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June 2020 Statistical inference in two-sample summary-data Mendelian randomization using robust adjusted profile score
Qingyuan Zhao, Jingshu Wang, Gibran Hemani, Jack Bowden, Dylan S. Small
Ann. Statist. 48(3): 1742-1769 (June 2020). DOI: 10.1214/19-AOS1866


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.


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Qingyuan Zhao. Jingshu Wang. Gibran Hemani. Jack Bowden. Dylan S. Small. "Statistical inference in two-sample summary-data Mendelian randomization using robust adjusted profile score." Ann. Statist. 48 (3) 1742 - 1769, June 2020.


Received: 1 February 2018; Revised: 1 March 2019; Published: June 2020
First available in Project Euclid: 17 July 2020

zbMATH: 07241610
MathSciNet: MR4124342
Digital Object Identifier: 10.1214/19-AOS1866

Primary: 65J05
Secondary: 46N60 , 62F35

Keywords: Causal inference , errors in variables , limited information maximum likelihood , path analysis , pleiotropy effects , weak instruments

Rights: Copyright © 2020 Institute of Mathematical Statistics


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Vol.48 • No. 3 • June 2020
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