季节性差分自回归滑动平均模型对肺结核发病情况的预测效果研究

doi:10.19982/j.issn.1000-6621.20220517

摘要/Abstract

摘要： 目的分析季节性差分自回归滑动平均(seasonal auto regressive integrated moving average,SARIMA)模型用于肺结核发病情况预测的准确性。方法通过“中国疾病预防控制信息系统”子系统“传染病监测系统”收集浙江省湖州市2010年1月至2021年12月肺结核发病数据。利用2010年1月至2020年12月湖州市肺结核月报告数据,分别建立月报告发病数SARIMA模型与发病率SARIMA模型,以2021年1—12月肺结核报告发病数据验证模型,并用平均绝对百分比误差(mean absolute percentage error,MAPE)和均方根误差百分比(relative root mean square error percentage,RMSEP)评价两种模型的预测效果。结果肺结核月报告发病数SARIMA(0,0,1)(0,1,1)₁₂模型和月报告发病率SARIMA(0,0,1)(1,1,1)₁₂模型为最佳拟合模型。经模型验证,2021年9月湖州市肺结核真实报告发病数(112例)与模型预测发病数相差28.571%,且高于95%CI上限值(109例),其他月报告发病数均在预测值95%CI范围内;2021年湖州市肺结核月报告发病率均在预测值95%CI范围内,其中真实值与预测值最大百分比误差为8.665%。按全年累计发病统计,月报告发病数模型与发病率模型的2021年预测值与真实值百分比误差分别为4.866%和2.483%。月报告发病数模型的MAPE为9.925%、RMSEP为14.167%,月报告发病率模型的MAPE为3.798%、RMSEP为4.463%。从评价效果看,月报告发病率SARIMA模型的MAPE和RMSEP均小于月报告发病数SARIMA模型。结论基于2010—2020年湖州市肺结核月报告发病数与发病率建立的SARIMA模型有较好的拟合效果,且月报告发病率模型预测效果优于月报告发病数模型。

关键词: 结核,肺, 预测, 模型,统计学

Abstract:

Objective: To analyze the accuracy of seasonal difference auto regressive moving average (SARIMA) model in predicting the incidence of pulmonary tuberculosis (PTB). Methods: From January 2010 to December 2021, PTB incidence data of Huzhou City, Zhejiang Province collected through “Infectious Disease Reporting System” which was a subsystem of the “Chinese Disease Prevention and Control Information System”. SARIMA models based on monthly incidence rate and case number were established using data from January 2010 to December 2020 while the validation of the model used data from January to December 2021. Prediction effect of the two models were evaluated by two indexes, the mean absolute percentage error (MAPE) and the relative root mean square error percentage (RMSEP). Results: The best model of SARIMA were (0,0,1)(0,1,1)₁₂ for the case number and (0,0,1)(1,1,1)₁₂ for the incidence. The actual reported case number in September 2021 was above the upper limit of 95% confidence interval of the model prediction with a difference of 28.571%. The reported case number of other months were all within the predicted 95% confidence interval (109 cases). All monthly reported incidences were within the predicted 95%CI range. The maximum difference between the predicted incidence and the actual incidence was 8.665%. Counting annual cumulative case number and incidence in 2021, the differences between the predicted value and the true value of the case number model and the incidence model were 4.866% and 2.483%, respectively. MAPE of the case number model was 9.925%, and RMSEP was 14.167%. MAPE of the incidence model was 3.798%, and RMSEP was 4.463%, both were smaller than those of the case number SARIMA model. Conclusion: The SARIMA model based on the monthly reported PTB incidence and case number in Huzhou City from 2010 to 2020 had a good fitting effect. The predictive effect of SARIMA model of the incidence was better than that of the case number model.

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

中图分类号:

R521
R824

任飞林, 刘小琦, 金玫华, 孙秀秀. 季节性差分自回归滑动平均模型对肺结核发病情况的预测效果研究[J]. 中国防痨杂志, 2023, 45(5): 514-519. doi: 10.19982/j.issn.1000-6621.20220517

Ren Feilin, Liu Xiaoqi, Jin Meihua, Sun Xiuxiu. Study on the predictive effect of seasonal auto regressive integrated moving average model on the incidence of pulmonary tuberculosis[J]. Chinese Journal of Antituberculosis, 2023, 45(5): 514-519. doi: 10.19982/j.issn.1000-6621.20220517

图/表 6

图1

表1

图2

图3

表2

表3

参考文献 18

[1]	World Health Organization.Global tuberculosis report 2022. Geneva: World Health Organization, 2022.
[2]	王众楷, 张白玉, 贾善群, 等. 2008—2020年中国法定传染病的流行趋势分析. 郑州大学学报(医学版), 2022, 57(3): 350-356. doi:10.13705/j.issn.1671-6825.2021.10.061. doi: 10.13705/j.issn.1671-6825.2021.10.061
[3]	Becerra M, Jerez A, Garces HO, et al. Copper price: A brief analysis of China’s impact over its short-term forecasting. Resour policy, 2022, 75(3):102449-102453. doi:10.1016/j.resourpol.2021.102449. doi: 10.1016/j.resourpol.2021.102449 URL
[4]	Jean F, Talirongan H, Orong MY. Modeling national trends on health in the philippines using ARIMA. J Health Med Informat, 2020, 11(1). doi:10.37421/jhmi.2020.11.342. doi: 10.37421/jhmi.2020.11.342
[5]	周扬, 梁士杰. ARIMA乘积季节模型在郑州市肺结核月发病趋势预测中的应用. 中国卫生统计, 2021, 38(4):554-555. doi:10.3969/j.issn.1002-3674.2021.04.019. doi: 10.3969/j.issn.1002-3674.2021.04.019
[6]	Cong J, Ren M, Xie S, et al. Predicting seasonal influenza based on SARIMA model,in Mainland China from 2005 to 2018. Int J Environ Res Public Health, 2019, 16(23):4760.doi:10.3390/ijerph16234760. doi: 10.3390/ijerph16234760 URL
[7]	Obi CV, Okoli CN. Comparative Performance of the ARIMA, ARIMAX and SES Model for Estimating Reported Cases of Diabetes Mellitus in Anambra State,Nigeria. Eur J Eng Res Sci, 2021, 6(1):63-68. doi:10.24018/ejers.2021.6.1.2321. doi: 10.24018/ejers.2021.6.1.2321 URL
[8]	郭在金, 龚浩, 周罗晶. SARIMA模型和Holt-Winters指数平滑法在江苏省肺结核发病数预测中的应用. 疾病监测, 2022, 37(8):1042-1047. doi:10.3784/jbjc.202201300027. doi: 10.3784/jbjc.202201300027
[9]	邹博, 吴日娜, 吴俐健, 等. 中国人20年间肺结核病患病率与生活习惯的相关因素荟萃分析. 现代预防医学, 2013, 40(11):1993-1996.
[10]	刘家起, 孙德斌, 姜婧, 等. 2000—2015年全球结核病患病率宏观影响因素分析. 中国公共卫生管理, 2021, 37(2):261-264. doi:10.19568/j.cnki.23-1318.2021.02.0033. doi: 10.19568/j.cnki.23-1318.2021.02.0033
[11]	张慧, 成君, 屈燕, 等. “三新一加强”结核病综合防治服务模式的验证,示范与推广:中国国家卫生健康委员会-比尔及梅琳达·盖茨基金会结核病项目. 中国防痨杂志, 2021, 43(8):757-760. doi:10.3969/j.issn.1000-6621.2021.08.001. doi: 10.3969/j.issn.1000-6621.2021.08.001
[12]	陈文明, 张钰, 周琳, 等. 浙江省2005年至2014年结核病登记的空间扫描研究. 中华传染病杂志, 2017, 35(2):88-92. doi:10.3760/cma.j.issn.1000-6680.2017.02.006. doi: 10.3760/cma.j.issn.1000-6680.2017.02.006
[13]	吴倩, 张钰, 刘魁, 等. 2016—2020年浙江省肺结核流行特征分析. 预防医学, 2022, 34(5):487-491. doi:10.19485/j.cnki.issn2096-5087.2022.05.013. doi: 10.19485/j.cnki.issn2096-5087.2022.05.013
[14]	陈新邦, 卫平民. 四种模型在驻苏部队肺结核发病率预测中的比较研究. 中国卫生统计, 2019, 36(3): 388-391.
[15]	王迎丹, 高春洁, 王蕾. 5种时间序列模型预测肺结核发病比较. 预防医学, 2022, 34(12):1194-1200. doi:10.19485/j.cnki.issn2096-5087.2022.12.002. doi: 10.19485/j.cnki.issn2096-5087.2022.12.002
[16]	茅蓉, 王远航, 葛锐. 基于自回归移动平均模型的浙江省肺结核发病趋势预测. 疾病监测, 2022, 37(5):652-656. doi:10.3784/jbjc.202109240520. doi: 10.3784/jbjc.202109240520
[17]	任嘉豪, 徐洁, 杨海燕. ARIMA及Holt-Winters指数平滑模型在河南省肺结核流行趋势预测中的应用. 郑州大学学报(医学版), 2022, 57(6):756-760. doi:10.13705/j.issn.1671-6825.2022.02.040. doi: 10.13705/j.issn.1671-6825.2022.02.040
[18]	张顺先, 邱磊, 张少言, 等. ARIMA模型的建立及对中国肺结核月报告例数的预测效果研究. 中国防痨杂志, 2020, 42(6): 614-620. doi:10.3969/j.issn.1000-6621.2020.06.014. doi: 10.3969/j.issn.1000-6621.2020.06.014

时间序列变量	模型阶数	残差检验(P值)	BIC值	稳定R²值	MAPE值(%)	MAE值
发病数	(0,0,1)(0,1,1)₁₂	0.347	5.459	0.404	11.610	11.651
发病数	(0,0,1)(1,1,1)₁₂	0.159	5.484	0.418	11.368	11.469
发病数	(1,0,1)(0,1,1)₁₂	0.272	5.487	0.416	11.476	11.467
发病数	(1,0,1)(0,1,1)₁₂	0.494	5.491	0.442	11.184	11.467
发病率	(0,0,1)(1,1,1)₁₂	0.734	-1.279	0.451	10.699	0.386
发病率	(0,0,1)(0,1,1)₁₂	0.525	-1.273	0.426	11.062	0.398
发病率	(1,0,1)(0,1,1)₁₂	0.420	-1.225	0.426	11.065	0.398
发病率	(1,0,1)(1,1,1)₁₂	0.622	-1.223	0.452	11.065	0.389

月份	月报告发病数(例)		PE值 (%)	95%CI值 (例)
月份	真实值	预测值	PE值 (%)	95%CI值 (例)
1	83	83.229	0.276	56.021~110.437
2	79	65.108	-17.722	36.130~94.085
3	90	88.643	-1.111	59.665~111.620
4	93	99.439	6.452	70.461~128.417
5	82	99.957	21.951	70.979~128.935
6	99	94.244	-5.051	65.267~123.222
7	87	90.992	4.598	62.014~119.969
8	92	87.405	-5.435	58.427~116.382
9	112	80.293	-28.571	51.316~109.271
10	84	75.328	-10.714	46.350~104.305
11	72	68.759	-4.167	39.782~97.737
12	75	64.793	-13.333	35.816~93.770
合计	1048	998.190	4.866	-

月份	月报告发病率(/10万)		PE值 (%)	95%CI值 (/10万)
月份	真实值	预测值	PE值 (%)	95%CI值 (/10万)
1	2.807	2.822	0.513	1.884~3.759
2	2.085	2.205	5.775	1.228~3.182
3	3.049	2.997	-1.715	2.020~3.974
4	3.026	3.182	5.152	2.205~4.159
5	3.183	3.296	3.551	2.319~4.273
6	2.870	3.119	8.665	2.142~4.096
7	2.957	2.975	0.605	1.998~3.952
8	2.805	2.946	5.031	1.969~3.923
9	2.746	2.789	1.559	1.811~3.766
10	2.813	2.658	-5.510	1.681~3.635
11	2.235	2.350	5.178	1.373~3.327
12	2.219	2.270	2.321	1.293~3.247
合计	32.794	33.608	2.483	-