We propose a novel method for robust estimation of causal effects in two-sample Mendelian randomization analysis using potentially large number of genetic instruments. We consider a "working model" for bi-variate effect-size distribution across pairs of traits in the form of normal-mixtures which assumes existence of a fraction of the genetic markers that are valid instruments, i.e. they have only direct effect on one trait, while other markers can have potentially correlated, direct and indirect effects, or have no effects at all. We show that model motivates a simple method for estimating causal effect (𝜽) through a procedure for maximizing the probability concentration of the residuals, (𝜷𝑻𝒓𝒂𝒊𝒕𝟐 − 𝜽𝜷𝑻𝒓𝒂𝒊𝒕𝟏), at the "null" component of a two-component normal-mixture model. Simulation studies showed that MRMix provides nearly unbiased or/and substantially more robust estimates of causal effects compared to alternative methods under various scenarios. Further, the studies showed that MRMix is sensitive to direction and can achieve much higher efficiency (up to 3-4 fold) relative to other comparably robust estimators. We applied the proposed methods for conducting MR analysis using largest publicly available datasets across a number of risk-factors and health outcomes. Notable findings included identification of causal effects of genetically determined BMI and age-at-menarche, which have relationship among themselves, on the risk of breast cancer; detrimental effect of HDL on the risk of breast cancer; no causal effect of HDL and triglycerides on the risk of coronary artery disease; a strong detrimental effect of BMI, but no causal effect of years of education, on the risk of major depressive disorder.

Mendelian Randomization Analysis Using Mixture Models (MRMix) for Genetic Effect-Size-Distribution Leads to Robust Estimation of Causal Effects