Avoiding dynastic, assortative mating, and population stratification biases in Mendelian randomization through within-family analyses

Abstract

Estimates from Mendelian randomization studies of unrelated individuals can be biased due to uncontrolled confounding from familial effects. Here we describe methods for within-family Mendelian randomization analyses and use simulation studies to show that family-based analyses can reduce such biases. We illustrate empirically how familial effects can affect estimates using data from 61,008 siblings from the Nord-Trøndelag Health Study and UK Biobank and replicated our findings using 222,368 siblings from 23andMe. Both Mendelian randomization estimates using unrelated individuals and within family methods reproduced established effects of lower BMI reducing risk of diabetes and high blood pressure. However, while Mendelian randomization estimates from samples of unrelated individuals suggested that taller height and lower BMI increase educational attainment, these effects were strongly attenuated in within-family Mendelian randomization analyses. Our findings indicate the necessity of controlling for population structure and familial effects in Mendelian randomization studies.

Fig. 1. Directed acyclic graphs illustrating how population structure and familial effects can cause confound MR studies.

Black arrows indicate causal paths in the index individual, red arrows indicate causal paths in the parents, and dashed red arrows indicate confounding paths. The MR estimate of the causal effect of the exposure on the outcome is biased because of potentially unobserved confounders between the SNPs and the exposure and the outcome. a Illustrates how population demography and structure can confound the SNP-outcome association. b Illustrates how dynastic effects can induce the same statistical confounding structure of the SNP-outcome association through an entirely different mechanism. The solid red vertical arrow indicates the genetic inheritance of germline DNA. The dotted line indicates the direct (dynastic) effect of the parents on the offspring’s outcomes. These can either be mediated via the exposure, the outcome or some other mechanism indicated by the direct arrow from SNP to offspring outcome. MR estimates of the effect of the exposure on the outcome in samples of unrelated individuals will be biased because there is a path between offspring SNP and the outcome via the effect of the parents’ phenotypes on their offspring’s outcomes (dynastic effects). The presence of dynastic effects would violate one of three key MR (instrumental variable) assumptions—the independence assumption. Estimates that control for mother or father genotype, or sibling genotype will close this path and be unbiased. c Illustrates how assortative mating is a third mechanism that can confound the SNP-outcome association. In this example we present cross-trait assortative mating where there is a pathway between the mother’s genotype and offspring’s outcome via the father’s genotype for the outcome. All these forms of SNP-trait confounding can be accounted for by using methods based on within-family contrasts.

Fig. 2. Results of simulations comparing different Mendelian randomization study designs for power and bias.

a SNP-exposure r² = 0.05; sample size = 10000 singletons, sibs, or trios; simulation involves an influence of parental exposure influencing child’s confounder, which explains 10% of variance in child exposures and outcomes. For a simulated causal effect = 0, we expect the false discovery rate to be 0.05. b Estimated bias by sample size using different Mendelian randomization designs. The simulations are similar to a but allow sample size to vary and fixing the causal effect of an exposure x on an outcome y to 1% of variance explained. The bias in within-family Mendelian randomization estimates is slightly elevated when sample sizes are small due to weak instrument bias, but are otherwise are protected from the large bias seen when using unrelated samples.

Fig. 3. Estimates of the effect of BMI on self-reported diabetes and high blood pressure and height and BMI on educational attainment using ordinary least squares, Mendelian randomization in unrelated individuals and samples of siblings, point estimates and 95% confidence intervals reported.

All methods were consistent with higher BMI increasing diabetes and high blood pressure risk. Being taller and having lower BMI were observationally associated with higher educational attainment. The effects of height and BMI on educational attainment were attenuated but still apparent when using Mendelian randomization estimates based on unrelated individuals from HUNT and UK Biobank. The effects were eliminated after allowing for a family effect using individual-level or summary data Mendelian randomization.