Outlier Detection in Mendelian Randomization

Abstract

Mendelian randomization (MR) uses genetic variants as instrumental variables to infer causal effects of exposures on an outcome. One key assumption of MR is that the genetic variants used as instrumental variables are independent of the outcome conditional on the risk factor and unobserved confounders. Violations of this assumption, that is, the effect of the instrumental variables on the outcome through a path other than the risk factor included in the model (which can be caused by pleiotropy), are common phenomena in human genetics. Genetic variants, which deviate from this assumption, appear as outliers to the MR model fit and can be detected by the general heterogeneity statistics proposed in the literature, which are known to suffer from overdispersion, that is, too many genetic variants are declared as false outliers. We propose a method that corrects for overdispersion of the heterogeneity statistics in uni- and multivariable MR analysis by making use of the estimated inflation factor to correctly remove outlying instruments and therefore account for pleiotropic effects. Our method is applicable to summary-level data.

Keywords: Mendelian randomization; instrumental variables; invalid instruments; outlier detection; pleiotropy.

FIGURE 1

Causal directed acyclic graph (DAG) for the univariable Mendelian randomization setting. Genetic variants are denoted as $G_i$ for $i\in 1,\dots ,n$, the set of confounders as $U$ and the causal effect of the risk factor $X$ on the outcome $Y$ being $\theta$. The red dashed lines represent the effect of the instrumental variable(s) on the outcome through paths other than the risk factor included in the model, for example, caused by pleiotropy.

FIGURE 2

Causal directed acyclic graph (DAG) for the multivariable Mendelian randomization setting. Genetic variants $G_i$ ($i\in 1\dots n$), set of confounders $U$ and causal effects of the risk factors $X_j$ ($j\in 1\dots d$) on the outcome $Y$ being ${\theta }_j$. The red dashed lines represent the effect of the instrumental variable(s) on the outcome through paths other than the risk factors included in the model, for example, caused by pleiotropy.

FIGURE 3

Violin plots for the bias of the causal effect estimates of ${\theta }_1$ (red), ${\theta }_2$ (green), and ${\theta }_3$ (blue) in the multivariate simulation setting (15% outliers) after outlier adjustment and for the full model.