Short and Long term predictions of Hospital emergency department attendances

Abstract

Objective: Emergency departments in the United Kingdom (UK) experience significant difficulties in achieving the 95% NHS access standard due to unforeseen variations in patient flow. In order to maximize efficiency and minimize clinical risk, better forecasting of patient demand is necessary. The objective is therefore to create a tool that accurately predicts attendance at emergency departments to support optimal planning of human and physical resources.

Methods: Historical attendance data between Jan-2011 - December-2015 from four hospitals were used as a training set to develop and validate a forecasting model. To handle weekday variations, the data was first segmented into each weekday time series and a separate model for each weekday was performed. Seasonality testing was performed, followed by Box-Cox transformations. A modified heuristics based on a fuzzy time series model was then developed and compared with autoregressive integrated moving average and neural networks models using Harvey, Leybourne and Newbold (HLN) test. The time series models were tested in four emergency department sites to assess forecasting accuracy using the root mean square error and mean absolute percentage error. The models were tested for (i) short term prediction (four weeks ahead), using weekday time series; and (ii) long term predictions (four months ahead) using monthly time series.

Results: Data analysis revealed that presentations to emergency department and subsequent admissions to hospital were not a purely random process and therefore could be predicted with acceptable accuracy. Prediction accuracy improved as the forecast time intervals became wider (from daily to monthly). For each weekday time series modelling using fuzzy time series, for forecasting daily admissions, the mean absolute percentage error ranged from 2.63% to 4.72% while for monthly time series mean absolute percentage error varied from 2.01%-2.81%. For weekday time series, the mean absolute percentage error for autoregressive integrated moving average and neural network forecasting models ranged from 6.25% to 7.47% and 6.04%-7.42% respectively. The proposed fuzzy time series model proved to have statistically significant performance using Harvey, Leybourne and Newbold (HLN) test. This was explained by variations in attendances in different sites and weekdays.

Conclusions: This paper described a heuristic-based fuzzy logic model for predicting emergency department attendances which could help resource allocation and reduce pressure on busy hospitals. Valid and reproducible prediction tools could be generated from these hospital data. The methodology had an acceptable accuracy over a relatively short time period, and could be used to assist better bed management, staffing and elective surgery scheduling. When compared to other prediction models usually applied for emergency department attendances prediction, the proposed heuristic model had better accuracy.

Keywords: Autoregressive integrated moving average model (ARIMA); Fuzzy times series; Hospital emergency department (ED) predictions; Mean absolute percentage error (MAPE); Neural network for time series modelling; Root mean square error (RMSE).