MR.RGM: Bayesian Multivariable Bidirectional Mendelian Randomization
Fits multivariable bidirectional Mendelian randomization networks with Bayesian directed cyclic graphical models (reciprocal graphical models; Ni, Ji and Mueller (2018) <doi:10.1214/17-BA1087>), an earlier version of which is described in Sarkar and Ni (2025) <doi:10.1093/bioinformatics/btaf130>. The causal effects among the responses, which may form directed cycles, are estimated with spike-and-slab or threshold priors, and posterior probabilities of network motifs are provided. With a known instrument-response map the instrument effects obey the exclusion restrictions; with an unrestricted map they are selected by a spike-and-slab prior, which allows invalid instruments (horizontal pleiotropy). The input can be individual-level data, the second-moment matrices of one sample, or marginal instrument-response regressions, with optional measured covariates. The error covariance can be diagonal, inverse-Wishart, or a stochastic search structure learning prior (Wang (2015) <doi:10.1214/14-BA916>) whose inclusion indicators describe unmeasured confounding among the responses. Inference is by Markov chain Monte Carlo with exact Gibbs updates of the instrument effects and adaptive random-walk Metropolis updates of the causal effects (Roberts and Rosenthal (2009) <doi:10.1198/jcgs.2009.06134>); the fitting function reports diagnostics of weak instruments, weak identification and convergence.
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