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Forecast model analysis for the morbidity of tuberculosis in Xinjiang, China.

Zheng YL, Zhang LP, Zhang XL, Wang K, Zheng YJ - PLoS ONE (2015)

Bottom Line: Recently, the Box-Jenkins approach, specifically the autoregressive integrated moving average (ARIMA) model, is typically applied to predict the morbidity of infectious diseases; it can take into account changing trends, periodic changes, and random disturbances in time series.Autoregressive conditional heteroscedasticity (ARCH) models are the prevalent tools used to deal with time series heteroscedasticity.Comparative analyses show that the combined model is more effective.

View Article: PubMed Central - PubMed

Affiliation: College of Public Health, Xinjiang Medical University, Urumqi, 830011, People's Republic of China; College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi, 830011, People's Republic of China.

ABSTRACT
Tuberculosis is a major global public health problem, which also affects economic and social development. China has the second largest burden of tuberculosis in the world. The tuberculosis morbidity in Xinjiang is much higher than the national situation; therefore, there is an urgent need for monitoring and predicting tuberculosis morbidity so as to make the control of tuberculosis more effective. Recently, the Box-Jenkins approach, specifically the autoregressive integrated moving average (ARIMA) model, is typically applied to predict the morbidity of infectious diseases; it can take into account changing trends, periodic changes, and random disturbances in time series. Autoregressive conditional heteroscedasticity (ARCH) models are the prevalent tools used to deal with time series heteroscedasticity. In this study, based on the data of the tuberculosis morbidity from January 2004 to June 2014 in Xinjiang, we establish the single ARIMA (1, 1, 2) (1, 1, 1)12 model and the combined ARIMA (1, 1, 2) (1, 1, 1)12-ARCH (1) model, which can be used to predict the tuberculosis morbidity successfully in Xinjiang. Comparative analyses show that the combined model is more effective. To the best of our knowledge, this is the first study to establish the ARIMA model and ARIMA-ARCH model for prediction and monitoring the monthly morbidity of tuberculosis in Xinjiang. Based on the results of this study, the ARIMA (1, 1, 2) (1, 1, 1)12-ARCH (1) model is suggested to give tuberculosis surveillance by providing estimates on tuberculosis morbidity trends in Xinjiang, China.

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Fitted values of ARIMA (1, 1, 2) (1, 1, 1)12 model and ARIMA (1, 1, 2) (1, 1, 1)12-ARCH (1) model versus the actual monthly morbidity of tuberculosis before December 2013.We can see fitting performance of the two models by this Figure.
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pone.0116832.g005: Fitted values of ARIMA (1, 1, 2) (1, 1, 1)12 model and ARIMA (1, 1, 2) (1, 1, 1)12-ARCH (1) model versus the actual monthly morbidity of tuberculosis before December 2013.We can see fitting performance of the two models by this Figure.

Mentions: Objective to improve the precision of ARIMA (1, 1, 2) (1, 1, 1)12 model, we analyze residual series carefully. Although Box-Jenkins Q test suggest that autocorrelation function of residual series with different lags do not differ from zero (p>0.05), p = 0.559 (corresponding to the Q24 = 17.457) is not big enough. After that, we do Histogram-Normality test (as shown in Fig. 4), the result shows that heavier-tailed distribution of residual series exists; we do ARCH LM test with the 1st lag, the result shows that a clear ARCH effect of residual series exists (significant level p<0.05), and the ARCH effect do not exist when lag is more than 1. Therefore, we consider establishing ARIMA (1, 1, 2) (1, 1, 1)12-ARCH (1) model to improve the precision of prediction. By the diagnostic checking, we find the residual of the combined model is white noise, and there is no ARCH effect longer. The values of AIC and SBC of the combined model (AIC = 4.68 and SBC = 4.92) are less than the corresponding values of single ARIMA (1, 1, 2) (1, 1, 1)12 model (AIC = 5.09 and SBC = 5.252), which suggest the proposed combined model is able to achieve significant performance improvement. Fig. 5 shows the actual monthly morbidity of TB and fitted morbidity of ARIMA model and ARIMA-ARCH model.


Forecast model analysis for the morbidity of tuberculosis in Xinjiang, China.

Zheng YL, Zhang LP, Zhang XL, Wang K, Zheng YJ - PLoS ONE (2015)

Fitted values of ARIMA (1, 1, 2) (1, 1, 1)12 model and ARIMA (1, 1, 2) (1, 1, 1)12-ARCH (1) model versus the actual monthly morbidity of tuberculosis before December 2013.We can see fitting performance of the two models by this Figure.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4356615&req=5

pone.0116832.g005: Fitted values of ARIMA (1, 1, 2) (1, 1, 1)12 model and ARIMA (1, 1, 2) (1, 1, 1)12-ARCH (1) model versus the actual monthly morbidity of tuberculosis before December 2013.We can see fitting performance of the two models by this Figure.
Mentions: Objective to improve the precision of ARIMA (1, 1, 2) (1, 1, 1)12 model, we analyze residual series carefully. Although Box-Jenkins Q test suggest that autocorrelation function of residual series with different lags do not differ from zero (p>0.05), p = 0.559 (corresponding to the Q24 = 17.457) is not big enough. After that, we do Histogram-Normality test (as shown in Fig. 4), the result shows that heavier-tailed distribution of residual series exists; we do ARCH LM test with the 1st lag, the result shows that a clear ARCH effect of residual series exists (significant level p<0.05), and the ARCH effect do not exist when lag is more than 1. Therefore, we consider establishing ARIMA (1, 1, 2) (1, 1, 1)12-ARCH (1) model to improve the precision of prediction. By the diagnostic checking, we find the residual of the combined model is white noise, and there is no ARCH effect longer. The values of AIC and SBC of the combined model (AIC = 4.68 and SBC = 4.92) are less than the corresponding values of single ARIMA (1, 1, 2) (1, 1, 1)12 model (AIC = 5.09 and SBC = 5.252), which suggest the proposed combined model is able to achieve significant performance improvement. Fig. 5 shows the actual monthly morbidity of TB and fitted morbidity of ARIMA model and ARIMA-ARCH model.

Bottom Line: Recently, the Box-Jenkins approach, specifically the autoregressive integrated moving average (ARIMA) model, is typically applied to predict the morbidity of infectious diseases; it can take into account changing trends, periodic changes, and random disturbances in time series.Autoregressive conditional heteroscedasticity (ARCH) models are the prevalent tools used to deal with time series heteroscedasticity.Comparative analyses show that the combined model is more effective.

View Article: PubMed Central - PubMed

Affiliation: College of Public Health, Xinjiang Medical University, Urumqi, 830011, People's Republic of China; College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi, 830011, People's Republic of China.

ABSTRACT
Tuberculosis is a major global public health problem, which also affects economic and social development. China has the second largest burden of tuberculosis in the world. The tuberculosis morbidity in Xinjiang is much higher than the national situation; therefore, there is an urgent need for monitoring and predicting tuberculosis morbidity so as to make the control of tuberculosis more effective. Recently, the Box-Jenkins approach, specifically the autoregressive integrated moving average (ARIMA) model, is typically applied to predict the morbidity of infectious diseases; it can take into account changing trends, periodic changes, and random disturbances in time series. Autoregressive conditional heteroscedasticity (ARCH) models are the prevalent tools used to deal with time series heteroscedasticity. In this study, based on the data of the tuberculosis morbidity from January 2004 to June 2014 in Xinjiang, we establish the single ARIMA (1, 1, 2) (1, 1, 1)12 model and the combined ARIMA (1, 1, 2) (1, 1, 1)12-ARCH (1) model, which can be used to predict the tuberculosis morbidity successfully in Xinjiang. Comparative analyses show that the combined model is more effective. To the best of our knowledge, this is the first study to establish the ARIMA model and ARIMA-ARCH model for prediction and monitoring the monthly morbidity of tuberculosis in Xinjiang. Based on the results of this study, the ARIMA (1, 1, 2) (1, 1, 1)12-ARCH (1) model is suggested to give tuberculosis surveillance by providing estimates on tuberculosis morbidity trends in Xinjiang, China.

Show MeSH
Related in: MedlinePlus