End-to-End Mediation Analysis at Scale: From High-Dimensional Causal Discovery to Path-Level Effects, with a Human Phenotype Application

Causal mediation analysis reveals how an exposure affects an outcome, but requires the mediator and the variables to adjust for to be specified in advance; with thousands of variables, both must be inferred from a causal structure learned from the data. Learned structures are uncertain and may disagree on what to adjust for, and existing pipelines face three obstacles at this scale: structure learning grows quadratically with the number of variables, averaging estimates across structures targets no single adjustment, and estimators must commit to an unknown functional form. We propose Channel-Additive Robust Mediation (Charm), an end-to-end framework that estimates mediation effects from incomplete, high-dimensional data. Charm searches for structure only among each variable's strongest partners and registered role pairs, so its cost grows linearly; fixes, before estimation, one adjustment set valid under every structure supporting a path, and withholds the path when none exists; and estimates every path with one flexible model that learns how the mediator acts on the outcome, rather than fixing its form in advance. In simulations, screened discovery matches the accuracy of the full search at a fraction of its cost on data with $10\%$ of values missing; under a complete public tier order, Charm recovers the target path and estimates its effects accurately up to ten thousand variables, never issues an invalid adjustment set where the structures disagree, and stays accurate across linear and nonlinear mechanisms. On the Human Phenotype Project, it recovers mediation chains that survive multiple-testing correction and reproduce reported biology, such as Prevotella acting on blood glucose through branched-chain amino acids.