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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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The ACF and PACF graphs of stabilized tuberculosis morbidity series.ACF = autocorrelation function, PACF = partial autocorrelation function. Based on the ACF, we determine the possible values of q (q = 1, 2 or 3) and Q(Q = 1) of ARIMA (p, d, q) (P, D, Q) 12, and based on PACF, we determine the possible values of p (p = 1, 2 or 3) and P (P = 1) of ARIMA (p, d, q) (P, D, Q)12.
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pone.0116832.g003: The ACF and PACF graphs of stabilized tuberculosis morbidity series.ACF = autocorrelation function, PACF = partial autocorrelation function. Based on the ACF, we determine the possible values of q (q = 1, 2 or 3) and Q(Q = 1) of ARIMA (p, d, q) (P, D, Q) 12, and based on PACF, we determine the possible values of p (p = 1, 2 or 3) and P (P = 1) of ARIMA (p, d, q) (P, D, Q)12.

Mentions: All further statistical procedures are performed on the stationary series. We plot ACF and PACF graphs (as shown in Fig. 3) of the stationary series. By analyzing Fig. 3, we conduct nine models: ARIMA (1, 1, 1) (1, 1, 1)12, ARIMA (1, 1, 2) (1, 1, 1)12, ARIMA (1, 1, 3) (1, 1, 1)12, ARIMA (2, 1, 1) (1, 1, 1)12, ARIMA (2, 1, 2) (1, 1, 1)12, ARIMA (2, 1, 3) (1, 1, 1)12, ARIMA (3, 1, 1) (1, 1, 1)12, ARIMA (3, 1, 2) (1, 1, 1)12, ARIMA(3, 1, 3)(1, 1, 1)12. By diagnostic checking including residual analysis, we establish six models shown in Table 2 with their AIC and SBC, the six models can be used to predict TB morbidity in Xinjiang, China. It is seen from Table 2 that ARIMA (1, 1, 1) (1, 1, 1)12 model and ARIMA (1, 1, 2) (1, 1, 1)12 model are better than the other four models, since the two models have lower AIC and lower SBC values. Compared with ARIMA (1, 1, 1) (1, 1, 1)12 model (the p value of Box-Jenkins Q test is 0.434), the ARIMA (1, 1, 2) (1, 1, 1) 12 model (the p value of Box-Jenkins Q test is 0.559) has better residual test results, therefore, the ARIMA (1, 1, 2) (1, 1, 1)12 model is the better model to fit the data.


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

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

The ACF and PACF graphs of stabilized tuberculosis morbidity series.ACF = autocorrelation function, PACF = partial autocorrelation function. Based on the ACF, we determine the possible values of q (q = 1, 2 or 3) and Q(Q = 1) of ARIMA (p, d, q) (P, D, Q) 12, and based on PACF, we determine the possible values of p (p = 1, 2 or 3) and P (P = 1) of ARIMA (p, d, q) (P, D, Q)12.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0116832.g003: The ACF and PACF graphs of stabilized tuberculosis morbidity series.ACF = autocorrelation function, PACF = partial autocorrelation function. Based on the ACF, we determine the possible values of q (q = 1, 2 or 3) and Q(Q = 1) of ARIMA (p, d, q) (P, D, Q) 12, and based on PACF, we determine the possible values of p (p = 1, 2 or 3) and P (P = 1) of ARIMA (p, d, q) (P, D, Q)12.
Mentions: All further statistical procedures are performed on the stationary series. We plot ACF and PACF graphs (as shown in Fig. 3) of the stationary series. By analyzing Fig. 3, we conduct nine models: ARIMA (1, 1, 1) (1, 1, 1)12, ARIMA (1, 1, 2) (1, 1, 1)12, ARIMA (1, 1, 3) (1, 1, 1)12, ARIMA (2, 1, 1) (1, 1, 1)12, ARIMA (2, 1, 2) (1, 1, 1)12, ARIMA (2, 1, 3) (1, 1, 1)12, ARIMA (3, 1, 1) (1, 1, 1)12, ARIMA (3, 1, 2) (1, 1, 1)12, ARIMA(3, 1, 3)(1, 1, 1)12. By diagnostic checking including residual analysis, we establish six models shown in Table 2 with their AIC and SBC, the six models can be used to predict TB morbidity in Xinjiang, China. It is seen from Table 2 that ARIMA (1, 1, 1) (1, 1, 1)12 model and ARIMA (1, 1, 2) (1, 1, 1)12 model are better than the other four models, since the two models have lower AIC and lower SBC values. Compared with ARIMA (1, 1, 1) (1, 1, 1)12 model (the p value of Box-Jenkins Q test is 0.434), the ARIMA (1, 1, 2) (1, 1, 1) 12 model (the p value of Box-Jenkins Q test is 0.559) has better residual test results, therefore, the ARIMA (1, 1, 2) (1, 1, 1)12 model is the better model to fit the data.

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