When having access to demand forecasts, a crucial question is how to effectively use this information to make better resource allocation decisions, especially during demand surges like the COVID-19 pandemic. Despite the emergence of various advanced prediction models for hospital resources, there has been a lack of prescriptive solutions for hospital managers seeking concrete decision support, for example, guidance on whether to allocate beds from other specialties to meet the surge demand from COVID-19 patients by postponing elective surgeries. In their paper “Optimal Routing under Demand Surge: the Value of Future Arrival Rate,” the authors present a systematic framework to incorporate future demand into routing decisions in parallel server systems with partial flexibility and quantify the benefits of doing so. They propose a simple and interpretable two-stage index-based policy that explicitly incorporates demand forecasts into real-time routing decisions. Their analytical and numerical results demonstrate the policy’s effectiveness, even in the presence of large prediction errors.
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Abstract Background Advanced machine learning models have received wide attention in assisting medical decision making due to the greater accuracy they can achieve. However, their limited interpretability imposes barriers for practitioners to adopt them. Recent advancements in interpretable machine learning tools allow us to look inside the black box of advanced prediction methods to extract interpretable models while maintaining similar prediction accuracy, but few studies have investigated the specific hospital readmission prediction problem with this spirit.
Methods Our goal is to develop a machine-learning (ML) algorithm that can predict 30- and 90- day hospital readmissions as accurately as black box algorithms while providing medically interpretable insights into readmission risk factors. Leveraging a state-of-art interpretable ML model, we use a two-step Extracted Regression Tree approach to achieve this goal. In the first step, we train a black box prediction algorithm. In the second step, we extract a regression tree from the output of the black box algorithm that allows direct interpretation of medically relevant risk factors. We use data from a large teaching hospital in Asia to learn the ML model and verify our two-step approach.
Results The two-step method can obtain similar prediction performance as the best black box model, such as Neural Networks, measured by three metrics: accuracy, the Area Under the Curve (AUC) and the Area Under the Precision-Recall Curve (AUPRC), while maintaining interpretability. Further, to examine whether the prediction results match the known medical insights (i.e., the model is truly interpretable and produces reasonable results), we show that key readmission risk factors extracted by the two-step approach are consistent with those found in the medical literature.
Conclusions The proposed two-step approach yields meaningful prediction results that are both accurate and interpretable. This study suggests a viable means to improve the trust of machine learning based models in clinical practice for predicting readmissions through the two-step approach.
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Abstract In this article, we analyze a discrete‐time queue that is motivated from studying hospital inpatient flow management, where the customer count process captures the midnight inpatient census. The stationary distribution of the customer count has no explicit form and is difficult to compute in certain parameter regimes. Using the Stein's method framework, we identify a continuous random variable to approximate the steady‐state customer count. The continuous random variable corresponds to the stationary distribution of a diffusion process with
state‐dependent diffusion coefficients. We characterize the error bounds of this approximation under a variety of system load conditions—from lightly loaded to heavily loaded. We also identify the critical role that the service rate plays in the convergence rate of the error bounds. We perform extensive numerical experiments to support the theoretical findings and to demonstrate the approximation quality. In particular, we show that our approximation performs better than those based on constant diffusion coefficients when the number of servers is small, which is relevant to decision making in a single hospital ward.
