Multivariable Mendelian randomization: the use of pleiotropic genetic variants to estimate causal effects

Abstract

A conventional Mendelian randomization analysis assesses the causal effect of a risk factor on an outcome by using genetic variants that are solely associated with the risk factor of interest as instrumental variables. However, in some cases, such as the case of triglyceride level as a risk factor for cardiovascular disease, it may be difficult to find a relevant genetic variant that is not also associated with related risk factors, such as other lipid fractions. Such a variant is known as pleiotropic. In this paper, we propose an extension of Mendelian randomization that uses multiple genetic variants associated with several measured risk factors to simultaneously estimate the causal effect of each of the risk factors on the outcome. This "multivariable Mendelian randomization" approach is similar to the simultaneous assessment of several treatments in a factorial randomized trial. In this paper, methods for estimating the causal effects are presented and compared using real and simulated data, and the assumptions necessary for a valid multivariable Mendelian randomization analysis are discussed. Subject to these assumptions, we demonstrate that triglyceride-related pathways have a causal effect on the risk of coronary heart disease independent of the effects of low-density lipoprotein cholesterol and high-density lipoprotein cholesterol.

Keywords: Mendelian randomization; causal inference; epidemiologic methods; instrumental variables; lipid fractions; pleiotropy.

Figure 1.

Mendelian randomization assumptions for variant G with risk factor X in a confounded association with outcome Y. Confounders represented by U are assumed to be unknown.

Figure 2.

Causal directed acyclic graph illustrating vertical (A) and functional (B) pleiotropy in associations between variant G, risk factors X₁ and X₂, and outcome Y.

Figure 3.

Causal directed acyclic graph illustrating multivariable Mendelian randomization in associations between variants G₁, G₂, and G₃, risk factors X₁ and X₂, and outcome Y. Confounders U₁ and U₂ are assumed to be unknown. A) Risk factors are causally independent (no causal effects between X₁ and X₂); B) risk factors are causally dependent (X₁ has a causal effect on X₂).

Figure 4.

Associations of coronary heart disease (CHD) risk-increasing alleles of 28 genetic variants with all possible pairings of low-density lipoprotein cholesterol (LDL-C), high-density lipoprotein cholesterol (HDL-C), and triglycerides. Darker points correspond to stronger associations with CHD risk; larger points correspond to more precise estimates. Note that some points are overlapping.

Figure 5.

Associations of coronary heart disease (CHD) risk-increasing alleles of 28 genetic variants with odds of CHD and with low-density lipoprotein cholesterol (LDL-C) (A), high-density lipoprotein cholesterol (HDL-C) (B), and triglycerides (C). Darker points correspond to stronger associations with CHD risk; larger points correspond to more precise estimates. Note that some points are overlapping.