Leveraging family data to design Mendelian randomization that is provably robust to population stratification

Abstract

Mendelian randomization (MR) has emerged as a powerful approach to leverage genetic instruments to infer causality between pairs of traits in observational studies. However, the results of such studies are susceptible to biases owing to weak instruments, as well as the confounding effects of population stratification and horizontal pleiotropy. Here, we show that family data can be leveraged to design MR tests that are provably robust to confounding from population stratification, assortative mating, and dynastic effects. We show in simulations that our approach, MR-Twin, is robust to confounding from population stratification and is not affected by weak instrument bias, whereas standard MR methods yield inflated false positive rates. We then conduct an exploratory analysis of MR-Twin and other MR methods applied to 121 trait pairs in the UK Biobank data set. Our results suggest that confounding from population stratification can lead to false positives for existing MR methods, whereas MR-Twin is immune to this type of confounding, and that MR-Twin can help assess whether traditional approaches may be inflated owing to confounding from population stratification.

Figure 1.

Illustrations of Mendelian randomization (MR) assumptions and the MR-Twin framework. (A) Directed acyclic graph (DAG) depicting variables and their relationships in a typical MR study, where X is the genotypic instrument, E is the exposure trait, and O is the outcome trait. An external confounder Z, such as population stratification, can cause violations of the MR assumptions. (B) If we have the parental haplotypes A, then X is independent of Z given A. (C) Illustration of the MR-Twin workflow. Digital twin genotypes are sampled from the parental genotypes. MR-Twin is a conditional randomization test, conditioned on A and therefore immune to confounding from Z, in which the P-value is computed based on the quantile of the true offspring's MR-Twin statistic compared with the digital twins’ statistics.

Figure 2.

False-positive rate (FPR) and power comparison between various methods run on simulated data. (A) FPR (y-axis) under varying levels of confounding owing to population stratification (PS), with the x-axis describing the magnitude of the confounding effect of population labels on the exposure and outcome trait. (B) Power (y-axis) as a function of the magnitude of the causal effect of the exposure on the outcome trait (x-axis) in a setting with no confounding. Results are averaged over 1000 simulation replicates.

Figure 3.

FPR and power comparison between various methods run on simulated trio data. This is similar to Figure 2 except that IVW, Egger, Median, and Mode are run on the offspring of the trio data set instead of the large “external” group of unrelated individuals, such that all methods have the same sample size. (A) FPR (y-axis) under varying levels of confounding owing to population stratification (PS), with the x-axis describing the magnitude of the effect of the population labels on the exposure and outcome trait. (B) Power (y-axis) as a function of the causal effect size (x-axis). Results are averaged over 1000 simulation replicates.