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Meta-Analysis of Observational Studies with Unmeasured Confounders

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  • McCandless Lawrence C.

    (Simon Fraser University)

Abstract

Meta-analysis of observational studies is an exciting new area of innovation in statistical science. Unlike randomized controlled trials, which are the gold standard for proving causation, observational studies are prone to biases including confounding. In this article, we describe a novel Bayesian procedure to control for a confounder that is missing across the sequence of studies in a meta-analysis. We motivate the discussion with the example of a meta-analysis of cohort, case-control and cross-sectional studies examining the relationship between oral contraceptives and endometriosis. An important unmeasured confounder is dysmennoreah, which is an indication for oral contraceptive use. To adjust for unmeasured confounding, we combine random effects models with probabilistic sensitivity analysis techniques. Information about the unmeasured confounder is incorporated into the analysis via prior distributions, and we use MCMC to sample from posterior.

Suggested Citation

  • McCandless Lawrence C., 2012. "Meta-Analysis of Observational Studies with Unmeasured Confounders," The International Journal of Biostatistics, De Gruyter, vol. 8(2), pages 1-31, January.
    • Handle: RePEc:bpj:ijbist:v:8:y:2012:i:2:n:5
    DOI: 10.2202/1557-4679.1350
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    References listed on IDEAS

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    1. Sander Greenland, 2005. "Multiple‐bias modelling for analysis of observational data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(2), pages 267-306, March.
    2. Rebecca M. Turner & David J. Spiegelhalter & Gordon C. S. Smith & Simon G. Thompson, 2009. "Bias modelling in evidence synthesis," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(1), pages 21-47, January.
    3. N. J. Welton & A. E. Ades & J. B. Carlin & D. G. Altman & J. A. C. Sterne, 2009. "Models for potentially biased evidence in meta‐analysis using empirically based priors," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(1), pages 119-136, January.
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    2. Mathur, Maya B & VanderWeele, Tyler, 2018. "Statistical methods for evidence synthesis," Thesis Commons kd6ja, Center for Open Science.

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