Constrained maximum likelihood-based Mendelian randomization robust to both correlated and uncorrelated pleiotropic effects.

With the increasing availability of large-scale GWAS summary data on various complex traits and diseases, there have been tremendous interests in applications of Mendelian randomization (MR) to investigate causal relationships between pairs of traits using SNPs as instrumental variables (IVs) based on observational data. In spite of the potential significance of such applications, the validity of their causal conclusions critically depends on some strong modeling assumptions required by MR, which may be violated due to the widespread (horizontal) pleiotropy. Although many MR methods have been proposed recently to relax the assumptions by mainly dealing with uncorrelated pleiotropy, only a few can handle correlated pleiotropy, in which some SNPs/IVs may be associated with hidden confounders, such as some heritable factors shared by both traits. Here we propose a simple and effective approach based on constrained maximum likelihood and model averaging, called cML-MA, applicable to GWAS summary data. To deal with more challenging situations with many invalid IVs with only weak pleiotropic effects, we modify and improve it with data perturbation. Extensive simulations demonstrated that the proposed methods could control the type I error rate better while achieving higher power than other competitors. Applications to 48 risk factor-disease pairs based on large-scale GWAS summary data of 3 cardio-metabolic diseases (coronary artery disease, stroke, and type 2 diabetes), asthma, and 12 risk factors confirmed its superior performance.