Inferring causal direction between two traits in the presence of horizontal pleiotropy with GWAS summary data

Author summary In spite of its importance, due to technical challenges, orienting causal relationships between pairs of traits has been largely under-studied. Mendelian randomization (MR) Steiger's method has become increasingly used in the last two years. Here we point out several limitations with MR Steiger's method and propose alternative approaches. First, MR Steiger's method is based on using only one single SNP as the instrument variable (IV), for which we propose a correlation ratio-based method, called Causal Direction-Ratio, or simply CD-Ratio. An advantage of CD-Ratio is its inference of both the existence and (if so) the direction of a causal relationship, in contrast to MR Steiger's prior assumption of the existence and its poor performance if the assumption is violated. Furthermore, CD-Ratio can be extended to combine the results from multiple, possibly correlated, SNPs with improved statistical power. Second, we propose two methods, called CD-Egger and CD-GLS, for multiple and possibly correlated SNPs while allowing horizontal pleiotropy. Third, we propose three goodness-of-fit tests to check modeling assumptions for the three proposed methods. Finally, we introduce multivariable CD-Egger, analogous to multivariable MR, as a more robust approach, and an extension of CD-Ratio to cases with possibly bi-directional causal relationships. Our numerical studies demonstrated superior performance of our proposed methods over MR Steiger and bi-directional MR. Our proposed methods, along with freely available software, are expected to be useful in practice for causal inference. Orienting the causal relationship between pairs of traits is a fundamental task in scientific research with significant implications in practice, such as in prioritizing molecular targets and modifiable risk factors for developing therapeutic and interventional strategies for complex diseases. A recent method, called Steiger's method, using a single SNP as an instrument variable (IV) in the framework of Mendelian randomization (MR), has since been widely applied. We report the following new contributions. First, we propose a single SNP-based alternative, overcoming a severe limitation of Steiger's method in simply assuming, instead of inferring, the existence of a causal relationship. We also clarify a condition necessary for the validity of the methods in the presence of hidden confounding. Second, to improve statistical power, we propose combining the results from multiple, and possibly correlated, SNPs as multiple instruments. Third, we develop three goodness-of-fit tests to check modeling assumptions, including those required for valid IVs. Fourth, by relaxing one of the three IV assumptions in MR, we propose several methods, including an Egger regression-like approach and its multivariable version (analogous to multivariable MR), to account for horizontal pleiotropy of the SNPs/IVs, which is often unavoidable in practice. All our methods can simultaneously infer both the existence and (if so) the direction of a causal relationship, largely expanding their applicability over that of Steiger's method. Although we focus on uni-directional causal relationships, we also briefly discuss an extension to bi-directional relationships. Through extensive simulations and an application to infer the causal directions between low density lipoprotein (LDL) cholesterol, or high density lipoprotein (HDL) cholesterol, and coronary artery disease (CAD), we demonstrate the superior performance and advantage of our proposed methods over Steiger's method and bi-directional MR. In particular, after accounting for horizontal pleiotropy, our method confirmed the well known causal direction from LDL to CAD, while other methods, including bi-directional MR, might fail.