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Sensitivity Analysis for Unmeasured Confounding in Meta-Analyses

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  • Maya B. Mathur
  • Tyler J. VanderWeele

Abstract

Random-effects meta-analyses of observational studies can produce biased estimates if the synthesized studies are subject to unmeasured confounding. We propose sensitivity analyses quantifying the extent to which unmeasured confounding of specified magnitude could reduce to below a certain threshold the proportion of true effect sizes that are scientifically meaningful. We also develop converse methods to estimate the strength of confounding capable of reducing the proportion of scientifically meaningful true effects to below a chosen threshold. These methods apply when a “bias factor” is assumed to be normally distributed across studies or is assessed across a range of fixed values. Our estimators are derived using recently proposed sharp bounds on confounding bias within a single study that do not make assumptions regarding the unmeasured confounders themselves or the functional form of their relationships with the exposure and outcome of interest. We provide an R package, EValue, and a free website that compute point estimates and inference and produce plots for conducting such sensitivity analyses. These methods facilitate principled use of random-effects meta-analyses of observational studies to assess the strength of causal evidence for a hypothesis. Supplementary materials for this article are available online.

Suggested Citation

  • Maya B. Mathur & Tyler J. VanderWeele, 2020. "Sensitivity Analysis for Unmeasured Confounding in Meta-Analyses," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 163-172, January.
  • Handle: RePEc:taf:jnlasa:v:115:y:2020:i:529:p:163-172
    DOI: 10.1080/01621459.2018.1529598
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    Cited by:

    1. João Botelho & Paulo Mascarenhas & João Viana & Luís Proença & Marco Orlandi & Yago Leira & Leandro Chambrone & José João Mendes & Vanessa Machado, 2022. "An umbrella review of the evidence linking oral health and systemic noncommunicable diseases," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    2. Mathur, Maya B & VanderWeele, Tyler, 2021. "Methods to address confounding and other biases in meta-analyses: Review and recommendations," OSF Preprints v7dtq, Center for Open Science.

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