Background
With an increasing global population and economy, the demand for healthcare continues to rise. Hospital crowding has become a major problem faced by large hospitals. Hospital adverse events increase with crowding, and have further effects on patient satisfaction, quality of nursing, treatment, wait time, and length of stay [
1‐
4]. A vast literature about overcrowding focus on the outpatient wards [
1,
5] and emergence departments [
4,
6]. Overcrowding appearing in the inpatient wards should also be paid attention to. When no inpatient beds are available to admit new inpatients, overcrowding would occur. Often, inpatient beds may be scarce as a result of too many patients with non-urgent medical conditions seeking healthcare.
The prediction of admissions is one piece of larger equation in the using hospital census, patient acuity, disease burden, allocation of resources and general management to improve hospital performance and improve patient outcomes. Much of research on hospital management focuses on the emergence of demand predicting [
7‐
10], forecasting of outpatient visits [
11,
12], inpatients discharge [
13], and patient volume [
14]. However, little published research is available regarding predicting the number of new admission inpatients. Monitoring and forecasting for new admission inpatients are important processes in making feasibility decisions for hospital resource management, reducing crowding, and improving the quality of medical care delivered.
Time series forecasting approaches have been adopted in other research fields, such as infectious disease [
15‐
18], power and energy [
19], finance and economy [
20,
21], traffic [
22], environment [
23], and hydrology [
24]. Among these approaches, for problems involving linear time series forecasting, the autoregressive integrated moving average (ARIMA) model is linear in that predictions of the future values are constrained to be linear functions of past observations. However, the prediction accuracy of ARIMA model is restricted due to its inability to capture the nonlinear relationships of time series in the real world. For nonlinear problems, the artificial neural network (ANN) has enhanced forecasting accuracy due to its intrinsic properties that can approximate any sort of arbitrary nonlinear function [
25]. More recently, hybrid forecasting models that combine the ARIMA and ANN models to handle linear and nonlinear relationships that exist in time series data have been extensively applied in many fields with high predictive performance [
16,
17,
19,
21,
26‐
28] . These previous studies remind us that the number of new admission inpatients as time series could also be predicted by hybrid models.
Our team has successfully applied the hybrid model with ARIMA and the nonlinear autoregressive neural network (NARNN) to the field of infectious diseases, for example forecasting the prevalence of schistosomiasis in humans in Qianjiang City and Yangxin City, China [
17,
28], and the incident cases of hand, foot, and mouth disease in Shenzhen, China [
29]. Wu [
16] also verified the feasibility of a hybrid ARIMA-NARNN model in forecasting the incidence of hemorrhagic fever with renal syndrome in Jiangsu Province, China. These literatures indicate combining both the ARIMA and NARNN models could improve the forecasting performance due to incorporate both the linear and nonlinear patterns found in the real world.
In this paper, we will explore whether the ARIMA-NARNN hybrid model is reliable for forecasting the number of new admission inpatients to a large hospital. Our aim is to forecast the monthly and daily new admission inpatients using time series models. This will enable hospitals to provide more efficient and better quality care to their patients.
Discussion
To our knowledge, this study was the first to develop and apply the time series models in admission patients research, with the specific purpose of forecasting the number of new admission inpatients trends and guiding management strategies. We sought to construct a single SARIMA model, a single NARNN model, and a hybrid SARIMA-NARNN model based on the monthly and daily data of an entire hospital. The NARNN model and SARIMA-NARNN model were appropriate to forecast the number of new admission inpatients. But the results of forecasting performance were compared by using the RMSE, MAE, MAPE showing that the hybrid model does not necessarily achieved better prediction accuracy than either of the models used separately.
As shown in Fig.
5, the original new admission inpatients fluctuated every year based on the monthly data. However, an upward trend was observed overall. The result of the SARIMA model analysis incorporated a 12-step seasonal differencing operation. The monthly time series analysis supports a “month of the year” effect. The lowest numbers were observed in January or February each year, presumably due to the Spring Festival holiday. The numbers reached the maximum in March 2010, 2012, 2015 and 2016, and greater numbers in March compared to other months were also observed in other years, a phenomenon that could potentially be attributed to long holiday and seasonal replacement. Based on these findings, we suggest that hospital management should strategize and assign medical resources accordingly. The modeling RMSE, MAE, MAPE of the SARIMA-NARNN model decreased by 42.89, 47.85, 48.86% and the corresponding testing error decreased by 11.35, 20.25, 19.99%, respectively as compared to using the SARIMA model alone. When compared to the NARNN model, the modeling RMSE of the SARIMA-NARNN model decreased by 3.12%, and the testing RMSE, MAE, MAPE decreased by 57.35, 52.66, 52.11%, respectively. Interestingly, the modeling MAE and MAPE of the SARIMA-NARNN model increased by 28.47 and 27.26%, respectively. As mentioned in the article [
30,
31], the RMSE is not always a superior parameter over the MAE, a combination of metrics is often required to accurately evaluate model performance. However, all testing errors of the SARIMA-NARNN model were the lowest among the three models and overall, the predicted curves of the hybrid model was close to the original curves (Fig.
5 a, b and c). Therefore, we concluded that the hybrid model was the most appropriate for forecasting the monthly new admission inpatients.
As shown in Fig.
6a, b and c, our analysis of daily data indicates an obvious “day of the week” effect. Maximum values were usually observed on Mondays, while the minimum values tended to fall on Saturdays or Sundays every week. Some fluctuations were found under the influence of various festivals. For examples, the lowest number was observed during the 7th to the 13th of February likely due to the Spring Festival holiday and the one-week maximum was observed on Tuesday (3th of May) probably because this was the first day after the May Day holiday. In addition, the maximum value was also found on Sunday (18th of September) potentially due to the Mid Autumn Festival holidays from Thursday to Saturday prior. Forecasting performance could be greatly influenced by these fluctuations. If the time series predictions were within the range of these holidays, extra cautions should be paid on interpreting prediction results. As compared to using the SARIMA model alone, the modeling RMSE, MAE, and MAPE of the NARNN model decreased by 55.28, 44.01, and 49.01% and the corresponding one-week and four-weeks testing errors dropped by 34.20, 30.65, 30.05 and 0.15%, 3.66, and 4.45%, respectively. When compared to the SARIMA-NARNN model, the modeling RMSE, MAE, MAPE of the NARNN model decreased by 10.54, 8.22 and 9.23%, respectively, while the corresponding one-week and four-weeks testing errors reduced by 31.50, 24.74, 33.33 and 11.56%, 22.37, 31.72%, respectively. We, therefore, concluded that the NARNN model was suitable for forecasting the daily new admission inpatients.
According to the development trend of new admission inpatients, we can make some following suggestions for the hospital managers. Try to avoid the medical staff leave at the peak of admission; Carry out the repair work for the inpatient beds on Saturday or Sunday; Provide vacant beds by clinical departments with fewer admission inpatients to other departments with more admission inpatients. Set up some waiting beds for turnover in the whole hospital; Make an “emergence plan about overcrowding”- once overcrowding occur the “overcrowding beds” are opened. When the forecasting results indicate that the new admission inpatients are increasing, the plan is in a state of vigilance.
Although the ARIMA model is one of the most mature time series forecasting methods, our study [
17,
28] and other studies [
32] have indicated that its forecasting performance for predicting real world cases is slightly lower than other models. Therefore, we do not recommend using the ARIMA model exclusively. The NARNN model is capable of successfully simulating some time series due to its dynamic property, high fault tolerance performance, and ability to capture nonlinear information [
25,
33]. In practical data analysis, the NARNN model should be construct. In addition, our results were consistent with previous publication, which reported the comparative study of autoregressive neural network hybrids, showing that hybrid models are not always better and the model construction process should remain an important step despite the popularity of hybrid models [
34]. The four-weeks testing errors were much greater than those of one-week, showing that the prediction accuracy was obviously reduced with the increase of forecasting time. It is the inherent disadvantages of the time series forecasting model-the forecasting ability to extrapolate is limited, the longer the forecasting time, the lower the prediction accuracy. Further studies are needed to develop synthetic approaches combining various types of models to improve the ability of forecasting the new admission inpatients from different data.
From a clinical perspective, our research shows that it is benefit to monitor the change trend of admission inpatients by adding time series model to the hospital information system. When the predicted new admission inpatients are increasing, hospital managers can open more preparation beds or let doctors reduce the admissions. From a methodology perspective, our research shows that the time series model can be applied to study the development trend of admission inpatients. NARNN model was implemented based on the neural network time series tool of MATLAB which provided a graphical environment to make the design process of model easy. Although many researches have indicated hybrid models could improve the forecasting performance, our results do not support this point. Understanding how and which models could be implemented in which data requires hospital managers prudent choice.