A Comparison of Univariate and Multivariate Forecasting Models Predicting Emergency Department Patient Arrivals during the COVID-19 Pandemic

Abstract

The COVID-19 pandemic has heightened the existing concern about the uncertainty surrounding patient arrival and the overutilization of resources in emergency departments (EDs). The prediction of variations in patient arrivals is vital for managing limited healthcare resources and facilitating data-driven resource planning. The objective of this study was to forecast ED patient arrivals during a pandemic over different time horizons. A secondary objective was to compare the performance of different forecasting models in predicting ED patient arrivals. We included all ED patient encounters at an urban teaching hospital between January 2019 and December 2020. We divided the data into training and testing datasets and applied univariate and multivariable forecasting models to predict daily ED visits. The influence of COVID-19 lockdown and climatic factors were included in the multivariable models. The model evaluation consisted of the root mean square error (RMSE) and mean absolute error (MAE) over different forecasting horizons. Our exploratory analysis illustrated that monthly and weekly patterns impact daily demand for care. The Holt-Winters approach outperformed all other univariate and multivariable forecasting models for short-term predictions, while the Long Short-Term Memory approach performed best in extended predictions. The developed forecasting models are able to accurately predict ED patient arrivals and peaks during a surge when tested on two years of data from a high-volume urban ED. These short- and long-term prediction models can potentially enhance ED and hospital resource planning.

Keywords: COVID-19; deep learning; emergency department; emerging infectious disease; forecasting.

Figure A1

The loss function for ED patient arrival of the best LSTM: (A) univariate and (B) multivariate.

Figure 1

Forecasting modeling framework for ED patient arrivals. The proposed method has three main parts: data processing/statistical analysis, model building, and evaluation.

Figure 2

The structure of the LSTM model [34].

Figure 3

The ED patient arrivals for the two years. The figure depicts: (A) The average arrivals for 2019; (B) The average arrivals for 2020; (C) The weekday arrivals for 2019; and (D) The weekday arrivals for 2020.

Figure 4

Time series plot of total ED patient visits for 2019–2020. The solid red lines depict the changepoints that occurred in the time series data, while the red dash line depicts the start of the COVID lockdown in Michigan, USA.

Figure 5

Time series plot of the stationary ED patient visits for 2019 to 2020. The red dash line depicts the start of the COVID lockdown in Michigan, USA.

Figure 6

Tukey’s test: compare the mean difference of ED patient arrivals by (A) week day and (B) month.

Figure 7

The univariate model predicted values vs. observed data (i.e., test data) for patient arrivals with a one-day forecast horizon. SARIMA: seasonal autoregressive integrated moving average, FP: Facebook Prophet, HW: Holt–Winters, and LSTM: Long Short-Term Memory.

Figure 8

The multivariable model predicted values vs. observed data (i.e., test data) for the ED patient arrival with a one-day forecast horizon. SARIMAX: seasonal autoregressive integrated moving average exogenous, LSTM: Long Short-Term Memory, and FP: Facebook Prophet.