JointMR: A joint likelihood-based approach for causal effect estimation in overlapping Mendelian Randomization studies

The integration of causal effect estimates from multiple Mendelian Randomization studies has become increasingly popular. However, the presence of overlapping databases compromises traditional meta-analysis, leading to inflated variance and reduced statistical power. Here, we propose JointMR, a joint likelihood-based approach designed to integrate multiple GWAS summary databases while explicitly accounting for the covariance matrix of the Wald ratio estimates. Specifically, to accommodate potential cross-study heterogeneity, JointMR incorporates both fixed-effect and random-effects models. Simulations demonstrated that JointMR provides unbiased estimates with higher statistical power and superior Type I error control compared to conventional meta-analysis methods of standard MR estimates (e.g., IVW), especially as database correlation increases. In a real-data application examining total cholesterol, HDL-C, LDL-C and triglycerides on type 2 diabetes, JointMR resolved contradictions seen in standard approaches, generating stable and biologically plausible estimates. In conclusion, JointMR overcomes critical limitations of existing methods, offering a more powerful and reliable tool for robust causal inference from the growing repository of GWAS summary statistics.