Causal Matching with a Rank-Learned Prognostic Score

Can pairwise outcome order suffice to learn useful causal matches? We answer this question by fitting a scalar prognostic score from binary comparisons of observed historical control outcomes, then using it for matching in an independent future cohort. This learner discards outcome magnitudes and is invariant to strictly increasing transformations of historical outcomes, with the fitting procedure fixed. Under a Gumbel location model, comparison probabilities calibrate prognosis differences up to scale. Our matching-specific bound transfers score error to mean squared error (MSE) of the average treatment effect on the treated (ATT), accounting for future support, adaptive donor selection and reuse. Standard ranking theory provides individual-level learning guarantees under explicit finite-class conditions. Six outcome-noise settings and an independently seeded sample-size study delimit the empirical benefit. In simulation study, increasing historical fitting size from 300 to 2400 changes RankNet from nearly tied with the state of art method to up to 90.0% lower mean conditional design MSE. The results establish effective matching from coarsened outcome supervision in this setting, while also showing the advantage of flexible full-outcome regression.