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Network Biology, 2027, 17(2): 121-467
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Article

Meta-MR: The meta-methodology and the web platform for Mendelian Randomization analysis

WenJun Zhang
School of Life Sciences, Sun Yat-sen University, Guangzhou 510275, China; International Academy of Ecology and Environmental Sciences, Hong Kong, China

Received 26 February 2025;Accepted 1 June 2026;Published online 23 June 2026;Published 1 June 2027
IAEES

Abstract
Mendelian randomization (MR) has emerged as a powerful epidemiological strategy for inferring causal relationships from observational data by leveraging genetic variants as instrumental variables. The fixed nature of genotypes renders them largely immune to reverse causation and confounding, making MR particularly valuable when randomized controlled trials are infeasible. However, the growing diversity of MR methodologies and the often-inconsistent findings across different analytical approaches pose significant challenges for researchers seeking robust causal evidence. This study presents a comprehensive mathematical formalization of the major MR algorithms and introduces Meta-MR, an integrated web-based computational platform for systematic MR analysis. I detail the mathematical foundations of twelve single-variable MR methods, including the Inverse-Variance Weighted method, Weighted Median, MR-Egger, Maximum Likelihood, Mode-Based Estimation, Contamination Mixture Model, Heterogeneity Penalization, Lasso-based selection, Debiased IVW, Penalized IVW, Constrained Maximum Likelihood, and Leave-One-Out diagnostics. Additionally, I formalize seven multivariable MR approaches: Multivariable IVW, Multivariable Median, Multivariable Egger, Multivariable Lasso, Multivariable Constrained Maximum Likelihood, Multivariable Generalized Method of Moments, and Multivariable Principal Component GMM. The Meta-MR web platform, implemented entirely in JavaScript with HTML and CSS, addresses a critical gap in existing MR software by incorporating meta-analytic pooling across algorithm-specific estimates. The platform enables researchers to: (1) generate harmonized MR input data through direct JSON input, file upload, or AI-assisted GWAS data fetching; (2) execute user-selected MR methods dynamically; (3) assess between-algorithm heterogeneity using Cochran's Q test; (4) obtain pooled causal estimates with proper uncertainty quantification under both homogeneous and heterogeneous models; (5) generate interactive forest plots for visualizing SNP-level and method-level estimates; and (6) export comprehensive results to Word-compatible documents. The meta-pooling algorithm employs inverse-variance weighting to compute combined estimates, with the DerSimonian-Laird estimator for between-algorithm variance when significant heterogeneity is detected. This approach mitigates the impact of potentially biased or inefficient individual algorithms, providing more robust and reliable causal inferences. The significance of this work lies in its dual contribution: rigorous mathematical exposition of MR algorithms and a practical, accessible implementation that promotes evidence synthesis in precision medicine. By formalizing the underlying algorithms and enabling systematic pooling, Meta-MR facilitates more reliable causal insights for disease etiology and drug discovery.

Keywords Mendelian randomization;causal inference;instrumental variables;SNPs;algorithms;algorithm pooling;meta-analysis;AI;web platform;computational tool;JavaScript.


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