Time series model for forecasting the number of new admission inpatients

Abstract

Background: Hospital crowding is a rising problem, effective predicting and detecting managment can helpful to reduce crowding. Our team has successfully proposed a hybrid model combining both the autoregressive integrated moving average (ARIMA) and the nonlinear autoregressive neural network (NARNN) models in the schistosomiasis and hand, foot, and mouth disease forecasting study. In this paper, our aim is to explore the application of the hybrid ARIMA-NARNN model to track the trends of the new admission inpatients, which provides a methodological basis for reducing crowding.

Methods: We used the single seasonal ARIMA (SARIMA), NARNN and the hybrid SARIMA-NARNN model to fit and forecast the monthly and daily number of new admission inpatients. The root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) were used to compare the forecasting performance among the three models. The modeling time range of monthly data included was from January 2010 to June 2016, July to October 2016 as the corresponding testing data set. The daily modeling data set was from January 4 to September 4, 2016, while the testing time range included was from September 5 to October 2, 2016.

Results: For the monthly data, the modeling RMSE and the testing RMSE, MAE and MAPE of SARIMA-NARNN model were less than those obtained from the single SARIMA or NARNN model, but the MAE and MAPE of modeling performance of SARIMA-NARNN model did not improve. For the daily data, all RMSE, MAE and MAPE of NARNN model were the lowest both in modeling stage and testing stage.

Conclusions: Hybrid model does not necessarily outperform its constituents' performances. It is worth attempting to explore the reliable model to forecast the number of new admission inpatients from different data.

Keywords: Hybrid model; NARNN model; New admission inpatients; SARIMA model; Time series forecasting.

Fig. 1

The configuration of the NARNN. The NARNN consists of one output layer with 1 unit and one hidden layer with n units and D delays

Fig. 2

Trend and Correlation Analysis for different time series. a, b and c show the trend of new admission inpatients per month from January 2010 to June 2016, ACF and PACF plots of monthly original time series (MOS) respectively after one order of regular difference and one order of seasonal difference with the length of seasonal period 12. d, e and f show the trend of new admission inpatients per day from January 4 to September 4, 2016, ACF and PACF plots of daily original time series (DOS) respectively after one order of seasonal difference with the length of seasonal period 7

Fig. 3

Error autocorrelation plots of different time series from NARNN model. The error autocorrelation was one of the evaluation indices in the modeling process. The red dotted line indicate 95% confidence intervals. MOS = monthly original time series, MRS = monthly residual series, DOS = daily original time series, DRS = daily residual series

Fig. 4

The time-series response plots of different time series from NARNN model. a, b, c and d show the inputs, targets, and errors versus time and also give which time points were selected for training, testing, and validation

Fig. 5

The change trend of the monthly number of new admission inpatients from three models. a, b and c show the observations and predicted values from the SARIMA model , NARNN model and SARIMA-NARNN model respectively

Fig. 6

The change trend of the daily number of new admission inpatients from three models. a, b and c show the observations and predicted values from the SARIMA model , NARNN model and SARIMA-NARNN model respectively