Application of an autoregressive integrated moving average model for predicting injury mortality in Xiamen, China

Abstract

Objective: Injury is currently an increasing public health problem in China. Reducing the loss due to injuries has become a main priority of public health policies. Early warning of injury mortality based on surveillance information is essential for reducing or controlling the disease burden of injuries. We conducted this study to find the possibility of applying autoregressive integrated moving average (ARIMA) models to predict mortality from injuries in Xiamen.

Method: The monthly mortality data on injuries in Xiamen (1 January 2002 to 31 December 2013) were used to fit the ARIMA model with the conditional least-squares method. The values p, q and d in the ARIMA (p, d, q) model refer to the numbers of autoregressive lags, moving average lags and differences, respectively. The Ljung-Box test was used to measure the 'white noise' and residuals. The mean absolute percentage error (MAPE) between observed and fitted values was used to evaluate the predicted accuracy of the constructed models.

Results: A total of 8274 injury-related deaths in Xiamen were identified during the study period; the average annual mortality rate was 40.99/100,000 persons. Three models, ARIMA (0, 1, 1), ARIMA (4, 1, 0) and ARIMA (1, 1, (2)), passed the parameter (p<0.01) and residual (p>0.05) tests, with MAPE 11.91%, 11.96% and 11.90%, respectively. We chose ARIMA (0, 1, 1) as the optimum model, the MAPE value for which was similar to that of other models but with the fewest parameters. According to the model, there would be 54 persons dying from injuries each month in Xiamen in 2014.

Conclusion: The ARIMA (0, 1, 1) model could be applied to predict mortality from injuries in Xiamen.

Keywords: ARIMA; injury; prediction; time serial.

Figure 1

Annual mortality rate of injuries in Xiamen, China, from 2002 to 2013.

Figure 2

Series of monthly mortality after first differentiation. The data after first-order differentiation are dispersed horizontally around zero, suggesting they are stationary.

Figure 3

Autocorrelation function and partial autocorrelation function (ACF and PACF) graphs after first differentiation. The shaded portion is the 95% CI range. The ACF cuts off at lag 1 with slow decay in the PACF, suggesting a moving average model (q=1).

Figure 4

Autocorrelation function and partial autocorrelation function (ACF and PACF) graphs of the residuals for the autoregressive integrated moving average (0, 1, 1) model. The shaded portion is the 95% CI range. As their correlation values are not outside the 95% CI limits, the residuals errors are considered to be white noise, indicating that this model is appropriate for prediction.

Figure 5

Actual and predicted mortalities and 95% CI of predicted mortalities. Most actual observed data are contained within the 95% CI of the predicted value, revealing that the prediction for the monthly injury mortality in Xiamen using the autoregressive integrated moving average (0, 1, 1) model is acceptable.