Predicting use of Intensive Care Units during the COVID-19 Pandemic

doi:10.21203/rs.3.rs-2058082/v1

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Predicting use of Intensive Care Units during the COVID-19 Pandemic

https://doi.org/10.21203/rs.3.rs-2058082/v1

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With the prevalence of the SARS-CoV-2 pandemic, sudden planning needs emerged in intensive care units of health care centers in many countries, particularly in Chile. In such units, the most severe COVID-19 patient requires specific treatment. This fact stressed decision-making at the operational level. It then became necessary to understand the dynamics of patient arrival to predict the number of additional units required for the future. We propose ten approaches to represent the dynamics and predict the number of additional ICU beds required in the future. Machine learning models and classical time series analysis algorithms allow upper and lower bounds to be set for the number of units needed. Evaluating the predictions with 2020 and 2021 data in three representative geographic regions produces lower errors in the largest of the regions. The low errors produced by the classic Holt-Winters model suggest that the data series have seasonality and trend characteristics. Although the models were only evaluated in three regions, extension to other similar situations requires the training of models with the region's data.

COVID-19

machine learning

ICU beds prediction

The pandemic due to the SARS-CoV-2 coronavirus caused a sudden increase in the requirement for hospital facilities in Chile. This fact has highlighted the critical importance of intensive care units (ICU) to provide the appropriate treatment for each patient. The insufficient knowledge that existed about treatments for this disease in March 2020, when the World Health Organization (WHO) declared a world epidemic, produced a high demand in hospitals as a result of the complex health conditions presented by some of the patients who required the intensive care provided in ICUs hospitals ¹. Under the WHO recommendations, countries have adopted various measures to stop the spread of the contagion between people. In Chile, the authorities have established mandatory lockdowns of cities, banning of essential and nonessential businesses, travel restrictions, quarantines, and individual temporary permits to limit population movement within confined areas ². Despite these restrictions, it has been necessary to significantly increase the number of ICU units available in the country; however, the number of cases arising each day suggests that at some point, the available capacity could be insufficient.

The ICU is a critical unit in the operational planning of a health care facility because it provides life support to critically ill patients. Typically, patients are admitted to the ICU from other units of the hospital care center with different pathologies. As a result of the pandemic, the new influx of patients stresses regular planning. In the daily dynamics of an ICU, and in the absence of a pandemic, a distinction is made between the arrival of scheduled and nonscheduled patients to predict the necessary resources for each period. Scheduled patients require the service at a specific time to perform a specific operation, such as treatments and examinations. Nonscheduled patients suddenly require intensive care, such as injured patients or those with complicated conditions due to a previous operation in a hospital care center. During the pandemic, the influx of patients suddenly increased, stressing decision-making to deal with the available capacity ^3–5. During the pandemic, the arrival of patients suddenly increased. As such, knowing the number of patients who would require intensive care would allow for tackling the emergency in the best possible way. Likewise, by knowing in advance the possible point of collapse, the number of additional units needed could be identified by measuring the need for logistical resources ^6–9.

To predict the necessary resources needed for an ICU, it is convenient to identify a set of variables with direct influence that allows for obtaining a prediction model. From such variables, it is possible to partially characterize the growth pattern of the pandemic. Alban et al. ¹⁰ studied the flow of COVID-19 patients as it relates to scheduled patients, and the difference was observed in patients who presented with the disease because they have uncertain arrival rates. Zhao et al. ¹¹ performed a regression model that predicts the arrival of patients in the ICU. The model considers the existence of previous diseases, demographic data, symptoms, vital signs, and results of medical examinations. Ritter et al. ¹² infer the future ICU load from notified infections through a simpler statistical model that considers time lags. In a study by Chowdhury et al. ¹³, a multivariate prediction model based on clinical and transmission parameters is used to simulate the trajectories of COVID-19 outbreaks in 16 countries and estimate the number of new infections and deaths. Additionally, combining machine learning and epidemiological models allows for a short-term forecast of ICU burden ¹⁴. In such a study, the authors considered both the test’s positivity and the number of new infections. In turn, various machine learning models have made it possible to forecast the number of new cases ¹⁵. Rees et al. ¹⁶ consider the duration of stay of a COVID-19 patient in the ICU as crucial data for decision-making and establish that the average duration is from 4 to 21 days. Hao et al. ¹⁷ develop predictive models for disease severity according to the influence of socioeconomic factors and racial equity. In contrast to the main approaches in the literature, we predict the number of COVID-19 ICU beds at the regional level by considering data from PCR tests and measures taken to prevent spread in the region. Each region has several health care centers, and patients can be assigned to any of them.

Different geographical regions of a country present different dynamics of virus spread. The regions of Chile, distributed along a long and narrow country separated by the sea on one side and by the Andes Mountain range on the other side, generate a particular dynamic of disease spread. Determining the most suitable model for each case requires the selection of the appropriate variables and the specification of the model parameters according to the specific availability of resources present in the region. Then, variables such as the number of tests taken, the rate of positivity, and restrictions to mobility adopted are relevant in predicting the ICU burden. In turn, the versatility of the machine learning and forecasting models allows for testing multiple regressors and selecting the most appropriate for each case. A predictive model would allow early estimation of the arrival of patients in the ICU to meet the emergent need for planning and ensure the best use of available resources.

Our current study reveals that an ensemble of forecast models generates lower and upper bounds for the number of COVID-19 ICU beds needed in the future. The models process a set of relevant data recorded during 2020 and 2021 in three regions of Chile. The three regions are representative of the other regions of the country in terms of their population. Specifically, we selected a small population region, an intermediate population region, and the country's largest region. Prediction models are designed with two approaches: the first approach considers time series data on the number of COVID-19 ICU beds used, and the second approach includes feature data that could influence the time series.

Our study consists of the following sections: Section 2 describes the modeling, and Section 3 contains the results. In Section 4, the discussion of the results is presented, and in Section 5, conclusions and future work are detailed.

Selection of regions

Most of the Chilean mainland is a long, narrow strip of land with natural lateral borders with the Andes Mountains and the Pacific Ocean. The geography and the measures taken at border posts and at the main airport affected the dynamics of the pandemic's spread. To study the prediction of the number of COVID-19 ICU beds required for the future, we selected three regions: the Metropolitan Region, which has the largest population; an intermediate region, the BioBío Region; and a small region, the Ñuble Region. Table 1 shows the three regions' characteristics ¹⁸. Note that the Population Percentage column corresponds to a percentage related to the country's population.

Table 1

Characteristics of the three regions.
	Population	Population Percentage [%]	Area [Km²]	Population Density per Km²
Region 1 (Ñuble)	480,609	2.7	13,178.5	36.47
Region 2 (BioBío)	1,556,805	8.9	23,890.2	65.17
Region 3 (Metropolitana)	7,112,808	40.5	15,403.2	61.77

Modeling description

This section presents both the modeling used to predict the number of COVID-19 ICU beds required for the future and the description of the data. Two approaches are considered for prediction: the first approach predicts directly from the series with the number of occupied COVID-19 ICU beds (Series Modeling, SM). In SM, the data of the series are ordered in such a way that one can predict a fourth data point from three data points in sequence. The second approach performs the prediction, including the influence of related data series, and then modeling considers several features (Features Modeling, FM). FM defines the variables that influence the predicted variable using machine learning and classical algorithms. The independent variables or features are the number of PCR tests, the number of positive PCR tests, the number of ICU beds available, the number of deaths, and a numerical factor characterizing the degree of confinement. In both approaches, we shift the data series of the number of occupied COVID-19 ICU beds in 2 days to establish a prediction for the following two days.

Machine learning is a discipline that contains tools needed to build mathematical models that reflect the behavior of a phenomenon taking into consideration a set of historical data ^19,20. The resulting model can be a regressor or a classifier. The output variable y in Eq. (1) assumes a numerical value in the former case. In the second equation, y is a vector containing as many numerical values as data classes. Eq. (1) has a fixed structure; however, its unknown parameters must be adjusted so that the solved equation is representative of the historical data. In models such as neural networks or linear regression, the parameters of the equation are obtained by solving an optimization problem that minimizes the error produced between the given equation and the actual value stored in the data. In the case of the random forest, the resulting model is a set of decision trees, each tuned for a part of the data. To evaluate the model's performance, it is typical to separate the data into two sets, one to obtain the parameters and the other to evaluate the resulting model.

y = f (x₁, x₂, …, x_n) (1)

We consider six approaches to represent f(x) from Eq. 1. A set of decision trees is combined in a random forest (RF) in the first approach. Similarly, a linear equation whose parameters are estimated by linear regression constitutes the second approach (LR). The third approach is a feed-forward neural network corresponding to a multilayer perceptron (MLP), while the fourth approach is a recurrent neural network with long short-term memory (LSTM) cells. The remaining models are the moving average (MA) and the Holt-Winters model (HW). A short description of the models follows below, and for more details, we suggest consulting Goodfellow et al. ¹⁹ and Hyndman & Athanasopoulus ²¹.

RF: this is a machine learning algorithm that builds a family of decision trees to relate the available data. The algorithm constructs each decision tree with a randomly selected data subset. Such a subset is chosen with part of the rows and a part of the columns of the data. The constructed forest produces the result as a weighting of the partial responses coming from the decision trees. We use ten decision trees as a parameter of the Sci-kit learn function ²².
LR: this algorithm considers a linear equation for f(x) according to Eq. (2). Each variable x_j in the equation is weighted with a parameter w_j, which must be determined. Then, the LR linearly relates the dependent variable to the independent variables of a given phenomenon. The solution to an optimization problem that minimizes the difference between the value generated by Eq. (2) and the actual value corresponds to the parameter values. We use the Scikit-learn LR.

$$y= {w}_{0}+{w}_{1}{x}_{1}+\dots +{w}_{n}{x}_{n}$$

MLP: the neural network f(x) is a complex equation to represent a phenomenon according to Eq. (1). f(x) can be represented graphically by a graph whose nodes are the algebraic terms of the equation, and the weights of the arcs correspond to the parameters. The algebraic term defined at each node of the graph is the activation function. As in LR, an optimization problem allows for estimating the value of the parameters that minimizes the error produced by the equation.
RNN: this is a particular neural network representing phenomena that occur as a time series. Thus, if y_t is the value of the dependent variable at time t, then y_t+1 can be estimated as a function of the value of the variable and parameters of the equation that occurred at a previous timestep (y_t, w_t), as represented in Eq. (3) for n timesteps. We consider an RNN with nodes of long short-term memory type that contains components of the equation to facilitate the convergence of the optimization algorithm.

$${y}_{t+1}=f\left({y}_{t},{w}_{t}\right) t=\text{0,1},\dots ,n$$

HW: this method performs the prediction considering the trend and seasonality of the series. The series is considered with the number of COVID-19 ICU beds available. Thus, if b_t estimates the trend in period t, s_t estimates the seasonality, and m is the period of seasonality, then a trend-seasonality value l_t can be obtained according to Equations (5), (6) and (7). From l_t, Eq. (4) predicts the variable y_t+h for periods y + 1, y + 2, and so on. The model considers the parameters w₁, w_2, and w₃.

$${y}_{t+h|t}={l}_{t}+{hb}_{t}+{s}_{t+h-m\left(k+1\right)} h=1, 2,\dots$$

$${l}_{t}={w}_{1}\left({{y}_{t}-s}_{t-m)}\right)+{(1-{w}_{1})(l}_{t-1}+{b}_{t-1})$$

$${s}_{t}={w}_{3}\left({{y}_{t}-l}_{t-1}-{b}_{t-1}\right)+{\left(1-{w}_{3}\right)s}_{t-m}$$

$${b}_{t}={w}_{2}\left({{l}_{t}-l}_{t-1}\right)+{\left(1-{w}_{2}\right)b}_{t-1}$$

AM: in this equation, y_t is obtained by averaging the values of the series within k periods with m = 2k + 1, and is known as AM of order m, as shown in Eq. (8).

${y}_{t}$ = $\frac{1}{m}\sum _{j=-k}^{j=k}{y}_{t+j}$ (8)

Selection of variables

The speed with which measures were taken from the beginning of the pandemic allowed numerical data to be systematically generated from the first day. Although in the early days, some data required verification on subsequent days, as time went by, such data were confirmed, providing more accurate reliability to the reported values. This fact was due to the construction of computational tools that were gradually implemented to allow data input in real time via the internet. Access to all data used in this study is freely available ²³. This section presents the description of 5 features: x₁ is the daily number of PCR tests performed; x₂ is the daily number of tests that are positive; x₃ is the number of ICU beds available on a particular day; x₄ is the number of deaths on that day due to COVID-19; and x₅ is the daily rate of regional confinement. The variable y corresponds to the number of COVID-19 ICU beds required on that day with a shift of two days.

Number of performed and positive PCR tests (x₁, x₂). The databases allow for direct extraction of the variable x₁ and include a daily positivity index calculated as the number of PCR tests performed that were positive, divided by the total number of tests performed on that day. Then, the variable x₂ is obtained by multiplying the positivity index by the total number of tests performed on the same day. Figure 1 shows the evolution of both variables for the three regions. In alignment with the size of the regions, the figure shows that the highest number of PCR tests performed occurred in region 3, then in region 2, and then in region 1. In all three regions, the number of performed PCR tests and the number of positive tests have a regularity from Monday to Friday and decrease on weekends. During April, May, and June 2020, PCR testing was mainly concentrated in the largest region, and the highest number of positive cases was also found in this region.

The number of ICU COVID-19 beds enabled (x₃). The database contains the availability of critical beds at a regional level, aggregated by day as the number of ICU beds occupied by COVID-19 patients, ICU beds occupied by non-COVID-19 patients, and ICU beds enabled ²³. Figure 2 shows the progression of the number of COVID-19 ICU beds occupied and the number of positive PCR tests. In all three regions, there are similar trends between both curves, (i.e., increasing or decreasing the number of positive PCR tests is associated with increasing or reducing the use of the ICU). This pattern is more notable in region 3, showing a slight shift in the number of occupied beds in relation to the number of positive tests.

The number of deaths (x₄). The database contains the number of deaths caused by COVID-19 by region ²³. Figure 3 depicts the progression of the number of deaths. The daily raw data available are provided as a cumulative value. If i is the current day, i-1 is the previous day, and α is the accumulated value, then the daily value ω is given by Eq. (9). At first glance, the three graphs in Fig. 3 show similar trends; however, on the right-hand y-axis, there are significant differences in the number of fatalities between the first two and the third regions. While the maximum number of deaths by day is 12 and 47 for regions 1 and 2, respectively, in the third region, this number is 834. In addition, the figure depicts that the most significant impact of the pandemic in region 3 occurred in the first months; after that period, there was less variability in the number of deaths.

ω _i = α_i − α_i−1 (9)

Lockdown (x₅). The pandemic managers applied different degrees of lockdown in different periods in some cities. In some periods, there was a total lockdown of the population in some cities. We consider an index to measure the degree of daily lockdown of the population of a region ²⁴. The daily index of lockdown l_i corresponds to the daily percentage of people in lockdown in the region. Let a_ij =1 when city j is under lockdown on Day i and 0 otherwise. Moreover, let p_j be the number of people living in city j, let p_j be the region's population, and let n be the number of cities that belong to the region; then, Eq. (10) gives li.

$${l}_{i}=\frac{\sum _{j=1}^{n}{a}_{ij}{p}_{j}}{{p}_{T}}\times 100$$

Data availably

The datasets analysed during the current study are available in the Innovación, M. de C., Tecnología, Conocimiento, Datos-COVID19 repository, https://github.com/MinCiencia/Datos-COVID19/ or alternatively in the Gobierno de Chile website (Gob.cl), https://www.gob.cl/pasoapaso/cifrasoficiales/

Performance measures

To evaluate the performance of the algorithms, the data were separated into two groups divided into 80% with the first part of the series (training data) and 20% with the most recent data (testing data). To measure the prediction performance, we consider the mean absolute error (MAE), the root-mean-square error (RMSE) and the mean absolute percentage error (MAPE (%)) defined according to Equations (11), (12) and (13).

$MAE=\frac{1}{n}\sum _{i=1}^{n}|{y}_{i}-{\widehat{y}}_{i}$ | (11)

$$RMSE= \sqrt{{\sum }_{i=1}^{n}{({y}_{i}-{\widehat{y}}_{i})}^{2}/n}$$

$$MAPE\left(\%\right)= \frac{100}{n}\sum _{i=1}^{n}|{y}_{i}-{\widehat{y}}_{i}|/{y}_{i}$$

Software and hardware

The computational implementation was performed using several libraries. The RF, RL, and MLP models were implemented with the Scikit-learn library,²² and the neural network with LSTM cells was implemented in Keras,²⁵. For data preparation and visualization, the Pandas,²⁶ and Matplotlib,²⁷ libraries were used. The final computational code is contained in 3 Jupyter notebooks, one for each region,²⁸. The computational experiment was performed on a computer with Core i7 processor, 16 GB RAM and Windows 10.

The classical HW algorithm generates the smallest prediction errors under the SM approach. Table 2 presents the error evaluations for the six models. MAE, RSME, and MAPE (%) are obtained with the test period data from the three regions. In the SM approach, the data are treated as a time series, and a value of the series is predicted from past data. Although the prediction results have a low error in all models, the difference from the classical Holt and Winters model is noticeable, as observed in the last column of Table 2. In region 1, in which the values are lower-dimensional than in the other two regions, HM perfectly predicts the training data of the series. For this region, the neural networks have a slight advantage over the moving average, but the three models perform slightly worse than the prediction made by LR. Similar behavior is observed in the results for regions 2 and 3. Such results suggest that HW, with its three parameters, captures the seasonality and trend-cycle effects of the data series. In fact, in Fig. 2, which plots the data series, well-defined upward and downward trends are observed. In addition, peaks and valleys are observed, which for HW correspond to seasonality.

Table 2

Performance of SM predictions.
Region 1
Metrics	LR	LSTM	MLP	RF	MA	HW
MAE	0.88	0.93	0.93	1.24	0.94	0.00
RMSE	1.23	1.26	1.30	1.62	1.26	0.00
MAPE (%)	11.90	12.60	12.90	16.80	12.90	0.00
Region 2
MAE	2.43	2.99	2.37	3.93	3.19	1.51
RMSE	3.14	4.06	9.85	5.28	4.02	2.08
MAPE (%)	7.20	9.00	6.90	11.40	8.80	3.50
Region 3
MAE	9.26	12.85	11.09	14.57	14.06	8.62
RMSE	11.53	15.92	13.20	17.91	16.80	10.25
MAPE (%)	2.90	4.00	3.40	4.70	4.30	2.60

Neural networks have lower prediction error than LR and RF for all three regions considering the FM approach. Table 3 shows the results for the four models, LR, LSTM, MLP, and RF, for the three regions. The lowest error value among the four models is identified in bold font. In region 1, which is the smallest region in population size, the MLP network generates the lowest prediction error with the test data. Specifically, the observed error is approximately 3 ICU beds, which corresponds to approximately 25% of the estimate of the number of ICU beds needed for the next two days. Furthermore, the LSTM network produces the lowest errors for regions 2 and 3. In particular, in Region 2, the prediction has the lowest error with the LSTM network, while the other three models generate a similar performance. In Region 2, the percentage error increases relative to Region 1 (MAPE (%)) so that the prediction error occurring in the number of COVID-19 ICU beds is approximately 16 according to MAE. The percentage error in Region 3 is similar to that of Region 2 (33. 60%), implying an error in estimating the number of beds for the next two days of approximately 109–110 COVID-19 ICU beds. These results suggest that neural network-based modeling that considers the influence of characteristics on the dependent variable better captures the variation of the dataset over time.

Table 3

Performance of FM predictions.
	Region 1
Metrics	LR	LSTM	MLP	RF
MAE	2.92	6.95	1.72	11.14
RMSE	3.67	7.19	2.51	11.62
MAPE (%)	39.70	97.50	24.50	157.70
	Region 2
MAE	25.14	15.83	23.79	24.37
RMSE	31.43	22.85	30.64	28.55
MAPE (%)	58.90	33.40	53.60	68.10
	Region 3
MAE	128.30	109.06	171.45	131.28
RMSE	168.01	150.92	191.99	156.07
MAPE (%)	41.80	33.60	55.70	43.40

The combined prediction of all models indicates benchmarks to support decision-making on enabling and releasing COVID-19 ICU beds. Interpreting MAE as an indicator of the number of beds needed for the next two days during the period of the test data, it is observed that for Region 1, the number ranges between 0 and 2; for Region 2, the range is between 2 and 4, while for Region 3, the range is between 3 and 5. The models can then be assembled in a computational tool to provide direct support for hospital logistics decision-making.

The SARS-CoV-2 pandemic generated a sudden need for tools to support decision-making in the logistical management of health care institutions. A critical need arises in intensive care units where the most severe patients with COVID-19 require specific treatment. Thus, health care facilities have had to make decisions about additional ICU beds. The need then arose to understand the dynamics of patient arrivals to assess the number of ICU beds required for the future. Considering the tools available in machine learning and classical time series algorithms, we evaluated ten techniques to predict the number of COVID-19 ICU beds required over a period of two days. We have put forward two approaches for data analysis. The first approach considers the time series, while the second approach includes additional features that eventually influence the time series. We have found that by considering the results of the models together, it is possible to establish a lower and an upper limit for the number of beds required in an ICU for a future period.

This study showed that the isolated time series analysis approach produces better predictions for the number of COVID-19 ICU beds required over a period of two days. Under this approach, it was possible to consider classical forecasting models, particularly the Holt-Winters model, which produces the most numerically accurate prediction. In addition, the similarity between the predictions of the different models under this approach suggests that the models appropriately capture the phenomenon behind the time series. The highly effective performance of the Holt-Winters model suggests that the series has trend and seasonality behavior, which are factors in the fundamentals of this model. This fact is observed in the series’ graphic display in which variations correspond to clear upward and downward trends and identify outlining trends and seasonality.

The dynamics of events occurring during the pandemic naturally stress the management of health care institutions. This fact extends to the operational management of the ICU. This study presents a method to determine ranges to support decision-making about the eventual provision of new ICU beds. The prediction for the future may be upward or downward. In the first situation, the capacity of the facilities is at stake because additional units may eventually be needed. In the second situation, there is a release of ICU beds, increasing care capacity. As such, having the range of variation for the future allows for acting according to the needs. Although our study considers the prediction for a period of two days, this parameter can be adjusted for any number of days. The models can be trained by preparing the data within the required number of days since the evaluation and training phases of the models have low computational requirements.

Although our research only considers three regions of the country, these regions have been selected in a representative manner so that the models could be trained with data corresponding to any region. The results show a regular performance of the algorithms for the three regions, which allowed us to infer that the extension of the use of the models to the other regions could eventually yield similar results.

Our study presented tools for developing a technology that operates in real time and is available to the management team of a health care institution. We note that, a computational tool requires an appropriate user interface oriented toward specialized personnel in the health care field. Furthermore, the tool must consider that the data are updated daily and must therefore be synchronized automatically. In addition, the model training tool should be run automatically every time new data become available, ideally at the close of each day when the data are updated. The tool should immediately produce the forecast from such an update since the computational time is too low.

In this study, we evaluated prediction models to forecast the arrival of the number of COVID-19 patients in the ICU of a health care institution. Machine learning and time series forecasting models produced numerical results for two subsequent days. A different number of days requires only appropriate data preparation. A byproduct of the research is that computational codes are available to utilize software tools oriented to users in charge of managing health care institutions. The predictions made by the models allows for identifying ranges of the number of patients expected in the coming days. Although the study is limited to three regions of Chile, the models can be trained for similar situations in other regions of the country and potentially have applicability in other countries as well.

Author contributions

All authors had similar participation during the research and writing of the article.

Authors agreement

All authors have agreed to all the contents.

Disclosure Statement

The authors report no conflicts of interest

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No competing interests reported.

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Abstract

Figures

Introduction

Materials And Methods

Selection of regions

Modeling description

Selection of variables

Data availably

Performance measures

Software and hardware

Results

Discussion

Conclusion

Declarations

Author contributions

Authors agreement

Disclosure Statement

References

Additional Declarations

Status:

Version 1