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Mendelian Randomization (MR) is a popular method in epidemiology and geneticsthat uses genetic variation as instrumental variables for causal inference.Existing MR methods usually assume most genetic variants are valid instrumentalvariables that identify a common causal effect. There is a general lack ofawareness that this effect homogeneity assumption can be violated when thereare multiple causal pathways involved, even if all the instrumental variablesare valid. In this article, we introduce a latent mixture model MR-PATH thatgroups instruments that yield similar causal effect estimates together. Wedevelop a Monte-Carlo EM algorithm to fit this mixture model, deriveapproximate confidence intervals for uncertainty quantification, and adopt amodified Bayesian Information Criterion (BIC) for model selection. We verifythe efficacy of the Monte-Carlo EM algorithm, confidence intervals, and modelselection criterion using numerical simulations. We identify potentialmechanistic heterogeneity when applying our method to estimate the effect ofhigh-density lipoprotein cholesterol on coronary heart disease and the effectof adiposity on type II diabetes.

A Latent Mixture Model for Heterogeneous Causal Mechanisms in Mendelian Randomization