Mendelian randomization incorporating uncertainty about pleiotropy

John R. Thompson*, Cosetta Minelli, Jack Bowden, Fabiola M. Del Greco, Dipender Gill, Elinor M. Jones, Chin Yang Shapland, Nuala A. Sheehan

*Corresponding author for this work

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

29 Citations (Scopus)
260 Downloads (Pure)


Mendelian randomization (MR) requires strong assumptions about the genetic instruments, of which the most difficult to justify relate to pleiotropy. In a two-sample MR, different methods of analysis are available if we are able to assume, M1: no pleiotropy (fixed effects meta-analysis), M2: that there may be pleiotropy but that the average pleiotropic effect is zero (random effects meta-analysis), and M3: that the average pleiotropic effect is nonzero (MR-Egger). In the latter 2 cases, we also require that the size of the pleiotropy is independent of the size of the effect on the exposure. Selecting one of these models without good reason would run the risk of misrepresenting the evidence for causality. The most conservative strategy would be to use M3 in all analyses as this makes the weakest assumptions, but such an analysis gives much less precise estimates and so should be avoided whenever stronger assumptions are credible. We consider the situation of a two-sample design when we are unsure which of these 3 pleiotropy models is appropriate. The analysis is placed within a Bayesian framework and Bayesian model averaging is used. We demonstrate that even large samples of the scale used in genome-wide meta-analysis may be insufficient to distinguish the pleiotropy models based on the data alone. Our simulations show that Bayesian model averaging provides a reasonable trade-off between bias and precision. Bayesian model averaging is recommended whenever there is uncertainty about the nature of the pleiotropy.

Original languageEnglish
Pages (from-to)4627-4645
Number of pages19
JournalStatistics in Medicine
Issue number29
Early online date28 Aug 2017
Publication statusPublished - 20 Dec 2017

Bibliographical note

Accepted manuscript in publisher's template.


  • Bayesian model averaging
  • Mendelian randomization
  • meta-analysis
  • MR-Egger
  • pleiotropy


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