Discharge decisions can retrain the model: capacity-aware discharge cuts readmission-risk learning error by 24%–25%
Synopsis
Hospitals use readmission-risk predictions to decide who leaves first, but outcomes are recorded only for discharged patients, so retraining a predictor on that data can lock in censoring bias. Coupling a queueing-based Markov decision process with a periodically retrained risk predictor, the work finds that a discharge-up-to policy, which sets a target census and discharges by priority only when occupancy exceeds it, spreads observed lengths of stay through natural arrival variability. In synthetic experiments and calibrated simulations built on patient-level data from a partner hospital, the policy reduced learning error by 24%–25% relative to thresholding on risk and shrank baseline-adjusted readmission cost disparities by 38%–63%.
Interpretation
Discharge no longer thresholds on a risk score alone; the policy first sets a target number of patients to keep, and discharges by priority only when the census exceeds that target. Common fixed-threshold and state-aware threshold policies concentrate discharges in a narrow length-of-stay range, leaving readmission outcomes at other lengths unobserved. In the synthetic setting, the discharge-up-to policy reached a root mean squared error of 0.095, versus 0.1212 for the fixed-threshold policy and 0.123 for the state-aware threshold policy, reductions of 24.4% and 25.5%.
The policy splits the discharge decision into two parts: a target census that fixes how many patients remain after discharge, and a priority ordering that fixes who leaves first. Priority ranks patients by the marginal risk reduction from an extra day, so patients with little to gain leave first, while the target census follows the relative weight of readmission and congestion costs. In simulations calibrated to patient-level admissions data from an Indiana hospital covering January 2010 to September 2017, the discharge-up-to policy had the lowest error by the second retraining episode and ended below the best state-aware and threshold policies.
Random fluctuation in arrivals supplies the diversity learning needs, without adding randomized exploration for fairness. Static threshold systems leave covariate regions never observed, which require explicit exploration to fill. The analysis shows that under stochastic arrivals the discharge-up-to policy discharges every patient type at every length of stay with positive probability, whereas deterministic arrivals can leave some groups unobserved at some lengths of stay.
Perspective
The conclusions rest on a stylized queueing model, synthetic experiments and simulations calibrated to patient-level data from one Indiana hospital covering January 2010 to September 2017, run over 50 retraining episodes. The theoretical guarantee requires a well-specified risk model, or a known inverse-propensity weighting adjustment under misspecification.
The convergence result depends on stochastic arrivals; with deterministic arrivals, some patient groups may never be observed at some lengths of stay. Under misspecification, unweighted empirical risk minimization can converge to a biased solution. In the simulations, absolute between-group disparities in prediction error did not improve, and African-American patients had similar unadjusted readmission costs across policies.