Polynomial Mendelian randomization reveals non-linear causal effects for obesity-related traits

Causal inference is a critical step in improving our understanding of biological processes, and Mendelian randomization (MR) has emerged as one of the foremost methods to efficiently interrogate diverse hypotheses using large-scale, observational data from biobanks. Although many extensions have been developed to address the three core assumptions of MR-based causal inference (relevance, exclusion restriction, and exchangeability), most approaches implicitly assume that any putative causal effect is linear. Here, we propose PolyMR, an MR-based method that provides a polynomial approximation of an (arbitrary) causal function between an exposure and an outcome. We show that this method provides accurate inference of the shape and magnitude of causal functions with greater accuracy than existing methods. We applied this method to data from the UK Biobank, testing for effects between anthropometric traits and continuous health-related phenotypes, and found most of these (84%) to have causal effects that deviate significantly from linear. These deviations ranged from slight attenuation at the extremes of the exposure distribution, to large changes in the magnitude of the effect across the range of the exposure (e.g., a 1 kg/m(2) change in BMI having stronger effects on glucose levels if the initial BMI was higher), to non-monotonic causal relationships (e.g., the effects of BMI on cholesterol forming an inverted U shape). Finally, we show that the linearity assumption of the causal effect may lead to the misinterpretation of health risks at the individual level or heterogeneous effect estimates when using cohorts with differing average exposure levels.

Automated summary

Causal inference is crucial for understanding biological processes. Mendelian randomization (MR) has become a leading method for investigating hypotheses using observational data from biobanks. However, most MR methods assume that potential causal effects are linear. In this study, we propose PolyMR, an MR-based method that approximates any causal function between an exposure and an outcome using polynomials. We demonstrate that PolyMR provides more accurate inference of the shape and magnitude of causal functions compared to existing methods. Our analysis of data from the UK Biobank reveals that the causal effects between anthropometric traits and health-related phenotypes often deviate significantly from linearity. This has implications for interpreting health risks at the individual level and estimating effects in cohorts with different average exposure levels.