Establishment of ARIMA model and its application on the prediction of pulmonary tuberculosis incidence in Guangzhou

doi:10.3969/j.issn.1000-6621.2021.06.009

Abstract

Abstract:

ObjectiveTo establish an Auto-regressive Integrated Moving Average (ARIMA) model of tuberculosis (TB) in Guangzhou and use it to make prediction on the number of notified pulmonary tuberculosis (PTB) cases in Guangzhou, so as to provide a reference for the prevention and control of TB in Guangzhou. MethodsThe monthly notification incidence data of TB in Guangzhou from January 2010 to December 2019 was collected through the “Chinese Disease Prevention and Control Information System”. ARIMA model was established by conducting time series analysis to predict the notification incidence of PTB in Guangzhou in 2021. In addition, the stability of model parameters and the accuracy of prediction model were tested by re-fitting the model with data from 2010 to 2018. ResultsA total of 115887 PTB cases were notified in Guangzhou from 2010 to 2019, which showed a downward trend year by year together with a significant seasonality. The number of cases reached a peak from March to May every year, and the trough always occurred in February. The best fitting model was ARIMA(1,1,1)×(0,1,1)₁₂ (P_{residual test}=0.693, AIC=1215.300), and the mean absolute percentage error (MAPE) between the actual value and the predicted value fitted by the model for January to December 2020 was 7.29%. According to the data from 2010 to 2018, the optimal model was still ARIMA(1,1,1)×(0,1,1)₁₂ (P_{residual test}=0.847, AIC=1089.260) and MAPE between the actual value and the predicted value fitted by model for January to December in 2019 was 4.91%. The predicted number of PTB cases in Guangzhou in 2021 was 8270, and the average number of monthly cases was 689. The incidence level was slightly higher than that in 2020. Conclusion The ARIMA (1,1,1)×(0,1,1)₁₂ model made a good prediction on the number of notified PTB cases in Guangzhou, and could be used for short-term forecasting and dynamic analysis of TB in Guangzhou.

Key words: Tuberculosis,pulmonary, Disease notification, Forecasting, Models,statistical

LEI Yu, HE Li-qian, ZHANG Guang-chuan, LAI Keng, XIE Wei, DU Yu-hua. Establishment of ARIMA model and its application on the prediction of pulmonary tuberculosis incidence in Guangzhou[J]. Chinese Journal of Antituberculosis, 2021, 43(6): 569-575. doi: 10.3969/j.issn.1000-6621.2021.06.009

Figures/Tables 7

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参数	ARIMA(1,1,1)×(1,1,1)₁₂		ARIMA(1,1,1)×(0,1,1)₁₂		ARIMA(1,1,1)×(0,1,2)₁₂
参数	估计值	$s\bar{x}$值	估计值	$s\bar{x}$值	估计值	$s\bar{x}$值
AR1	0.192	0.137	0.230	0.134	0.192	0.140
MA1	-0.812	0.079	-0.830	0.077	-0.812	0.080
SAR1	-0.168	0.175	-	-	-0.867	0.103
SMA1	-0.523	0.175	-0.654	0.093	-0.097	0.112
AIC值	1216.430		1215.300		1216.550
P值	0.752		0.693		0.746

月份	实际例数	预测例数	95%CI值下限	95%CI值上限	绝对误差	绝对误差百分比(%)
1	701	705	575	835	4	0.57
2	494	546	409	682	52	10.53
3	671	832	692	973	161	23.99
4	655	821	677	964	166	25.34
5	695	814	668	959	119	17.12
6	746	743	596	891	3	0.40
7	754	785	636	933	31	4.11
8	769	763	614	912	6	0.78
9	693	687	537	836	6	0.87
10	666	677	527	827	11	1.65
11	650	644	494	794	6	0.92
12	617	625	474	775	8	1.30

参数	ARIMA(1,1,1)×(1,1,1)₁₂		ARIMA(1,1,1)×(0,1,1)₁₂		ARIMA(1,1,1)×(0,1,2)₁₂
参数	估计值	$s\bar{x}$值	估计值	$s\bar{x}$值	估计值	$s\bar{x}$值
AR1	0.191	0.154	0.244	0.153	0.195	0.158
MA1	-0.816	0.094	-0.842	0.095	-0.818	0.096
SAR1	-0.217	0.194	-	-	-	-
SMA1	-0.483	0.207	-0.658	0.109	-0.695	0.118
AIC值	1090.080		1089.260		1090.300
P值	0.890		0.847		0.773

月份	实际例数	预测例数	95%CI值下限(例)	95%CI值上限(例)	绝对误差	绝对误差百分比(%)
1	783	774	640	909	9	1.15
2	607	608	465	752	1	0.16
3	847	911	763	1058	64	7.56
4	858	877	726	1028	19	2.21
5	817	879	725	1033	62	7.59
6	742	821	663	978	79	10.65
7	819	831	671	991	12	1.47
8	771	827	664	990	56	7.26
9	706	741	575	906	35	4.96
10	712	709	540	877	3	0.42
11	673	694	523	866	21	3.12
12	614	690	516	864	76	12.38

月份	预测例数	95%CI值下限(例)	95%CI值上限(例)
1	685	525	845
2	523	361	684
3	807	644	969
4	793	630	956
5	784	620	947
6	712	548	875
7	751	587	915
8	729	565	893
9	651	487	815
10	641	477	805
11	607	443	772
12	587	422	751