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