Mendelian randomization (MR) serves as a valuable tool for investigating causal relationships between exposures and disease outcomes in observational studies. However, MR methods, operating under classical assumptions, may yield biased estimates and inflated false-positive causal relationships when faced with realistic and complex correlated horizontal pleiotropy (CHP). While numerous MR methods have emerged to address CHP effects, limited methods can effectively handle relatively large direct effects, commonly known as idiosyncratic pleiotropy. In response to this gap, we propose an efficient and Robust Mendelian Randomization method to account for Idiosyncratic and Correlated Pleiotropy, named RMR-ICP. Furthermore, our method employs paralleled Gibbs sampling to incorporate linkage disequilibrium structure, thereby enhancing statistical power. We demonstrate the robustness and efficiency of our method through extensive simulation studies and applications. Particularly, we apply RMR-ICP to study the effects of plasma proteins on stroke. Several notable associations are identified. For example, SELE has a positive causal effect on any stroke. An elevated BNP is associated with an increased risk of cardioembolic stroke, but not with other stroke subtypes. This offers a fresh perspective in the identification of plasma proteins associated with stroke.
