What Causes Delays in Admission to Rehabilitation Care? A Structural Estimation Approach

Problem definition: The increase in demand for rehabilitation care has led to long admission delays. These delays not only affect patient outcomes, but also lead to bed blocking in acute care. Admission delays can be caused by capacity constraints or extra processing requirements. Capacity-driven delays are due to a lack of capacity and are impacted by how the available capacity is allocated to patients, whereas processing delays correspond to the time required to plan rehabilitation activities. Standard data however only includes a single (combined) measure of delay, and the bed allocation decisions in practice can be quite complicated with multiple determinant factors. It is thus challenging to quantify the extent to which different sources contribute to admission delays. Methodology/Results: We propose a Hidden Markov Model (HMM) to estimate the unobserved processing times and the status-quo bed allocation policy. The utility of allocating capacity to a patient depends on the patient's characteristics, the system's state, and various other factors, leading to a multinomial discrete-choice model. Through a simulation optimization-based approach, we estimate the parameters of our structural model using real data. Our results provide insights into factors impacting the bed allocation decision and quantify the magnitude of each of the two sources of delays. We validate our estimated policy using a queueing model of patient flow. We find that ignoring processing delays or using simple policies such as First-Come, First-Served or strict priority results in up to 20% error in estimating average delays. In contrast, our estimated policy provides accurate estimates of the delay distributions and allows for evaluation of different operational interventions. Through counterfactual experiments, we examine interventions targeted at addressing different sources of delays and illustrate their effectiveness in reducing admission delays and inequities in delays between different patient types. Managerial implications: Our results demonstrate the importance of identifying and quantifying different sources of delays to develop effective targeted strategies to reduce admission delays. The proposed HMM can be applied in other healthcare/service settings with personalized prioritization and processing delays