When Reconstruction Is Not Enough: Doubly Robust Counterfactual and Interventional Mediation Analysis with Learned Multimodal Representations

Abstract

Learned representations of high-dimensional multimodal health records are increasingly used to adjust for confounding, yet they are usually trained to reconstruct the data rather than to preserve the information that causal identification requires. We study two families of estimands: counterfactual outcomes under alternative treatments, including phenotype-specific effects and patient-level counterfactual risk profiles of the kind digital twins provide, and interventional direct and indirect effects under exposure-induced intermediate confounding. We give conditions under which a representation preserves identification and show that interventional mediation is more demanding than counterfactual comparison. We prove that no training objective that depends only on the covariates, whether reconstruction, contrastive, or physics-informed, can certify that a representation is sufficient, and in a linear structural model we show that a representation can lose an arbitrarily small share of reconstruction accuracy yet induce arbitrarily large bias. We decompose the error of cross-fitted doubly robust estimators into a first-order representation bias, which neither double robustness nor cross-fitting removes, and a second-order remainder of nuisance-estimation errors, so coverage deteriorates as the sample size grows when the representation is insufficient. We propose a workflow combining modality-specific variational autoencoders trained outside the estimation sample, cross-fitted doubly robust and one-step estimators, locked phenotypes, select-then-confirm pathway analysis, portable representations for external replication, and diagnostics for representation insufficiency, exposure leakage, and sensitivity. In simulations, a representation that discarded a rare confounder gave interventional indirect-effect intervals with 2% coverage at n=3,000 when the confounder was moderately strong, reconstruction loss did not identify the problem, and a simple predictive diagnostic flagged it in 100% of replicates.