Mendelian randomization (MR) is a powerful tool for causal inference in epidemiology. However, the presence of weak instrumental variables (IVs) and pleiotropy can lead to biased causal effect estimates. To address these issues, we develop MR-GMM, a novel MR method based on a Gaussian Mixture Model. MR-GMM classifies IVs into four categories---invalid, valid, invalid\&null, and null IVs---and models their effects using a two-dimensional spike-and-slab distribution. Simulation studies demonstrate the high efficiency and robustness of MR-GMM compared to existing methods. More importantly, we propose a pseudo-p-value-based linkage disequilibrium (LD) clumping procedure to address selection bias. This refined procedure is capable of enhancing the performance of MR-GMM as well as many existing MR methods in real-world scenarios. Applying MR-GMM in a large-scale proteome-wide MR study, we identify 45 coronary heart disease-associated plasma proteins. Subsequent network and enrichment analyses highlight the potential of these proteins as biomarkers for disease diagnosis and therapeutic development.

The authors have declared no competing interest.

This research was supported by National Key R\&D Program of China [2023YFF1205101].

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All source data used in this study were openly accessible prior to the initiation of the research. These data can be obtained from the following sources: 1. MRC IEU OpenGWAS data infrastructure: Genome-wide association summary statistics for 2992 plasma proteins, 81 common traits, blonde hair color, and coronary heart disease. The datasets are available at https://gwas.mrcieu.ac.uk/datasets/. 2.Linkage disequilibrium reference panel. The dataset is available at https://github.com/perslab/CELLECT/blob/master/data/ldsc/1000G_EUR_Phase3_plink/.

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