From prediction to decision: Optimizing long-term care placements among older delayed discharge patients

This study examines long-term care (LTC) discharge planning among older delayed discharge patients. While awaiting placements in alternate care such as LTC, these patients occupy hospital beds despite not requiring an intensive level of care. This study proposes a novel discharge decision model based on the Markov decision process (MDP) framework, which incorporates predictions regarding the patients' health trajectory and the associated hospital costs. Our machine learning (ML)-based predictive analytics allow for considering heterogeneous health transitions, hence personalized decision making, leading to valuable information for reducing hospital costs. We also develop data-driven cost functions using patient characteristics to estimate the person-level costs associated with the decisions in the optimization model, that is, whether or not to discharge a patient to LTC. The data analyses and cost estimations are based on large historical data collected over 13 years in Ontario, Canada. To solve the resulting high-dimensional MDP models, we develop an index policy, where each patient's index value is calculated using their health complexity (comorbidity), sex, age, and acute length of stay in the hospital. Using extensive numerical experiments, we illustrate the superior performance of the proposed index policy against some benchmarking policies and demonstrate the significance of predictive information in optimizing discharge decisions. Our results also indicate that the value of predictive information increases with LTC bed availability and decreases with hospital capacity. We also demonstrate that with the anticipated exacerbating mismatch between supply and demand, targeted prediction-driven discharge policies, such as the proposed index policy, become even more critical.