Bayesian variable selection with a pleiotropic loss function in Mendelian randomization

Apostolos Gkatzionis*, Stephen Burgess, David V Conti, Paul J. Newcombe

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

Mendelian randomization is the use of genetic variants as instruments to assess the existence of a causal relationship between a risk factor and an outcome. A Mendelian randomization analysis requires a set of genetic variants that are strongly associated with the risk factor and only associated with the outcome through their effect on the risk factor. We describe a novel variable selection algorithm for Mendelian randomization that can identify sets of genetic variants which are suitable in both these respects. Our algorithm is applicable in the context of two-sample summary-data Mendelian randomization and employs a recently proposed theoretical extension of the traditional Bayesian statistics framework, including a loss function to penalize genetic variants that exhibit pleiotropic effects. The algorithm offers robust inference through the use of model averaging, as we illustrate by running it on a range of simulation scenarios and comparing it against established pleiotropy-robust Mendelian randomization methods. In a real-data application, we study the effect of systolic and diastolic blood pressure on the risk of suffering from coronary heart disease (CHD). Based on a recent large-scale GWAS for blood pressure, we use 395 genetic variants for systolic and 391 variants for diastolic blood pressure. Both traits are shown to have significant risk-increasing effects on CHD risk.
Original languageEnglish
Pages (from-to)5025-5045
Number of pages21
JournalStatistics in Medicine
Volume40
Issue number23
Early online date21 Jun 2021
DOIs
Publication statusPublished - 15 Oct 2021

Bibliographical note

Funding Information:
This work was supported by the UK Medical Research Council (Core Medical Research Council Biostatistics Unit Funding Code: MC UU 00002/7). Apostolos Gkatzionis and Paul Newcombe were supported by a Medical Research Council Methodology Research Panel grant (Grant Number RG88311). Paul Newcombe also acknowledges support from the NIHR Cambridge Biomedical Research Centre. Stephen Burgess was supported by a Sir Henry Dale Fellowship jointly funded by the Welcome Trust and the Royal Society (Grant Number 204623/Z/16/Z). David Conti was supported by a grant from the National Cancer Institute (Grant Number NIH/NCI P01CA196569). Finally, Apostolos Gkatzionis worked on editing the article during the review process while being employed by the Integrative Epidemiology Unit, which receives funding from the UK Medical Research Council and the University of Bristol (MC UU 00,011/3).

Funding Information:
information Medical Research Council, MC UU 00002/7; MC UU 00011/3; RG88311; National Cancer Institute, NIH/NCI P01CA196569; Wellcome Trust, 204623/Z/16/ZThis work was supported by the UK Medical Research Council (Core Medical Research Council Biostatistics Unit Funding Code: MC UU 00002/7). Apostolos Gkatzionis and Paul Newcombe were supported by a Medical Research Council Methodology Research Panel grant (Grant Number RG88311). Paul Newcombe also acknowledges support from the NIHR Cambridge Biomedical Research Centre. Stephen Burgess was supported by a Sir Henry Dale Fellowship jointly funded by the Welcome Trust and the Royal Society (Grant Number 204623/Z/16/Z). David Conti was supported by a grant from the National Cancer Institute (Grant Number NIH/NCI P01CA196569). Finally, Apostolos Gkatzionis worked on editing the article during the review process while being employed by the Integrative Epidemiology Unit, which receives funding from the UK Medical Research Council and the University of Bristol (MC UU 00,011/3).

Publisher Copyright:
© 2021 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Keywords

  • Mendelian Randomization
  • Instrumental Variable Analysis
  • Variable Selection
  • General Bayesian Inference
  • Pleiotropy

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