Weak-instrument robust tests in two-sample summary-data Mendelian randomization.

Mendelian randomization (MR) has been a popular method in genetic epidemiology to estimate the effect of an exposure on an outcome using genetic variants as instrumental variables (IV), with two-sample summary-data MR being the most popular. Unfortunately, instruments in MR studies are often weakly associated with the exposure, which can bias effect estimates and inflate Type I errors. In this work, we propose test statistics that are robust under weak-instrument asymptotics by extending the Anderson-Rubin, Kleibergen, and the conditional likelihood ratio test in econometrics to two-sample summary-data MR. We also use the proposed Anderson-Rubin test to develop a point estimator and to detect invalid instruments. We conclude with a simulation and an empirical study and show that the proposed tests control size and have better power than existing methods with weak instruments.