Testing for non-linear causal effects using a binary genotype in a Mendelian randomization study: application to alcohol and cardiovascular traits

Abstract

Background: Mendelian randomization studies have so far restricted attention to linear associations relating the genetic instrument to the exposure, and the exposure to the outcome. In some cases, however, observational data suggest a non-linear association between exposure and outcome. For example, alcohol consumption is consistently reported as having a U-shaped association with cardiovascular events. In principle, Mendelian randomization could address concerns that the apparent protective effect of light-to-moderate drinking might reflect 'sick-quitters' and confounding.

Methods: The Alcohol-ADH1B Consortium was established to study the causal effects of alcohol consumption on cardiovascular events and biomarkers, using the single nucleotide polymorphism rs1229984 in ADH1B as a genetic instrument. To assess non-linear causal effects in this study, we propose a novel method based on estimating local average treatment effects for discrete levels of the exposure range, then testing for a linear trend in those effects. Our method requires an assumption that the instrument has the same effect on exposure in all individuals. We conduct simulations examining the robustness of the method to violations of this assumption, and apply the method to the Alcohol-ADH1B Consortium data.

Results: Our method gave a conservative test for non-linearity under realistic violations of the key assumption. We found evidence for a non-linear causal effect of alcohol intake on several cardiovascular traits.

Conclusions: We believe our method is useful for inferring departure from linearity when only a binary instrument is available. We estimated non-linear causal effects of alcohol intake which could not have been estimated through standard instrumental variable approaches.

Keywords: Mendelian randomization; alcohol consumption; cardiovascular disease; causal inference; instrumental variables; local average treatment effects.

Figure 1.

Directed acyclic graphs encoding a) the standard Mendelian randomization assumptions: (i) G is associated with X, (ii) G is not associated with confounders U of the X-Y association, and (iii) G affects Y only via its association with X; (b) how these assumptions are affected by the discretization of X in the proposed non-linear Mendelian randomization approach.

Figure 2.

Local average treatment effects (LATEs) of log(weekly units of alcohol + 1) on systolic blood pressure. Circular markers are LATEs; bars are 95% pointwise confidence intervals; dashed line is estimated mean LATE; solid line is estimated linear LATE trend; dotted line is linear IV estimate using the ratio method (virtually indistinguishable from the estimated mean LATE).

Figure 3.

Predicted difference in non high-density lipoprotein cholesterol (non-HDL-C) relative to zero alcohol consumption across the range of values of observed alcohol consumption, with estimated optimal level of alcohol consumption (3.2 (95% confidence interval (CI): 0.7, 6.0) units/week), estimated difference in non-HDL-C relative to zero alcohol consumption at optimal level (−0.39 (95% CI: −0.85, −0.03) mmol/l), and estimated level of alcohol consumption with the same level of non-HDL-C as at zero (16.9 (95% CI: 2.1, 48.2) units/week) indicated.