Hospital vs. Home Care: Trading off Predischarge and Postdischarge Infection and Mortality Risks.

This article focuses on optimizing the length of stay (LOS) and discharge timing for hematology-oncology patients, who face a critical trade-off between hospital-acquired infection risks and mortality risks associated with infections occurring at home. Using a newsvendor-type model, the authors characterize the optimal LOS for individual patients based on infection hazard rates, survival probabilities, and care costs, and extend this to a capacitated hospital ward setting modeled as an overloaded queueing system. They develop a fluid approximation and prove that optimal discharge policies involve at most two discrete discharge thresholds per patient type, leading to the proposal of an index-based speedup policy (ISP) that dynamically prioritizes patient discharge decisions under capacity constraints. Numerical analyses based on real patient data demonstrate that ISP can reduce mortality rates by up to 27.7% compared to current practices, with about 75% of patients requiring some hospital observation, and that a single-threshold speedup policy is optimal for most patient types during high demand. The study highlights the importance of personalized, dynamic discharge decisions that balance infection and mortality risks while accounting for hospital capacity, offering practical insights for improving patient outcomes in hematology wards and potentially other healthcare settings.