Adjustment for unmeasured confounding through informative priors for the confounder-outcome relation

Rolf H.H. Groenwold*, Inbal Shofty, Milica Miočević, Maarten Van Smeden, Irene Klugkist

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)


Background: Observational studies of medical interventions or risk factors are potentially biased by unmeasured confounding. In this paper we propose a Bayesian approach by defining an informative prior for the confounder-outcome relation, to reduce bias due to unmeasured confounding. This approach was motivated by the phenomenon that the presence of unmeasured confounding may be reflected in observed confounder-outcome relations being unexpected in terms of direction or magnitude. Methods: The approach was tested using simulation studies and was illustrated in an empirical example of the relation between LDL cholesterol levels and systolic blood pressure. In simulated data, a comparison of the estimated exposure-outcome relation was made between two frequentist multivariable linear regression models and three Bayesian multivariable linear regression models, which varied in the precision of the prior distributions. Simulated data contained information on a continuous exposure, a continuous outcome, and two continuous confounders (one considered measured one unmeasured), under various scenarios. Results: In various scenarios the proposed Bayesian analysis with an correctly specified informative prior for the confounder-outcome relation substantially reduced bias due to unmeasured confounding and was less biased than the frequentist model with covariate adjustment for one of the two confounding variables. Also, in general the MSE was smaller for the Bayesian model with informative prior, compared to the other models. Conclusions: As incorporating (informative) prior information for the confounder-outcome relation may reduce the bias due to unmeasured confounding, we consider this approach one of many possible sensitivity analyses of unmeasured confounding.

Original languageEnglish
Article number174
JournalBMC medical research methodology
Issue number1
Publication statusPublished - 22 Dec 2018


  • Bayesian statistics
  • Bias
  • Confounding
  • Sensitivity analysis


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