Robust inference of bi-directional causal relationships in presence of correlated pleiotropy with GWAS summary data

To infer a causal relationship between two traits, several correlation-based causal direction (CD) methods have been proposed with the use of SNPs as instrumental variables (IVs) based on GWAS summary data for the two traits; however, none of the existing CD methods can deal with SNPs with correlated pleiotropy. Alternatively, reciprocal Mendelian randomization (MR) can be applied, which however may perform poorly in the presence of (unknown) invalid IVs, especially for bi-directional causal relationships. In this paper, first, we propose a CD method that performs better than existing CD methods regardless of the presence of correlated pleiotropy. Second, along with a simple but yet effective IV screening rule, we propose applying a closely related and state-of-the-art MR method in reciprocal MR, showing its almost identical performance to that of the new CD method when their model assumptions hold; however, if the modeling assumptions are violated, the new CD method is expected to better control type I errors. Notably bi-directional causal relationships impose some unique challenges beyond those for uni-directional ones, and thus requiring special treatments. For example, we point out for the first time several scenarios where a bi-directional relationship, but not a uni-directional one, can unexpectedly cause the violation of some weak modeling assumptions commonly required by many robust MR methods. We also offer some numerical support and a modeling justification for the application of our new methods (and more generally MR) to binary traits. Finally we applied the proposed methods to 12 risk factors and 4 common diseases, confirming mostly well-known uni-directional causal relationships, while identifying some novel and plausible bi-directional ones such as between body mass index and type 2 diabetes (T2D), and between diastolic blood pressure and stroke.Author summary: Inferring causal relationships between two traits based on observational data is one of the most important as well as challenging problems in scientific research. The potential impact of such an application on and beyond genetics/genomics is significant, such as in prioritizing molecular, clinical and behavioral targets for therapeutic and behavioral interventions. However, this problem, especially on a possibly bi-directional causal relationship between a pair of traits (in which the causal direction may be from either trait to the other, and both causal directions may be present at the same time), had been largely neglected until very recently. The increasing availability of large-scale GWAS summary data of various traits has popularized the development and application of Mendelian randomization (MR) methods for such a purpose. We point out some severe limitations with the current methods, mainly due to some new and unique challenges facing inference of bi-directional relationships as compared to that of uni-directional relationships that has been more commonly and exclusively considered in MR. By combining two basic ideas of bidirectional (or reciprocal) MR and Steiger’s correlation-based screening methods, we develop two new approaches based on constrained maximum likelihood (cML) and GWAS summary data to infer causal effects (as in typical MR) and SNP-trait correlations (as in Steiger’s method), called MR-cML and CD-cML respectively, demonstrating their similar effectiveness and more importantly their advantages over existing methods through extensive simulations, real data examples and statistical theory. In particular, our proposed two methods are robust to violations of all three valid IV assumptions, including presence of correlated pleiotropy.