Widespread genetic effect heterogeneity impacts bias and power in nonlinear Mendelian randomization

1Mendelian randomization (MR) uses genetic variants as instrumental variables to infer causal relationships between complex traits. Standard MR can be used to estimate an average causal effect at the population level, and typically assumes a linear exposure-outcome relationship. Recently, several methods for estimating nonlinear effects have been developed. However, many have been found to produce spurious empirical findings when subjected to negative control analyses. We propose that this poor performance may be attributable to heterogeneity in variant-exposure associations. We demonstrate that heterogeneous genetic effects on exposure lead to biased estimates, poor coverage, and inflated type I error in control function and stratification-based methods. In contrast, two-stage least squares (TSLS) methods are robust to such heterogeneity, but suffer from low precision and low power in some circumstances. We show that a statistical test for heterogeneity can be used to guide the choice of nonlinear MR methods. Using UK Biobank data, we reassess the causal effects of BMI, vitamin D, and alcohol consumption on blood pressure, lipid, C-reactive protein, and age (negative control). We find strong evidence of heterogeneity for all three exposures, and also recapitulate previous results that control function and stratification-based methods are prone to false positives. Finally, using nonparametric TSLS, we identify evidence of nonlinear causal effects of BMI on HDL cholesterol, triglycerides, and C-reactive protein; however, specific estimates of the shape of these relationships are imprecise. Altogether, our results suggest that common nonlinear MR methods are unreliable in the presence of realistic levels of heterogeneity, and that more methodological development is required before practically useful nonlinear MR is feasible.