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