Welch-weighted Egger regression reduces false positives due to correlated pleiotropy in Mendelian randomization

Modern population-scale biobanks contain simultaneous measurements of many phenotypes, providing unprecedented opportunity to study the relationship between biomarkers and disease. However, inferring causal effects from observational data is notoriously challenging. Mendelian randomization (MR) has recently received increased attention as a class of methods for estimating causal effects using genetic associations. However, standard methods result in pervasive false positives when two traits share a heritable, unobserved common cause. This is the problem of correlated pleiotropy. Here, we introduce a flexible framework for simulating traits with a common genetic confounder that generalizes recently proposed models, as well as a simple approach we call Welch-weighted Egger regression (WWER) for estimating causal effects. We show in comprehensive simulations that our method substantially reduces false positives due to correlated pleiotropy while being fast enough to apply to hundreds of phenotypes. We apply our method first to a subset of the UK Biobank consisting of blood traits and inflammatory disease, and then to a broader set of 411 heritable phenotypes. We detect many effects with strong literature support, as well as numerous behavioral effects that appear to stem from physician advice given to people at high risk for disease. We conclude that WWER is a powerful tool for exploratory data analysis in ever-growing databases of genotypes and phenotypes.