BWMR

BWMR infers causal relationships between exposures and outcomes from GWAS summary statistics using a Bayesian weighted Mendelian randomization framework that accounts for polygenicity and pleiotropy.

Key Features:

• Bayesian Framework: BWMR employs Bayesian inference to model uncertainty from weak genetic effects in GWAS summary statistics arising from polygenicity.
• Outlier Detection via Bayesian Weighting: BWMR applies Bayesian weighting to detect and down-weight pleiotropic outlier variants that violate instrumental variable assumptions.
• Variational Expectation-Maximization (VEM) Algorithm: BWMR uses a variational expectation-maximization algorithm for computational stability and scalability with large GWAS datasets.
• Posterior Covariance Correction: BWMR incorporates an exact closed-form formula to correct the underestimation of posterior covariance produced by variational inference.

Scientific Applications:

• Simulation evaluation: BWMR was evaluated in comprehensive simulation studies demonstrating improved robustness and precision compared with existing methods.
• Metabolite–trait causal analysis: BWMR was applied to infer causal relationships between 130 metabolites and 93 complex human traits, identifying novel causal links.

Methodology:

BWMR uses GWAS summary statistics and implements Bayesian inference with Bayesian-weighted outlier detection, a variational expectation-maximization algorithm, and an exact closed-form posterior covariance correction.