Inferring causal direction between two traits using R² with application to transcriptome-wide association studies

In Mendelian randomization, two single SNP-trait correlation-based methods have been developed to infer the causal direction between an exposure (e.g., a gene) and an outcome (e.g., a trait), called MR Steiger's method and its recent extension called Causal Direction-Ratio (CD-Ratio). Here we propose an approach based on R², the coefficient of determination, to combine information from multiple (possibly correlated) SNPs to simultaneously infer the presence and direction of a causal relationship between an exposure and an outcome. Our proposed method generalizes Steiger's method from using a single SNP to multiple SNPs as IVs. It is especially useful in transcriptome-wide association studies (TWASs) (and similar applications) with typically small sample sizes for gene expression (or another molecular trait) data, providing a more flexible and powerful approach to inferring causal directions. It can be applied to GWAS summary data with a reference panel. We also discuss the influence of invalid IVs and introduce a new approach called R2S to select and remove invalid IVs (if any) to enhance the robustness. We compared the performance of the proposed method with existing methods in simulations to demonstrate its advantages. We applied the methods to identify causal genes for high/low-density lipoprotein cholesterol (HDL/LDL) using the individual-level GTEx gene expression data and UK Biobank GWAS data. The proposed method was able to confirm some well-known causal genes while identifying some novel ones. Additionally, we illustrated an application of the proposed method to GWAS summary to infer causal relationships between HDL/LDL and stroke/coronary artery disease (CAD).