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

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Qingyuan Zhao, Jingshu Wang, Gibran Hemani, Jack Bowden, Dylan S. Small

Mendelian randomization (MR) is a method of exploiting genetic variation tounbiasedly estimate a causal effect in presence of unmeasured confounding. MRis being widely used in epidemiology and other related areas of populationscience. In this paper, we study statistical inference in the increasinglypopular two-sample summary-data MR design. We show a linear model for theobserved associations approximately holds in a wide variety of settings whenall the genetic variants satisfy the exclusion restriction assumption, or ingenetic terms, when there is no pleiotropy. In this scenario, we derive amaximum profile likelihood estimator with provable consistency and asymptoticnormality. However, through analyzing real datasets, we find strong evidence ofboth systematic and idiosyncratic pleiotropy in MR, echoing some recentdiscoveries in statistical genetics. We model the systematic pleiotropy by arandom effects model, where no genetic variant satisfies the exclusionrestriction condition exactly. In this case we propose a consistent andasymptotically normal estimator by adjusting the profile score. We then tacklethe idiosyncratic pleiotropy by robustifying the adjusted profile score. Wedemonstrate the robustness and efficiency of the proposed methods using severalsimulated and real datasets.