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. 2017 May 20;36(11):1783-1802.
doi: 10.1002/sim.7221. Epub 2017 Jan 23.

A framework for the investigation of pleiotropy in two-sample summary data Mendelian randomization

Jack Bowden  1 , Fabiola Del Greco M  2 , Cosetta Minelli  3 , George Davey Smith  1 , Nuala Sheehan  4 , John Thompson  4
Affiliations

A framework for the investigation of pleiotropy in two-sample summary data Mendelian randomization

Jack Bowden et al. Stat Med. .

Abstract

Mendelian randomization (MR) uses genetic data to probe questions of causality in epidemiological research, by invoking the Instrumental Variable (IV) assumptions. In recent years, it has become commonplace to attempt MR analyses by synthesising summary data estimates of genetic association gleaned from large and independent study populations. This is referred to as two-sample summary data MR. Unfortunately, due to the sheer number of variants that can be easily included into summary data MR analyses, it is increasingly likely that some do not meet the IV assumptions due to pleiotropy. There is a pressing need to develop methods that can both detect and correct for pleiotropy, in order to preserve the validity of the MR approach in this context. In this paper, we aim to clarify how established methods of meta-regression and random effects modelling from mainstream meta-analysis are being adapted to perform this task. Specifically, we focus on two contrastin g approaches: the Inverse Variance Weighted (IVW) method which assumes in its simplest form that all genetic variants are valid IVs, and the method of MR-Egger regression that allows all variants to violate the IV assumptions, albeit in a specific way. We investigate the ability of two popular random effects models to provide robustness to pleiotropy under the IVW approach, and propose statistics to quantify the relative goodness-of-fit of the IVW approach over MR-Egger regression. © 2017 The Authors. Statistics in Medicine Published by JohnWiley & Sons Ltd.

Keywords: MR-Egger regression; Mendelian randomization; instrumental variables; meta-analysis; pleiotropy.

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Figures

Figure 1
Figure 1
Illustrative diagram showing the hypothesised causal relationship between a genetic variable G j, environmental exposure X and outcome Y.
Figure 2
Figure 2
Illustrative diagram showing the causal and parametric relationships between genetic variable G j, X and Y. Solid lines on their own define G j as a valid IV, but the addition of dashed lines indicate violations of the IV assumptions.
Figure 3
Figure 3
Scatter plot of SNP‐outcome versus SNP‐exposure estimates for four fictional MR analyses. Left: under cases (a) (solid black dots) and (b) (hollow black dots). Right: under cases (c) (solid black dots) and (d) (hollow black dots).
Figure 4
Figure 4
Left: Scatter plot of γ + 0 × ψ versus α + 0 × ψ parameters, where α and γ are generated to satisfy Perfect InSIDE. Right: Scatter plot of γ + 3 × ψ versus α + 3 × ψ.
Figure 5
Figure 5
Theoretical bias in the MR‐Egger estimand β 1E (blue) and IVW estimand β IVW (red) as a function of InSIDE violation via ρ A for directional pleiotropy (left) and balanced pleiotropy (right). [Colour figure can be viewed at wileyonlinelibrary.com]
Figure 6
Figure 6
Top: Theoretical bias of the fixed effect estimand β IVW (red solid line) and additive random effect estimand βIVWARE (red dashed line) as a function of InSIDE violation in the case of directional pleiotropy (left) and balanced pleiotropy (right). Bottom: Funnel plots of the inverse standard errors versus their causal estimands β j at ρ=0 and σ Y = 0.3 for directional pleiotropy (left) and balanced pleiotropy (right). [Colour figure can be viewed at wileyonlinelibrary.com]
Figure 7
Figure 7
Left: scatter plot of the summary data estimates for the lipids data, with the IVW and MR‐Egger slope estimates. Right: corresponding funnel plot of the same data. ARE = additive random effects estimate β^IVWARE, MRE = fixed effect/multiplicative random effects estimate β^IVW.
Figure 8
Figure 8
SIMEX adjustment applied to the IVW (left) and MR‐Egger (right) causal effect estimate. [Colour figure can be viewed at wileyonlinelibrary.com]
Figure A.1
Figure A.1
Theoretical bias of the MR‐Egger estimand using the parameter values of Table A1, as the number of included SNPs is increased sequentially from 1:2 to 1:50. Note: the parameters of Table A1 are generated independently so that General InSIDE is satisfied under IV2 for any subset of the 50 SNPs, but that Perfect InSIDE is satisfied when all 50 are considered.
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