which parameters are affected by the heterogeneity prior and by the uncertainty in the within-study standard deviation values. In addition, we compare the impact of both heterogeneity priors and quantify how S - I values are affected by omitting one large study and by the randomization status. Finally, the range of applicability of S - I is extended to Bayesian NtHM. A dedicated R package facilitates automatic S - I quantification in applied Bayesian meta-analyses.

Keywords: Bayesian meta-analysis; formal sensitivity and identification diagnostics; normal-normal hierarchical model; normal-t hierarchical model; relative latent model complexity

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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, General Medicine, Statistics and Probability
Language:English
Date:1 December 2021
Deposited On:29 Dec 2021 13:47
Last Modified:26 Jun 2024 01:47
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:0323-3847
OA Status:Hybrid
Free access at:PubMed ID. An embargo period may apply.
Publisher DOI:https://doi.org/10.1002/bimj.202000193
PubMed ID:34378223
Project Information:
  • : FunderSNSF
  • : Grant ID200021_175933
  • : Project TitleSEDA: Sensitivity diagnostics for Bayesian hierarchical models
  • Content: Published Version
  • Licence: Creative Commons: Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)