基于贝叶斯变点模型的COVID-19发病与死亡序列趋势

贺娜娜; 赵航; 孙金芳; 余小金

doi:10.16462/j.cnki.zhjbkz.2022.12.007

基于贝叶斯变点模型的COVID-19发病与死亡序列趋势

doi: 10.16462/j.cnki.zhjbkz.2022.12.007

210009 南京，东南大学公共卫生学院流行病与卫生统计学系

基金项目:

江苏省研究生科研与实践创新计划项目 SJCX20_0064

中央高校基本科研业务费专项资金 3225002110D

详细信息

通讯作者:
余小金，E-mail: xiaojinyu@seu.edu.cn

中图分类号: R195.1
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出版历程
- 收稿日期: 2022-01-20
- 修回日期: 2022-04-20
- 网络出版日期: 2022-12-30
- 刊出日期: 2022-12-10

Trend analysis of COVID-19 incidence and death series based on Bayesian change point model

Department of Epidemiology and Health Statistics, School of Public Health, Southeast University, Nanjing 210009, China

Funds:

Postgraduate Research & Practice Innovation Program of Jiangsu Province SJCX20_0064

The Fundamental Research Funds for the Central Universities 3225002110D

More Information

Corresponding author: YU Xiao-jin, E-mail: xiaojinyu@seu.edu.cn

摘要

摘要: 目的基于COVID-19发病和死亡序列趋势分析，探讨评价传染病发病或死亡变化趋势的方法，为同类流行病学研究数据的分析提供可能的分析策略。方法提取中国31个省(自治区、直辖市)2020年1月23日至2020年3月18日的COVID-19累计确诊病例和累计死亡病例数据，基于贝叶斯变点分析模型确定时间序列变点，并应用间断时间序列(interrupted time series，ITS)构建分段线性回归(segmented linear regression，SLR)模型，评价序列变化趋势与干预措施、政策的一致性。结果武汉市累计确诊病例和累计死亡病例数据各有3次变点，湖北省(除武汉市)和除湖北省以外的30个省(自治区、直辖市)的确诊病例数、死亡病例数各有4次变点。武汉市累计确诊病例数3次变点后改变量分别为1 493.885(P＜0.001)、2 444.913(P＜0.001)、-4 061.038(P＜0.001)；累计死亡病例数第2次、第3次变点后改变量分别为-66.917(P＜0.001)、-19.845(P=0.034)。湖北省(除武汉市)累计确诊病例数第3次变点出现增幅降低且差异有统计学意义，改变量为-845.244(P＜0.001)；累计死亡病例数增幅降低出现在第3次、第4次变点，斜率改变量分别为-10.062(P＜0.001)、-12.245(P＜0.001)。除湖北省以外的30个省(自治区、直辖市)累计确诊病例数第2次变点后开始出现增幅降低，改变量分别为-281.494(P＜0.001)、-295.080(P＜0.001)、-145.054(P＜0.001)；累计死亡病例数差异有统计学意义的增幅降低出现在第3次、第4次变点，斜率改变量分别为-3.199(P＜0.001)、-1.706(P＜0.001)。结论结合贝叶斯变点分析和ITS分析可充分考虑时间序列趋势变化的不确定性，为传染病疫情分析和防控措施评价提供依据。
- COVID-19 /
- 贝叶斯变点分析 /
- 间断时间序列 /
- 分段线性回归
Abstract: Objective To analyze the trend of COVID-19 based on the trend analysis of incidence and mortality data and provide analysis strategies for similar epidemiological researches. Methods We used the Bayesian change point analysis model to obtain the time series change points based on the number of cumulative confirmed and cumulative death cases of COVID-19 from January 23, 2020 to March 18, 2020 in Chinese mainland. Interrupted time series (ITS) method was applied to build a segmented linear regression (SLR) model, evaluating the consistency of trends in the series with the intervention or policy. Results There were 3 change points in cumulative confirmed cases and deaths in Wuhan, and 4 change points in cumulative confirmed cases and deaths in Hubei Province (except Wuhan) and Chinese mainland (except Hubei Province). The changes in the number of cumulative confirmed cases in Wuhan after 3 change points were 1 493.885 (P < 0.001), 2 444.913 (P < 0.001) and -4 061.038 (P < 0.001), respectively. The number of cumulative deaths after the second and third change points were -66.917 (P < 0.001) and -19.845 (P=0.034), respectively. The increase in the number of cumulative confirmed cases in Hubei Province (except Wuhan) began to decrease after the third change point, and the change is -845.244 (P < 0.001). The the increase in the number of cumulative deaths decreased after the third and fourth change points, and the slope changes were -10.062 (P < 0.001) and -12.245 (P < 0.001), respectively. The increase in the number of cumulative confirmed cases in Chinese mainland decreased from the second change point, and the changes were -281.494 (P < 0.001), -295.080 (P < 0.001), -145.054 (P < 0.001), respectively. The statistically significant decrease in the increase of cumulative deaths appeared in the third and fourth change points, and the slope changes were -3.199 (P < 0.001) and -1.706 (P < 0.001), respectively. Conclusions The combination of interrupted time series analysis with Bayesian change point analysis can consider the uncertainty of time series trend changes, and provide a basis for epidemiological analysis of infectious diseases and evaluation of prevention and control measures.
- COVID-19 /
- Bayesian change point analysis /
- Interrupted time series /
- Segmented linear regression

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表 1 贝叶斯变点分析后验概率

Table 1. Posterior probability of Bayesian change point analysis

组别	武汉市		湖北省(除武汉市)		除湖北省以外的30个省(自治区、直辖市)
组别	日期(节点)	P值	日期(节点)	P值	日期(节点)	P值
确诊病例数	2.11(19)^a	1.000	2.20(28)^a	0.976	2.06(14)^a	0.974
	2.01(9)^a	0.687	2.11(19)^a	0.540	1.27(4)^a	0.876
	2.12(20)^a	0.651	2.15(23)^a	0.519	2.12(20)^a	0.726
	2.17(25)^a	0.649	2.06(14)^a	0.512	2.19(27)^a	0.587
	3.01(38)	0.383	1.27(4)	0.426	2.13(21)	0.211
死亡病例数	2.11(19)^a	1.000	2.16(24)^a	0.727	2.11(19)^a	0.994
	2.13(21)^a	0.643	1.28(5)^a	0.704	2.05(13)^a	0.765
	2.23(31)^a	0.538	2.23(31)^a	0.560	2.18(26)^a	0.733
	3.05(42)^a	0.509	2.08(16)^a	0.512	2.27(35)^a	0.554
	2.22(30)	0.464	3.06(43)	0.485	2.28(36)	0.271
注：^a变点，设定1月23日的节点为0，1月24日为1，依次类推。

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表 2 分段条件检验结果

Table 2. Conditional test results of segmented data

组别	第一段			第二段			第三段			第四段			第五段
组别	Z值	χ²值	DW	Z值	χ²值	DW	Z值	χ²值	DW	Z值	χ²值	DW	Z值	χ²值	DW
武汉市
确诊病例数	0.403	0.150	0.984	0.621	1.110	1.959	-0.443	1.640	1.458	1.140	0.480	0.060
死亡病例数	1.614	0.053	0.120	1.912 ^a	5.420 ^a	1.648	0.721	0.150	1.744	0.474	1.420	0.591
湖北省(除武汉市)
确诊病例数	1.004	0.340	0.208	0.434	0.460	1.559	1.404	0.020	2.008	1.233	0.240	2.760	4.530 ^a	26.970 ^a	1.961
死亡病例数	-1.043	1.230	2.598	0.998	0.710	1.646	1.069	1.060	2.285	-0.161	0.070	1.701	0.965	0.010	0.124
除湖北省以外的30个省(自治区、直辖市)
确诊病例数	0.544	0.050	1.424	0.092	0.830	1.424	1.164	0.000	1.213	0.246	0.240	0.835	-2.145	0.280	0.636
死亡病例数	2.395 ^a	2.080	1.155	-0.577	0.030	1.300	-1.095	0.000	1.415	-0.088	0.990	1.945	-0.473	0.010	1.662
注：^a P＜0.05。

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表 3 中国确诊与死亡序列不同变点即刻改变量和转折后斜率改变量估计

Table 3. The estimation of level change and slope change at different change points in the incidence and mortality series in China

组别	β₀值	β₁值	β₂值	β₃值	β₄值	β₅值	β₆值	β₇值	β₈值	β₉值	DW	R²值
武汉市
确诊病例数	263.683	312.275	252.238	1 493.885 ^a	1 676.628	2 444.913 ^a	-3 001.610	-4 061.038 ^a			1.4840 ^b	0.9849
死亡病例数	-45.334	41.111 ^a	48.720	57.623 ^a	33.040	-66.917 ^a	-8.276	-19.845 ^a			0.8839 ^b	0.9778
湖北省(除武汉市)
确诊病例数	-321.995	735.230 ^a	243.904	-11.136	-164.362	193.091	-602.376 ^a	-845.244 ^a	255.734	-52.994	0.5660 ^b	0.6949
死亡病例数	3.135	3.585	2.508	9.838 ^a	4.720	14.050 ^a	-3.243	-10.062 ^a	0.850	-12.245 ^a	0.3333 ^b	0.8525
除湖北省以外的30个省(自治区、直辖市)
确诊病例数	280.696 ^a	351.713 ^a	113.702	382.756 ^a	-8.556	-281.494 ^a	-146.379	-295.080 ^a	-52.547	-145.054 ^a	1.2365 ^b	0.9993
死亡病例数	1.060	0.954 ^a	-0.270	4.988 ^a	0.188	-0.642	0.897	-3.199	1.803	-1.706 ^a	1.6918 ^c	0.9990
注：^a P＜0.05; ^b存在一阶自相关性; ^c不确定是否存在自相关。

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