Two-sample bi-directional causality between two traits with some invalid IVs in both directions using GWAS summary statistics

Mendelian randomization (MR) is a widely used method for assessing causal relationships between risk factors and outcomes using genetic variants as instrumental variables (IVs). While traditional MR assumes uni-directional causality, bi-directional MR aims to identify the true causal direction. In uni-directional MR, invalid IVs due to pleiotropy can violate assumptions and introduce biases. In bi-directional MR, traditional MR can be performed separately for each direction, but the presence of invalid IVs poses even greater challenges. We introduce a new bi-directional MR method incorporating stepwise selection (Bidir-SW) designed to address these challenges. Our approach leverages public genome-wide association study (GWAS) datasets for two traits and uses model selection criteria to identify invalid IVs iteratively by stepwise selection. This method accounts for potential bi-directional causality in the presence of common invalid IVs for both directions, even if only GWAS summary statistics are provided. Through simulation studies, we demonstrate that our method outperforms traditional MR techniques, such as MR-Egger and inverse-variance weighted (IVW), with uncorrelated SNPs. We also provide simulations to compare our approach with existing transcriptome-wide association study (TWAS) to show its effectiveness. Finally, we apply the proposed method to genetic traits such as CRP levels and BMI to explore possible bi-directional relationships among these traits. We also used the proposed method to discover causal protein biomarkers. Our findings suggest that the Bidir-SW approach is a powerful tool for bi-directional MR or TWAS, which can provide a valuable framework for future genetic epidemiology studies.