A Latent Mixture Model for Heterogeneous Causal Mechanisms in Mendelian Randomization

Abstract

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.

Selecting invalid instruments to improve Mendelian randomization with two-sample summary data

“…The motivation for this is partly dimension reduction: genetic variants which belong to the same cluster suggest a similar value for the causal effect θ 0 , and would therefore impact the asymptotic bias in a similar way. However, the idea of forming candidate instrument sets by clustering variants offering similar ratio estimates has also been used to shed light on biological mechanisms that may drive heterogeneous causal effects; see, for example, Iong et al (2020) and Foley et al (2021).…”

Using clustering of genetic variants in Mendelian randomization to interrogate the causal pathways underlying multimorbidity

“…The blue line corresponds to the average slope identified by the IVW estimate when both groups of SNPs (𝐺 1 and 𝐺 2 ) are used, which is clearly not satisfactory. with different causal effects [7,8]. For example, it is suspected that general adiposity exerts a heterogeneous causal effect on type 2 diabetes (T2D) depending on its location in the body (e.g.…”

“…SNP group 𝐺 1 and 𝐺 2 could now represent instruments for sub-exposures 𝑋 1 and 𝑋 2 , each responsible for true but distinct causal effects represented by the black and red slopes respectively. We follow Iong et al [8] by referring to both correlated pleiotropy and causal effect heterogeneity under the umbrella term of 'mechanistic heterogeneity', since both features can give rise to the appearance of multiple slopes in the summary data, and it is impossible to discern the root cause without further data, domain knowledge and modelling assumptions.…”

“…Figure 2 (ii) shows a separate causal diagram representing violation of the causal homogeneity assumption, illustrating the scenario where the exposure X has been incorrectly defined as a single quantity when it is in fact made up of two or more sub-components (here X 1 and X 2 ) with different causal effects [7, 8]. For example, it is suspected that general adiposity exerts a heterogeneous causal effect on type 2 diabetes (T2D) depending on its location in the body (e.g.…”

“…There are several existing methods for detecting the variant clusters in MR, for example, the MR-Clust method proposed by Foley et al [7] and the MR-PATH method by Iong et al [8]. Like MR-AHC, these two methods do not fix the number of clusters a priori , allowing the data to determine this important parameter.…”