Forecasting daily emergency department arrivals using high-dimensional multivariate data: a feature selection approach

Abstract

Background and objective: Emergency Department (ED) overcrowding is a chronic international issue that is associated with adverse treatment outcomes. Accurate forecasts of future service demand would enable intelligent resource allocation that could alleviate the problem. There has been continued academic interest in ED forecasting but the number of used explanatory variables has been low, limited mainly to calendar and weather variables. In this study we investigate whether predictive accuracy of next day arrivals could be enhanced using high number of potentially relevant explanatory variables and document two feature selection processes that aim to identify which subset of variables is associated with number of next day arrivals. Performance of such predictions over longer horizons is also shown.

Methods: We extracted numbers of total daily arrivals from Tampere University Hospital ED between the time period of June 1, 2015 and June 19, 2019. 158 potential explanatory variables were collected from multiple data sources consisting not only of weather and calendar variables but also an extensive list of local public events, numbers of website visits to two hospital domains, numbers of available hospital beds in 33 local hospitals or health centres and Google trends searches for the ED. We used two feature selection processes: Simulated Annealing (SA) and Floating Search (FS) with Recursive Least Squares (RLS) and Least Mean Squares (LMS). Performance of these approaches was compared against autoregressive integrated moving average (ARIMA), regression with ARIMA errors (ARIMAX) and Random Forest (RF). Mean Absolute Percentage Error (MAPE) was used as the main error metric.

Results: Calendar variables, load of secondary care facilities and local public events were dominant in the identified predictive features. RLS-SA and RLS-FA provided slightly better accuracy compared ARIMA. ARIMAX was the most accurate model but the difference between RLS-SA and RLS-FA was not statistically significant.

Conclusions: Our study provides new insight into potential underlying factors associated with number of next day presentations. It also suggests that predictive accuracy of next day arrivals can be increased using high-dimensional feature selection approach when compared to both univariate and nonfiltered high-dimensional approach. Performance over multiple horizons was similar with a gradual decline for longer horizons. However, outperforming ARIMAX remains a challenge when working with daily data. Future work should focus on enhancing the feature selection mechanism, investigating its applicability to other domains and in identifying other potentially relevant explanatory variables.

Keywords: Crowding; Emergency department; Feature selection; Machine learning; Statistical learning; Time series forecasting.

Fig. 1

Temporal availability of beds in 33 catchment area hospitals or health centres as extracted from Uoma© which is a software developed by Unitary Healthcare Ltd. used to facilitate easier patient transfers. Negative availability is drawn as 0 for clarity. White space represents missing data, caused mainly by sequential introduction of the software. There are interesting differences between facilities, some demonstrating constant overload which likely significantly contributes to catchment area access block

Fig. 2

Predictions superimposed with ground truth. Light grey line = ground truth, dark grey line = prediction. RF = random forest, RLS = recursive least squares, LMS = least mean squares, ARIMA = autoregressive integrated moving average, ARIMAX = regression with ARIMA errors, FS = floating search, SA = simulated annealing

Fig. 3

Three best performing models. Light grey line = ground truth, dark grey line = prediction. ARIMAX-W = regression with ARIMA errors using features identified by Whitt et al. [13], RLS = recursive least squares, SA = simulated annealing, FS = floating search

Fig. 4

Error as function of predictive horizon for the three best performing models. ARIMAX-W = regression with ARIMA errors using features identified by Whitt et al. [13], RLS = recursive least squares, SA = simulated annealing, FS = floating serach, MAPE = mean absolute percentage error