Compressing health records for causal analysis can drop a rare code, cutting mediation interval coverage to 2%
Synopsis
Multimodal health records are often compressed into low-dimensional representations and used as adjustment sets, yet variational autoencoders are trained to reconstruct data rather than to preserve what causal identification needs. In simulations, a representation that discarded a rare code affecting both treatment and mediator gave 95% intervals for the interventional indirect effect with 2% coverage at n = 3,000 under moderate confounding, while reconstruction loss did not reveal the problem; a diagnostic comparing nuisance-function predictive loss flagged it in every replicate.
Interpretation
Replacing raw multimodal records with a learned low-dimensional representation for causal adjustment can discard information the identification needs, and that loss does not shrink as the sample grows. The prior practice compressed records into a low-dimensional representation and used it directly as the adjustment set, assuming the representation retained what identification requires; a reconstruction objective depends only on the marginal law of the covariates. In simulation, the representation that dropped a rare code gave interventional indirect-effect bias 0.186 and coverage 0.015 at confounding strength κ = 1 and n = 3,000, while the average treatment effect under the same representation had bias 0.004.
Interventional mediation demands more of a representation than treatment comparison does: a representation adequate for comparing treatments need not be adequate for splitting an effect into direct and indirect parts. A balancing or prognostic representation identifies counterfactual means, but the authors prove that balancing does not imply the interventional effects are identified. At κ = 1 and n = 3,000 the same representation gave an interventional direct-effect bias of −0.181, opposite in sign to the indirect effect, so the split between pathways was distorted far more than the total effect.
Reconstruction loss cannot be used to choose the representation; the choice should instead use the predictive losses of the nuisance functions the estimator relies on, together with diagnostics. Selecting the latent dimension by validation reconstruction loss picked d = 8 in every replicate, yet the correlation between reconstruction loss and absolute indirect-effect bias was −0.81 and −0.82 at κ = 1, so better reconstruction went with larger bias. At κ = 1 and n = 3,000 the reconstruction-selected dimension gave bias 0.127 and coverage 0.185, the nuisance-loss-selected dimension gave 0.163 and 0.110, and diagnostic D1 flagged the d = 4 representation in 100% of replicates at κ = 1 and 0% at κ = 0.
Perspective
The conclusions rest on simulated data with one data-generating mechanism, sample sizes of 1,000 and 3,000, and 200 replicates per setting, and the mediation estimator uses a single binary intermediate confounder; all results assume no unmeasured confounding given the observed covariates.
The author notes that the diagnostics detect predictive insufficiency of the representation relative to measured covariates, not unmeasured confounding, and that a non-significant diagnostic is not proof of sufficiency; the closed-form bias is derived for a linear Gaussian model, and full-sample unsupervised training requires an additional stability condition; whether mechanism-informed objectives linking exposure, mediator and outcome reduce representation bias remains an empirical question left to future work.