Research Brief

Anticipating Overcrowding Risk in the ICU

A model vastly outperforms predictions based on prior hospital data

The intensive care unit provides a sanctuary for the most critically ill or injured patients in a hospital, representing the height of specialized medical care and monitoring. But a surge in new patients can jeopardize the delicate balance between staffing, resources and bed turnover required for high-quality treatment and can lead to suboptimal health outcomes. 

The task of preventing overcrowding, also known as congestion, is a complex operational challenge. Patients admitted to an ICU come from various areas of the hospital, including surgical, emergency and inpatient departments. Not only do these patients have different diagnoses, but they also have different recovery times. So, to control congestion, the ICU must monitor other units in the hospital for the likelihood of those patients needing to move into the ICU and consider the potential length of stay for current and future ICU patients to know when beds will be available. 

Many ICUs currently use reactive policies under which decisions on patient admissions and discharges are simply based on the level of occupancy and demand for care at any particular moment in time. This means that efforts to reduce overcrowding are only made once high occupancy levels are already occurring.

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In a paper published by Stochastic Systems, UCLA Anderson’s Fernanda Bravo, Duke’s Cynthia Rudin, University of Rochester’s Yaron Shaposhnik and William & Mary’s Yuting Yuan provide a method to predict days in advance when an ICU is likely to face a high risk of congestion. Armed with this advanced warning, an ICU can alleviate congestion and keep a high standard of care by implementing timely measures, such as increasing staffing levels, reducing service times and diverting or postponing arriving patients.

Rules Anyone Can Follow

The researchers propose a model-based approach to develop simple rules to predict the status of the ICU. The role of interpretability is paramount in practical settings: The approach provides healthcare workers with clear, easy-to-understand-and-communicate rules to make predictions about the risk of ICU congestion in the near future. They show that their method outperforms data-driven methods, which depend on historical data to identify patterns. Data-driven methods often only provide the end-user with a black box prediction. This manifests in the difference between healthcare workers having a laminated card with interpretable rules versus only being able to see a computer output with a predicted congestion risk and no context as to how the prediction was made.

Bravo, Rudin, Shaposhnik and Yuan’s approach combines queueing theory (which predicts queue lengths and wait times) with simulation and machine learning methods to devise interpretable rules. Their methodology involves several steps. 

First a queueing model of the ICU is created to simulate its dynamics and patient flow. This model is used to simulate a large number of scenarios that an ICU can face — labeled as either “high risk” or “not high risk” for congestion. 

Next, several features are created to summarize the status of the unit. A key predictor of risk is the remaining length of stay profile for patients in a hospital’s units. Using an intermediate machine learning model, the method identifies patients’ profiles based on remaining length of stay. The unit utilization status is then summarized according to the number of patients within each length of stay profile. These engineered features, plus the knowledge about likelihood of ICU transfers from each profile, are then used to train a linear machine learning model to predict the ICU congestion risk. 

The approach outputs simple linear rules based on the status of the unit (i.e., number of patients within each length of stay profile).

Six Times Fewer Errors in Estimating ICU Congestion

More precisely, the researchers illustrated their approach using a realistic queuing model of a hospital with several units. Using the simulation model, they generated 1,000 sample Saturdays as their starting scenarios and, with these, predicted the risk for the most congested days in the ICU, which are Tuesday through Friday. They compared their results with the results of other variants of model-based methods and data-driven methods. 

The error rate for their model-driven method was below 5%, while the error for the data-driven methods was roughly six times higher. A reason for the outperformance of the researchers’ model-based approach, over data-driven approaches, is that they can generate unlimited amounts of data simulated by their queueing model and better estimate congestion risk labels with this larger amount of data. 

In the end, the researchers’ method provides the ICU with rules to determine congestion risk based on the number of patients in the hospital system and their expected remaining time in the different units. They believe other service operations could benefit from additional research on the combination of queueing theory and simulation with interpretable machine learning algorithms.

Featured Faculty

  • Fernanda Bravo

    Assistant Professor of Decisions, Operations and Technology Management

About the Research

Bravo, F., Rudin, C., Shaposhnik, Y., & Yuan, Y. (2023). Interpretable Prediction Rules for Congestion Risk in Intensive Care Units. Stochastic Systems.

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