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A Bayesian approach to Mendelian randomization with multiple pleiotropic variants.

Authors
  • Berzuini, Carlo1
  • Guo, Hui1
  • Burgess, Stephen2
  • Bernardinelli, Luisa3
  • 1 Centre for Biostatistics, The University of Manchester, Jean McFarlane Building, University Place, Oxford Road, Manchester M13 9PL, UK.
  • 2 Department of Public Health and Primary Care, University of Cambridge, Cambridge, UK and MRC Biostatistics Unit, University of Cambridge, Cambridge, UK.
  • 3 Department of Brain and Behavioral Sciences, University of Pavia, Pavia, Italy. , (Italy)
Type
Published Article
Journal
Biostatistics (Oxford, England)
Publication Date
Jan 01, 2020
Volume
21
Issue
1
Pages
86–101
Identifiers
DOI: 10.1093/biostatistics/kxy027
PMID: 30084873
Source
Medline
Keywords
Language
English
License
Unknown

Abstract

We propose a Bayesian approach to Mendelian randomization (MR), where instruments are allowed to exert pleiotropic (i.e. not mediated by the exposure) effects on the outcome. By having these effects represented in the model by unknown parameters, and by imposing a shrinkage prior distribution that assumes an unspecified subset of the effects to be zero, we obtain a proper posterior distribution for the causal effect of interest. This posterior can be sampled via Markov chain Monte Carlo methods of inference to obtain point and interval estimates. The model priors require a minimal input from the user. We explore the performance of our method by means of a simulation experiment. Our results show that the method is reasonably robust to the presence of directional pleiotropy and moderate correlation between the instruments. One section of the article elaborates the model to deal with two exposures, and illustrates the possibility of using MR to estimate direct and indirect effects in this situation. A main objective of the article is to create a basis for developments in MR that exploit the potential offered by a Bayesian approach to the problem, in relation with the possibility of incorporating external information in the prior, handling multiple sources of uncertainty, and flexibly elaborating the basic model. © The Author 2018. Published by Oxford University Press.

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