Open Access
June 2024 A latent mixture model for heterogeneous causal mechanisms in Mendelian randomization
Daniel Iong, Qingyuan Zhao, Yang Chen
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Ann. Appl. Stat. 18(2): 966-990 (June 2024). DOI: 10.1214/23-AOAS1816


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.


We would like to thank Xuelu Wang for helpful comments on the type II diabetes example.


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Daniel Iong. Qingyuan Zhao. Yang Chen. "A latent mixture model for heterogeneous causal mechanisms in Mendelian randomization." Ann. Appl. Stat. 18 (2) 966 - 990, June 2024.


Received: 1 June 2022; Published: June 2024
First available in Project Euclid: 5 April 2024

Digital Object Identifier: 10.1214/23-AOAS1816

Keywords: Causal inference , diabetes , EM algorithm , HDL cholesterol , instrumental variables , Monte Carlo sampling

Rights: This research was funded, in whole or in part, by EPSRC, EP/V049968/1. A CC BY 4.0 license is applied to this article arising from this submission, in accordance with the grant’s open access conditions.

Vol.18 • No. 2 • June 2024
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