Mendelian randomization with invalid instruments: effect ...
Mendelian randomization with invalid instruments: Egger regression and Weighted Median Approaches David Evans What is the problem?
Mendelian Randomization (MR) uses genetic variants to test for causal relationships between phenotypic exposures and disease-related outcomes Due to the proliferation of GWAS, it is increasingly common for MR analyses to use large numbers of genetic variants
Increased power but greater potential for pleiotropy Pleiotropic variants affect biological pathways other than the exposure under investigation and therefore can lead to biased causal estimates and false positives under the null Two Sample MR:
Single Variants Wald = Beta-GY BetaGX Causal estimate using Wald method: Two Sample MR: Multiple Variants Causal estimate using IVW
from summarised data: (Approximates TSLS) MR with direct pleiotropy . Single variant Wald estimate: Multiple variant
TSLS / IVW : Egger Regression: Central concept In Mendelian Randomization when multiple genetic variants are being used as IVs, Egger regression can: o Identify the presence of directional pleiotropy (biasing the IV estimate) o provide a less biased causal estimate
(in the presence of pleiotropy) InSIDE Assumption Relaxing MRs assumptions . W Example:
SNP outcome association ALL INVALID INSTRUMENTS INSIDE ASSUMPTION SATISFIED SNP exposure association InSIDE:
SNP outcome association Bias of ratio estimator SNP exposure association Egger regression: Intercept not constrained to zero Eggers test assesses whether the intercept term is
significantly different from zero. The estimated values of the intercept can be interpreted as the average pleiotropic effect across all genetic variants. An intercept term different from zero indicates directional pleiotropy SNP-Height SNP-Lung Function Height and lung function
SNP - Height Causal estimate IVW = 0.59 (95% CI: 0.50, 0.67 ) Egger = 0.58 (95% CI: 0.50, 0.67); intercept -0.001 p=0.5 BP and Coronary Disease FUNNEL PLOTS
Visual evidence for asymmetry BP and Coronary Disease FUNNEL PLOTS BP and Coronary Disease Scatter Plots Egger test for intercept p=0.2
Egger test for intercept p=0.054 BP and Coronary Disease FUNNEL PLOTS IVW= 0.054 logOR/mmHg p=4x10-6 Egger =0.015 logOR/mmHg p=0.6 IVW= 0.083 logOR/mmHg p=1x10-5
Egger =-0.024 logOR/mmHg p=0.7 Simple Median Method Order instrumental variables estimates and take the median Like all subsequent estimators it enjoys a 50% breakdown limit Weighted Median Method
^2 j ___ wj = 2 Yj wj ____ wj =
jwj Penalized Weighted Median Method ough the invalid IVs do not contribute directly to the median estimate, they do uence it in small samples Like all subsequent estimators it enjoys a 50% breakdown limit Penalized Weighted
Median Method One way of minimizing this problem is down-weighting the contribution to the analysis of genetic variants with heterogeneous ratio estimates Heterogeneity between estimates can be quantified by Cochranes Q statistic: ^ ^2 Q = jQj =jwj( j - )
The Q statistic has a chi-squared distribution on J 1 degrees of freedom under the null hypothesis of no heterogeneity Each individual component of Q has a chi-square distribution with 1 df. Bowden proposes using a one sided upper P value (denoted qj): wj* = wj min(1, 20qj) Penalized Weighted Median Method
References Mendelian randomization with invalid instruments : effect estimation and bias detection through Egg er regression. Bowden J, Davey Smith G, Burgess S. Int J Epidemiol. 2015 Apr;44(2):512-25. Consistent Estimation in Mendelian Randomizatio n with Some Invalid Instruments Using a Weighte d Median Estimator. Bowden J, Davey Smith G, Haycock
PC, Burgess S. Genet Epidemiol. 2016 May;40(4):304-14.
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