NARX Neural Networks Model for Forecasting Daily Patient Arrivals in the Emergency Department

Introduction

Emergency departments are the most crucial departments within hospitals, which meet emergency patient demand by delivering urgent care in normal and crisis times (Gul and Celik, 2018). These departments are the access points of a majority of patients looking for immediate treatment without appointment (Khaldi et al. 2019; Yeh and Lin, 2007). One of the most crucial processes in ED operations is patient arrivals. It is a measure of how many patients are visiting a healthcare provider at a specific point in time (Berglind, 2019). This process is usually predicted based on the ED patient arrival volume over a time period such as hourly, daily, weekly, monthly and annually (Gul and Celik, 2018; Hertzum, 2017; Gul and Guneri, 2016; Aladeemy et al. 2016). Accurate forecasting of ED arrivals contributes to better allocation of human resources and medical equipment (Yucesan et al. 2019) and decreasing of overcrowding on patient flow (Yucesan et al. 2018; Aladeemy et al. 2016).

In the literature, several approaches are developed to analyze ED patient arrivals. These include regression analysis and machine learning-based approaches (Sariyer et al. 2019; Ordu et al. 2019). For a detailed reading, scholars can refer to Gul and Celik (2018) to see what the forecasting themes, methods used to forecast ED arrivals, data characteristics and type used for forecasting of ED arrivals, study objectives and performance measures and publication trends are. Some previous studies have modeled the approximation as a linear combination of independent variables using calendar data and in some cases climate data (Gul and Celik, 2018). Later studies attempted more sophisticated statistical models like the Autoregressive Integrated Moving Average (ARIMA) models and seasonal ARIMA models that model the approximation based on the historical time series within a short range (Berglind, 2019). Also, neural network models such as back-propagation neural network (BPNN) and radial basic function neural network (RBFNN) are widely used. But the available methods have a slow convergence and data overfitting problem can mislead decision makers. NARX neural networks perform well in the ANN-based algorithm pool in terms of learning ability, convergence rate, generalization performance and high accuracy (Lipu et al. 2018; He et al. 2004). Therefore, in this chapter, we have employed a NARX model to forecast ED patient arrivals. By the chapter, NARX model has been applied to such problem for the first time in the literature. As inputs for the study, calendar and climatic variables were used. Two different algorithms of LM and BR have been tested to find the best network architecture for the problem.