Role-Reversed Auxiliary Calibration for Treatment Effects under Selection on Potential Outcomes

This paper develops a role-reversed auxiliary-calibration framework for identifying average and conditional treatment effects when treatment selection may depend directly on both potential outcomes. The framework uses two side-specific auxiliary measurements: a baseline-side measurement Q and a response-side measurement S. Their roles are reversed across the two potential-outcome means: Q calibrates treatment selection and S represents the outcome for E[Y1], whereas S calibrates selection and Q represents the outcome for E[Y0]. Unlike proximal causal inference or shadow-variable methods, the proposed approach targets generalized Roy selection on potential outcomes rather than adjustment for a common latent confounder. We establish identification of average, conditional, subgroup, and restricted-time treatment effects without recovering the joint distribution of (Y1, Y0). The resulting calibrated orthogonal moment is twin-pair doubly robust: within each treatment arm, either the selection calibrator or the adjoint outcome representer is sufficient for valid estimation. When both nuisance functions are estimated, first-order bias reduces to the product of their estimation errors, yielding product-rate robustness and supporting cross-fitted inference. Monte Carlo experiments illustrate the transition from accidental strong ignorability to selection on gains, showing that the proposed estimator reproduces the standard AIPW benchmark under the former while remaining accurate under the latter, where latent-confounder and armwise shadow-variable methods fail. The methodology is further illustrated using a full-counterfactual benchmark based on the Beat AML ex vivo drug-response resource and an observational study of ESBL bloodstream infection, in which the estimated treatment effect agrees in direction with randomized-trial evidence.