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Table 5 Comparison of the forecasting performance achieved with related works stratified by forecasting horizon

From: Enhanced forecasting of emergency department patient arrivals using feature engineering approach and machine learning

Forecasting Horizon

Reference and year

Method(s) used

MAPE(%)

RMSE

3 up to 7 days ahead

Marcilio et al. [42] 2013

GLM and GEE

4,5–9,9

not applied

Xu [18] 2016

ARIMA-LR (smoothing), ARIMA-LR and GLM

6,8–9,6

70,5–104

Calegari et al. [46] 2016

SARIMA, SS and SMHW

10,67–12,01

not applied

Asheim et al. [48] 2019

Poisson time-series regression model

31–38

not applied

Jilani et al. [15] 2019

NN e FTS

3.03–7,42

6,16–16,55

Whitt et al. [3] 2019

SARIMAX

8,4–10,59

not applied

Zhang et al. [35] 2019

ARIMA, SVR and ARIMA-SVR

7,02–7,36

19,20–20,34

Choudhury and Urena [1] 2020

ARIMA, HW and NN

not applied

1,55–27,86

Yousefi et al. [21] 2020

LSTM

5,59–6,31

not applied

Erkamp et al. [6] 2021

MLR

8.68–12.20

not applied

Rocha and Rodrigues [5] 2021

RNN, XGBoost and RNN-XGBoost

not applied

4,7–4,9

Vollmer et al. [20] 2021

GLMNET, LM and GBM

6,7–8,6

not applied

Sudarshan et al. [7] 2021

RF, LSTM and CNN

8,91–10,69

not applied

Cheng et al. [61] 2021

SARIMAX, HW and VAR

5–15,3

not applied

Murtas et al. [83] 2022

ARIMA

6,6–11,2

not applied

Petsis et al. [40] 2022

XGBoost

6,5–6,91

22,96–23,9

Tuominen et al. [54] 2022

ARIMAX, RLS-FS and RLS-SA

6,6–6,9

not applied

Tello et al. [57] 2022

ARIMA and SVR

3,34–5,17

14,10–20,57

Zhang et al. [41] 2022

SVR, RF and KNN

8,81–9,63

26,84–30,23

Current study 7-day test set

ED ARMA

GLMNET and SVM-RBF

5,48–5,52

11,44–11,69

ED JOON

SVM-RBF and LightGBM

4,61–4.73

15,95–16,22

ED RG

RF and LightGBM

6,55–6,81

11,93–12,87

ED RPH

XGBoost and SVM-RBF

5,90–6,21

14,89–15,45

ED SCG

XGBoost and NNAR

5,08–5,21

11,73–11,93

8 up to 45 days ahead

Marcilio et al. [42] 2013

GLM and GEE

8,7–12,8

not applied

Bergs et al. [45] 2014

ETS

2,63–4,76

not applied

Calegari et al. [46] 2016

SARIMA, SS and SMHW

11,35–12,29

not applied

Juang [19] 2017

ARIMA

8,91

not applied

Carvalho-Silva et al. [23] 2018

ARIMA

5,22–9,29

not applied

Jilani et al. [15] 2019

NN e FTS

2,01–2,81

57,30–167,89

Khaldi et al. [27] 2019

EEMD-ANN, DWT-ANN and ANN

not applied

52,86–149,23

Vollmer et al. [20] 2021

GLMNET, LM and GBM

6,8–8,9

not applied

Pekel et al. [39] 2021

PSO-ANN, Bayesian ANN and GA-ANN

6–8,8

53.29–83.85

Tuominen et al. [54] 2022

ARIMAX, RLS-FS and RLS-SA

7,4–7,8

not applied

Susnjak et al. [78] 2023

Voting regressor

8,9–12,8

10,60–15,9

Gafni-Pappas et al. [50] 2023

RF and XGBoost

not applied

18,94–18,96

Current study 45-day test set

ED ARMA

XGBoost and GLMNET

5,90–5,90

12,62–12,64

ED JOON

SVM-RBF and RF

4.98–5.01

17,25–17,43

ED RG

XGBoost and RF

6,23–6,28

11,42–11,47

ED RPH

SVM-RBF and NNAR

5,71–5,85

14,25–14,37

ED SCG

XGBoost and RF

5,64–5,69

12,61–12,56

  1. ANN Artificial Neural Networks, ARIMA Autoregressive Integrated Moving Average, ARIMAX Autoregressive Integrated Moving Average with Explanatory Variable, ARIMA-LR ARIMA-Linear regression, CNN Convolutional Neural Networks, DBN Deep Belief Network, EEMD-ANN Artificial Neural Networks with Ensemble Empirical Mode decomposition, XGBoost Extreme Gradient Boosting, RLS-FS Floating Search with Recursive Least Squares, FTS Fuzzy Time Series, CNN-GRU Gated recurrent unit with convolutional neural networks, GA-ANN Genetic Algorithm-based ANN, GLMNET Generalized Linear Models via Coordinate Descent, GLM generalized linear model, GBM Gradient Boosting Machines, HW Holt-Winters, KNN k-nearest neighbours, LM Linear model, LSTM Long Short-Term Memory, MLR Multiple Linear Regression, MSARIMA Multivariate Autoregressive Integrated Moving Average, NN Neural Network, NNAR Neural Network Autoregression, PSO-ANN Particle Swarm Optimization algorithm-based ANN, RF Random Forest, RNN Recurrent Neural Networks, RBM Restricted Boltzmann machines, SARIMA Seasonal Autoregressive Integrated Moving Average, SARIMAX Seasonal Autoregressive Integrated Moving Average with external variables, SS Simple Seasonal Exponential Smoothing, RLS-SA Simulated Annealing with Recursive Least Squares, SVM-RBF Support Vector Machine with Radial Basis Function, SVR Support Vector Regression, VAR Vector Autoregression Model