A Tri-Model Prediction Approach for COVID-19 ICU Bed Occupancy: A Case Study
<p>An illustration of the SEIR epidemiological model [<a href="#B2-algorithms-16-00140" class="html-bibr">2</a>].</p> "> Figure 2
<p>Impact on model outputs according to covariates from government interventions [<a href="#B24-algorithms-16-00140" class="html-bibr">24</a>].</p> "> Figure 3
<p>Research methodology flowchart for all predictive models.</p> "> Figure 4
<p>ARTXP and ARIMA process.</p> "> Figure A1
<p>One week Predicted vs. Actual ICUs—Thessaloniki.</p> "> Figure A2
<p>Two weeks Predicted vs. Actual ICUs—Thessaloniki.</p> "> Figure A3
<p>Three weeks Predicted vs. Actual ICUs—Thessaloniki.</p> "> Figure A4
<p>One week Predicted vs. Actual ICUs—Northern Greece.</p> "> Figure A5
<p>Two weeks Predicted vs. Actual ICUs—Northern Greece.</p> "> Figure A6
<p>Three weeks Predicted vs. Actual ICUs—Northern Greece.</p> "> Figure A7
<p>One week Predicted vs. Actual ICUs—Greece.</p> "> Figure A8
<p>Two weeks Predicted vs. Actual ICUs—Greece.</p> "> Figure A9
<p>Three weeks Predicted vs. Actual ICUs—Greece.</p> "> Figure A10
<p>One week Predicted vs. Actual ICUs—Attica.</p> "> Figure A11
<p>Two weeks Predicted vs. Actual ICUs—Attica.</p> "> Figure A12
<p>Three weeks Predicted vs. Actual ICUs—Attica.</p> ">
Abstract
:1. Introduction
2. Literature Review
3. Research Design
3.1. Data Collection & Pre-Processing
3.2. Models & Algorithms
3.2.1. ARIMA and SARIMAX
3.2.2. ARTXP and ARIMA
3.2.3. Multivariate Regression
3.3. Evaluation Metrics
3.3.1. Mean Absolute Percentage Error (MAPE)
3.3.2. Root Mean Squared Error (RMSE)
3.3.3. R-Squared ()
3.3.4. Mean Absolute Error (MAE)
3.4. Limitations
4. Results & Evaluation
5. Conclusions
5.1. Implications
5.2. Future Work
- Regarding the choice of features for forecasting, the utilization of a correlation process that relates virus epidemiological characteristics with metrics may yield even better results [67]. In addition, the impact of temperature, climate and incubation period are important factors which can be used in correlation with demographics or country characteristics [11]. Furthermore, different government mitigation actions (lockdown, social distancing etc.) in terms of time and strictness are also crucial and could be assigned extra weight in the aggregated formula for the predictions [11,68].
- Time series modelling, especially predicting infectious diseases like COVID-19, has heavily exploited LSTM and RNN models. These models predict complex time series trends. They rely on time series length, frequency of observations, number of variables, and training data. These algorithms learn from similar trends, and with more data forecasting accuracy may be improved. Data augmentation and subsampling handle the trade-off between enough data to train the model and too much data that makes it computationally intractable or may cause overfitting. Greece initially had low volume of data. A held-out validation set should rigorously examine the model to avoid overfitting to training data. Thus, enough data against too much data must be carefully considered. Considering the above, future research could also include tests with LSTM and RNN algorithms.
- We also aim to enhance the forecasting capabilities in geographical partitions by utilizing Deep Learning (DL) and ANN. An extra step regarding COVID-19 ICU forecasting would be the use of different and/or combined machine and deep learning algorithms. Since the amount of data is increasing over time and there might be also other parameters that could have a significant impact on COVID-19 infection [9], utilizing DL and ANNs could make a difference. Moreover, other regression algorithms, like RF regressor or XGB regressor could be tested, possibly combined with ANNs like LSTMs [16].
- Finally, according to the reported limitations, identification of time series trend traversal could improve forecasting accuracy. We aim to develop a rule-based methodology that effectively analyses trends in ICU time series and fully adapts them according to changes in trends. Hence, this process would enhance forecasting capabilities by improving the selection of the time series training dataset.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
ICU | Intensive Care Unit |
ARTXP | Autoregressive Tree Models for Time-Series Analysis |
ARIMA | Autoregressive Integrated Moving Average |
SARIMAX | Seasonal Autoregressive Integrated Moving Average with Exogenous Regressors |
MAPE | Mean Absolute Percentage Error |
SIR | Susceptible-Infectious-Recovered |
SEIR | Susceptible-Exposed-Infectious-Recovered |
SIRD | Susceptible-Infectious-Recovered-Dead |
ML | Machine Learning |
RF | Random Forest |
ROC | Receiver Operating Characteristic |
AUC | Area Under the ROC Curve |
LoS | Length of Stay |
CDC | Centres for Disease Control and Prevention |
RNN | Recurrent Neural Network |
LSTM | Long Short Term Memory |
GRU | Gated Recurrent Units |
DT | Decision Trees |
ANN | Artificial Neural Network |
K-NN | K-Nearest Neighbour |
LR | Linear Regression |
BMI | Body Mass Index |
XGB | Extreme Gradient Boosting |
Coefficient of Determination | |
AR | Autoregression |
MA | Moving Average |
ARX | Autoregressive Exogenous Regressors |
MAX | Moving Average Exogenous Regressors |
DL | Deep Learning |
Appendix A. Supplementary Captions
Appendix A.1. Table
ICU Predictions on data from 1 October 2020 to 22 March 2021 with Output Variance: 61.436 | ||||||||||||
Date | Lower Limit | Output Over Error | Output | Upper Limit | Avg Output | Pred. Value | Actual ICU | Success on Pred. Value(%) | Sucess on Output(%) | Within Limits | Error on Week(%) | |
Week 1 | 23/03 | 631 | 675 | 692 | 753 | 688 | 690 | 678 | 98 | 98 | Yes | −2.51 |
24/03 | 632 | 676 | 693 | 754 | 689 | 691 | 681 | 99 | 98 | Yes | ||
25/03 | 631 | 675 | 692 | 753 | 688 | 690 | 703 | 98 | 98 | Yes | ||
26/03 | 633 | 677 | 694 | 755 | 690 | 692 | 704 | 98 | 99 | Yes | ||
27/03 | 638 | 681 | 699 | 760 | 695 | 697 | 718 | 97 | 97 | Yes | ||
28/03 | 645 | 688 | 706 | 767 | 702 | 704 | 726 | 97 | 97 | Yes | ||
29/03 | 653 | 696 | 714 | 775 | 710 | 712 | 723 | 98 | 99 | Yes | ||
Week 2 | 30/03 | 660 | 610 | 721 | 782 | 693 | 707 | 735 | 96 | 98 | Yes | −15.39 |
31/03 | 667 | 616 | 728 | 789 | 700 | 714 | 738 | 97 | 99 | Yes | ||
01/04 | 674 | 622 | 735 | 796 | 707 | 721 | 741 | 97 | 99 | Yes | ||
02/04 | 681 | 628 | 742 | 803 | 713 | 728 | 747 | 97 | 99 | Yes | ||
03/04 | 689 | 635 | 750 | 811 | 721 | 736 | 750 | 98 | 100 | Yes | ||
04/04 | 697 | 641 | 758 | 819 | 729 | 743 | 750 | 99 | 99 | Yes | ||
05/04 | 706 | 649 | 767 | 828 | 737 | 752 | 748 | 99 | 97 | Yes | ||
Week 3 | 06/04 | 715 | 589 | 776 | 837 | 729 | 753 | 746 | 99 | 96 | Yes | −24.10 |
07/04 | 724 | 596 | 785 | 846 | 738 | 761 | 762 | 100 | 97 | Yes | ||
08/04 | 734 | 603 | 795 | 856 | 747 | 771 | 772 | 100 | 97 | Yes | ||
09/04 | 744 | 611 | 805 | 866 | 757 | 781 | 764 | 98 | 95 | Yes | ||
10/04 | 755 | 619 | 816 | 877 | 767 | 791 | 777 | 98 | 95 | Yes | ||
11/04 | 766 | 628 | 827 | 888 | 777 | 802 | 786 | 98 | 95 | Yes | ||
12/04 | 778 | 637 | 839 | 900 | 788 | 814 | 790 | 97 | 94 | Yes | ||
Average Accuracy: | 98 | 97 |
Appendix A.2. Figures
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Variable | Model Execution Date |
---|---|
16 November 2020 | |
23 November 2020 | |
30 November 2020 | |
… | … |
1 March 2020 | |
8 March 2020 |
Geographical Area | Weeks Ahead Prediction Target | ARTXP and ARIMA (Actual/3d) (%) | ARIMA and SARIMAX (Actual/3d) (%) | Multivariate Regression (Actual/3d) (%) | All Models’ Average (Actual/3d) (%) |
---|---|---|---|---|---|
Thessaloniki | 1 | 12.22/11.36 | 13.35/12.41 | 13.09/11.88 | 11.53/10.69 |
2 | 26.46/25.12 | 27.86/25.74 | 22.63/20.77 | 21.80/19.53 | |
3 | 41.97/39.89 | 32.72/31.82 | 35.95/34.17 | 29.80/27.95 | |
Northern Greece | 1 | 17.26/15.92 | 9.36/7.99 | 9.74/8.12 | 10.88/9.12 |
2 | 32.05/29.52 | 21.80/19.40 | 18.80/16.50 | 20.61/17.98 | |
3 | 52.56/49.56 | 34.44/33.77 | 30.05/29.18 | 31.94/30.94 | |
Greece | 1 | 8.15/7.51 | 5.05/4.69 | 5.53/4.80 | 5.45/4.73 |
2 | 16.73/15.48 | 13.90/13.11 | 9.73/8.52 | 11.40/10.24 | |
3 | 24.15/23.28 | 23.49/22.87 | 21.32/19.80 | 18.81/17.86 | |
Attica | 1 | 7.07/6.47 | 5.83/4.60 | 7.92/6.26 | 6.26/4.79 |
2 | 14.76/13.79 | 12.20/10.87 | 14.07/12.74 | 12.14/11.07 | |
3 | 23.96/23.50 | 17.63/16.69 | 21.42/20.19 | 18.55/17.81 | |
Overall Average | 23.11/21.78 | 18.14/17.00 | 17.52/16.08 | 16.60/15.23 |
Geographical Area | Weeks Ahead Prediction Target | ARTXP and ARIMA (Actual/3d) (ICUs) | ARIMA and SARIMAX (Actual/3d) (ICUs) | Multivariate Regression (Actual/3d) (ICUs) | All Models’ Average (Actual/3d) (ICUs) |
---|---|---|---|---|---|
Thessaloniki | 1 | 16.88/16.00 | 16.81/15.25 | 15.98/14.17 | 16.56/15.14 |
2 | 35.58/33.38 | 33.13/30.13 | 25.03/22.33 | 31.25/28.61 | |
3 | 49.57/46.88 | 34.97/33.03 | 36.28/33.86 | 40.27/37.92 | |
Northern Greece | 1 | 41.96/39.20 | 20.54/16.86 | 76.28/74.66 | 46.26/43.57 |
2 | 70.25/65.88 | 48.01/43.60 | 39.26/35.50 | 52.51/48.33 | |
3 | 107.01/102.87 | 66.60/64.29 | 59.29/56.03 | 77.63/74.40 | |
Greece | 1 | 54.47/52.32 | 32.71/28.12 | 34.14/28.91 | 40.44/36.45 |
2 | 100.46/94.69 | 73.40/69.97 | 61.64/55.47 | 78.50/73.38 | |
3 | 139.97/134.86 | 124.58/122.09 | 113.60/107.02 | 126.05/121.32 | |
Attica | 1 | 19.87/19.32 | 18.17/15.21 | 23.29/18.08 | 20.44/17.54 |
2 | 46.40/45.08 | 35.21/32.10 | 42.24/37.27 | 41.28/38.15 | |
3 | 83.28/82.27 | 55.60/52.41 | 69.02/63.98 | 69.30/66.22 | |
Overall Average | 63.81/61.06 | 46.64/43.59 | 49.67/45.61 | 53.37/50.09 |
Geographical Area | Weeks Ahead Prediction Target | ARTXP and ARIMA (Actual/3d) (%) | ARIMA and SARIMAX (Actual/3d) (%) | Multivariate Regression (Actual/3d) (%) | All Models’ Average (Actual/3d) (%) |
---|---|---|---|---|---|
Thessaloniki | 1 | 94/95 | 94/95 | 91/93 | 93/94 |
2 | 86/88 | 85/88 | 83/88 | 85/88 | |
3 | 64/70 | 69/72 | 56/62 | 63/68 | |
Northern Greece | 1 | 91/92 | 97/98 | 96/97 | 95/96 |
2 | 76/79 | 91/94 | 85/87 | 84/87 | |
3 | 44/49 | 77/79 | 69/72 | 63/66 | |
Greece | 1 | 89/90 | 96/98 | 96/97 | 94/95 |
2 | 68/71 | 87/89 | 87/90 | 81/83 | |
3 | 45/48 | 70/72 | 58/62 | 58/61 | |
Attica | 1 | 99/99 | 98/99 | 98/98 | 98/99 |
2 | 93/94 | 97/97 | 96/96 | 95/96 | |
3 | 88/89 | 92/93 | 91/92 | 90/91 | |
Overall Average | 78/80 | 88/89 | 84/86 | 83/85 |
Geographical Area | Weeks Ahead Prediction Target | ARTXP and ARIMA (Actual/3d) (ICUs) | ARIMA and SARIMAX (Actual/3d) (ICUs) | Multivariate Regression (Actual/3d) (ICUs) | All Models’ Average (Actual/3d) (ICUs) |
---|---|---|---|---|---|
Thessaloniki | 1 | 11.67/10.26 | 12.52/11.59 | 12.19/11.29 | 12.13/11.04 |
2 | 27.37/25.63 | 25.53/23.37 | 19.26/17.71 | 24.05/22.24 | |
3 | 38.41/36.59 | 27.71/26.51 | 27.88/26.21 | 31.33/29.77 | |
Northern Greece | 1 | 33.38/30.49 | 15.19/12.27 | 31.90/28.99 | 26.83/23.92 |
2 | 58.37/54.49 | 37.95/34.32 | 32.58/29.33 | 42.96/39.38 | |
3 | 84.82/81.08 | 55.24/53.57 | 50.06/47.92 | 63.37/60.86 | |
Greece | 1 | 40.10/37.28 | 22.76/20.72 | 26.81/23.30 | 29.89/27.10 |
2 | 81.79/76.25 | 63.37/59.13 | 47.11/41.28 | 64.09/58.89 | |
3 | 112.47/107.98 | 104.12/100.45 | 100.24/93.55 | 105.61/100.66 | |
Attica | 1 | 17.91/17.45 | 15.00/11.94 | 20.27/15.88 | 17.73/15.09 |
2 | 41.30/38.79 | 32.80/29.29 | 36.20/32.49 | 36.77/33.52 | |
3 | 74.00/72.26 | 49.78/46.48 | 61.00/56.14 | 61.59/58.29 | |
Overall Average | 51.80/49.04 | 38.50/35.80 | 38.79/35.34 | 43.03/40.06 |
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Stasinos, N.; Kousis, A.; Sarlis, V.; Mystakidis, A.; Rousidis, D.; Koukaras, P.; Kotsiopoulos, I.; Tjortjis, C. A Tri-Model Prediction Approach for COVID-19 ICU Bed Occupancy: A Case Study. Algorithms 2023, 16, 140. https://doi.org/10.3390/a16030140
Stasinos N, Kousis A, Sarlis V, Mystakidis A, Rousidis D, Koukaras P, Kotsiopoulos I, Tjortjis C. A Tri-Model Prediction Approach for COVID-19 ICU Bed Occupancy: A Case Study. Algorithms. 2023; 16(3):140. https://doi.org/10.3390/a16030140
Chicago/Turabian StyleStasinos, Nikolaos, Anestis Kousis, Vangelis Sarlis, Aristeidis Mystakidis, Dimitris Rousidis, Paraskevas Koukaras, Ioannis Kotsiopoulos, and Christos Tjortjis. 2023. "A Tri-Model Prediction Approach for COVID-19 ICU Bed Occupancy: A Case Study" Algorithms 16, no. 3: 140. https://doi.org/10.3390/a16030140