Mendelian randomization: A comprehensive statistical approach and applications to preventing heart disease

Mendelian randomization (MR) can give unbiased estimate of a confounded causal effect by using genetic variants as instrumental variables (IV). The summary-data MR design is rapidly gaining popularity in practice due to the increasing availability of large-scale genome-wide association studies (GWAS). As we are entering the "MR of every risk factor on every disease outcome" era, existing statistical methods still lack theoretical grounding and face at least four major challenges: measurement error in the genetic associations, invalid IVs due to pleiotropy, weak IV bias, and selection bias IV screening.

To overcome these challenges, I will formulate the summary-data MR problem as a linear errors-in-variables regression problem with over-dispersion and occasional outliers. This means that none of the genetic IVs is strictly valid. This model is inspired by our exploratory data analysis and the recent omnigenic model for complex traits. I will present a new approach based on adjusting and robustifying the profile score function, with provable consistency and asymptotic normality when the IVs are collectively strong but may be individually weak. The efficiency of this method can be further increased by empirical (partially) Bayes shrinkage. The new methods will be used to re-analyze several cardiometabolic diseases and risk factors, yielding new insights into the role of HDL particles (the "good" cholesterol) in coronary artery disease.