Self-Consistent Conformal Prediction: Reliable Decisions under Performative Feedback

Conformal prediction affords finite-sample marginal coverage under exchangeability, making it attractive for medical decision support. Yet in sequential care, when a prediction set contains clinically concerning outcomes, clinicians may be more likely to initiate preventive treatment or intensify an existing intervention, changing the very outcome the model aims to predict. This can break the exchangeability assumption underlying the coverage guarantee. A seemingly simple workaround is to ignore this feedback and calibrate under the historical treatment process. However, ignoring treatment feedback can lead to systematic coverage errors at deployment, so the nominal coverage level may no longer provide a reliable measure for clinical decision making. For all that, we show that this feedback can nevertheless be handled before deployment. We propose Self-Consistent Conformal Prediction (SCCP), a method for reliable uncertainty quantification in sequential care under performative feedback. The central difficulty is that the deployment distribution itself depends on the threshold being calibrated. We formulate this coupling as a self-consistent calibration problem, show that its stagewise coverage can be identified from historical trajectories, and use this result to construct a threshold schedule for the treatment process induced by its own use. We prove asymptotic stagewise marginal coverage without requiring post-deployment outcomes. Experiments on one synthetic benchmark and semi-synthetic treatment settings built from four clinical datasets show that SCCP maintains coverage close to the nominal level while retaining informative prediction sets.