自回归移动平均模型的建立及在广州市肺结核发病预测中的应用

doi:10.3969/j.issn.1000-6621.2021.06.009

摘要/Abstract

摘要：

目的建立自回归移动平均(autoregressive integrated moving average,ARIMA)模型并对广州市2021年肺结核月报告发病数进行预测,为广州市肺结核防控提供参考。方法通过《中国疾病预防控制信息系统》中的《传染病报告信息管理系统》,收集广州市2010年1月至2019年12月肺结核月报告发病数据,通过时间序列分析建立ARIMA模型,并对2021年广州市肺结核发病情况进行预测。再通过2010—2018年报告发病数据重新拟合模型,检验模型参数的稳定性和预测的准确性。结果2010—2019年广州市肺结核共报告发病115887例,并呈逐年下降趋势,报告发病数具有明显的季节性,在每年3—5月报告发病例数出现高峰,报告发病低谷则为2月份。广州市肺结核发病数拟合最佳模型为ARIMA(1,1,1)×(0,1,1)₁₂(P_残差检验=0.693,AIC=1215.300),该模型拟合的2020年1—12月的预测值与实际值的平均绝对百分比误差(MAPE)=7.29%。通过2010—2018年的报告发病数据拟合最优模型仍为ARIMA(1,1,1)×(0,1,1)₁₂(P_残差检验=0.847,AIC=1089.260),该模型拟合的2019年1—12月的预测值与实际报告值的MAPE为4.91%。广州市2021年肺结核预测发病数为8270例,月平均报告发病数为689例,报告发病水平较2020年略有上升。结论ARIMA(1,1,1)×(0,1,1)₁₂模型对广州市肺结核报告发病患者例数有较好的预测效果,可用于广州市肺结核的短期预期和动态分析。

关键词: 结核,肺, 疾病报告, 预测, 模型,统计学

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

雷宇, 何立乾, 张广川, 赖铿, 谢玮, 杜雨华. 自回归移动平均模型的建立及在广州市肺结核发病预测中的应用[J]. 中国防痨杂志, 2021, 43(6): 569-575. doi: 10.3969/j.issn.1000-6621.2021.06.009

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

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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