Statistical inference in two-sample summary-data Mendelian randomization using robust adjusted profile score

TLDR

Mendelian randomization uses genetic variation to estimate causal effects free of unmeasured confounding and is increasingly applied across epidemiology and population science. This paper investigates statistical inference for two‑sample summary‑data Mendelian randomization. The authors develop a maximum profile likelihood estimator, extend it with a random‑effects model to account for systematic pleiotropy, and then adjust and robustify the profile score to handle idiosyncratic pleiotropy, yielding a consistent and asymptotically normal estimator. They show the linear model is valid when the exclusion restriction holds, but real data reveal pervasive pleiotropy, and the proposed adjusted and robust profile‑score methods are both robust and efficient in simulations and real datasets.

Abstract

Mendelian randomization (MR) is a method of exploiting genetic variation to unbiasedly estimate a causal effect in presence of unmeasured confounding. MR is being widely used in epidemiology and other related areas of population science. In this paper, we study statistical inference in the increasingly popular two-sample summary-data MR design. We show a linear model for the observed associations approximately holds in a wide variety of settings when all the genetic variants satisfy the exclusion restriction assumption, or in genetic terms, when there is no pleiotropy. In this scenario, we derive a maximum profile likelihood estimator with provable consistency and asymptotic normality. However, through analyzing real datasets, we find strong evidence of both systematic and idiosyncratic pleiotropy in MR, echoing the omnigenic model of complex traits that is recently proposed in genetics. We model the systematic pleiotropy by a random effects model, where no genetic variant satisfies the exclusion restriction condition exactly. In this case, we propose a consistent and asymptotically normal estimator by adjusting the profile score. We then tackle the idiosyncratic pleiotropy by robustifying the adjusted profile score. We demonstrate the robustness and efficiency of the proposed methods using several simulated and real datasets.