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Article(id=1240651445805044497, tenantId=1146029695717560320, journalId=1227665162245664772, issueId=1240651438955754377, articleNumber=null, orderNo=null, doi=10.20043/j.cnki.MPM.202312041, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1701619200000, receivedDateStr=2023-12-04, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773723954869, onlineDateStr=2026-03-17, pubDate=1719244800000, pubDateStr=2024-06-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773723954869, onlineIssueDateStr=2026-03-17, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773723954869, creator=13701087609, updateTime=1773723954869, updator=13701087609, issue=Issue{id=1240651438955754377, tenantId=1146029695717560320, journalId=1227665162245664772, year='2024', volume='51', issue='12', pageStart='2113', pageEnd='2912', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773723953236, creator=13701087609, updateTime=1773723953236, updator=13701087609, preIssue=null, nextIssue=null, ext=null, issueFiles=null}, startPage=2287, endPage=2293, ext={EN=ArticleExt(id=1240651446069285677, articleId=1240651445805044497, tenantId=1146029695717560320, journalId=1227665162245664772, language=EN, title=Establishments of a prediction model for hantavirus hemorrhagic fever with renal syndrome, Hubei, columnId=1228016569138213037, journalTitle=Modern Preventive Medicine, columnName=Clinical Medicine and Prevention, runingTitle=null, highlight=null, articleAbstract=
Objective

To explore the optimal prediction model for hantavirus hemorrhagic fever with renal syndrome (HFRS) in Hubei province, and to provide a basis for establishing a monitoring and early warning model for HFRS.

Methods

Using monthly surveillance data of HFRS incidence in Hubei province from 2005 to 2021, eight single time series models based on exponential smoothing (ETS), seasonal autoregressive integrated moving average (SARIMA) with and without regression variables, a state space model with Box-Cox transformation, ARMA errors, trend, and seasonal components (TBATS), a time series neural network model (NNETAR) with and without regression variables, a linear regression time series model (TSLM), and a cubic spline prediction model (SPLINEF) were used to build 162 models through 1-4 model combinations. The mean absolute percentage error (MAPE) was used as an evaluation index to evaluate the fitting and prediction performance of the models. The comprehensive fitting and prediction performance were evaluated by calculating the mean MAPE of fitting and prediction.

Results

The TSLM model and its combined models had a comprehensive MAPE of more than 100%. Among the other 98 models, the optimal fitting models for single, two, three, and four-model combinations were SPLINEF (11.98%), SARIMA-SPLINEF (15.14%), SARIMA-NNETAR-REG-SPLINEF (16.06%), and SARIMA-TBAT-NNETAR-REG-SPLINEF (17.75%), respectively. The optimal prediction models for single, two, three, and four-model combinations were SARIMA-REG (34.48%), SARIMA-REG-TBATS (22.77%), SARIMA-TBATS-SPLINEF (23.84%), and SARIMA-SARIMA-REG-TBATS-SPLINEF (22.31%), respectively. The optimal fitting and prediction models for single, two, three, and four-model combinations were SPLINEF (24.75%), SARIMA-SPLINEF (22.55%), SARIMA-TBATS-SPLINEF (20.92%), and SARIMA-SARIMA-REG-TBATS-SPLINEF (20.75%), respectively.

Conclusion

Based on the number of models, fitting and prediction accuracy, SARIMA-TBATS-SPLINEF is considered the optimal prediction model and can be used for monitoring and early warning of HFRS in Hubei.

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目的

探讨湖北省肾综合出血热最优预测模型，为建立湖北省肾综合征出血热监测预警模型提供依据。

方法

利用2005—2021年湖北省肾综合征出血热逐月发病率监测数据，以指数平滑模型（ETS），乘积季节自回归移动平均模型（SARIMA）及带回归变量的SARIMA-REG，具有 Box-Cox变换、ARMA误差、趋势和季节性分量的指数平滑状态空间模型（TBATS），时间序列神经网络模型（NNETAR）及带回归变量的NNETAR-REG，线性回归时间序列模型（TSLM）和三次样条预测模型（SPLINEF）8种单一时间序列模型为基础，通过1~4个模型进行组合，共建立162个模型。采用平均绝对百分比误差 (MAPE)作为评价指标，评价模型拟合及预测效果。拟合及预测综合效果通过计算拟合、预测MAPE均值评价。

结果

TSLM模型及其构建组合模型拟合及预测综合MAPE均超过100%。其它98个模型中，单一模型、2个模型的组合模型、3个模型的组合模型、4个模型的组合模型最优拟合模型分别为SPLINEF（11.98%），SARIMA-SPLINEF（15.14%），SARIMA-NNETAR-REG-SPLINEF（16.06%），SARIMA-TBAT-NNETAR-REG-SPLINEF（17.75%）。单一模型、2个模型的组合模型、3个模型的组合模型、4个模型的组合模型最优预测模型分别为SARIMA-REG（34.48%），SARIMA-REG-TBATS（22.77%），SARIMA-TBATS-SPLINEF（23.84%），SARIMA-SARIMA-REG-TBATS-SPLINEF（22.31%）。单一模型、2个模型的组合模型、3个模型的组合模型、4个模型的组合模型最优拟合及预测模型分别为SPLINEF（24.75%），SARIMA-SPLINEF（22.55%），SARIMA-TBATS-SPLINEF（20.92%），SARIMA-SARIMA-REG-TBATS-SPLINEF（20.75%）。

结论

综合模型数量、模型拟合及预测精度认为SARIMA-TBATS-SPLINEF为最优预测模型，可以用于湖北省肾综合征出血热监测预警。

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赵婧，E-mail：
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刘天（1991—），男，本科，主管医师，研究方向：急性传染病防制工作

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刘天（1991—），男，本科，主管医师，研究方向：急性传染病防制工作

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注：ETS:指数平滑模型;SARIMA:乘积季节自回归移动平均模型; SARIMA-REG:及带回归变量的乘积季节自回归移动平均模型; TBATS:具有 Box-Cox变换、ARMA误差、趋势和季节性分量的指数平滑状态空间模型; NNETAR:时间序列神经网络模型; NNETAR-REG:带回归变量的时间序列神经网络模型; TSLM:线性回归时间序列模型; SPLINEF:三次样条预测模型。

, figureFileSmall=EHZXfFFOVtqxFlfqMKCP+g==, figureFileBig=00DjKmv7Ke9uJpnDW8Xr9w==, tableContent=null), ArticleFig(id=1240651456848646513, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240651445805044497, language=EN, label=Fig.3, caption=The comprehensive accuracy of fitting and forecasting for 98 models, including 8 individual and combined models such as ETS, was evaluated, figureFileSmall=4wlpECRdw4wbs0hQbJEDgg==, figureFileBig=+ATKY/9YSMBJtiE5QHfeOQ==, tableContent=null), ArticleFig(id=1240651456991252859, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240651445805044497, language=CN, label=图3, caption=ETS等8个单一和组合模型共98个模型的拟合及预测综合精度

注：ETS:指数平滑模型;SARIMA:乘积季节自回归移动平均模型; SARIMA-REG:及带回归变量的乘积季节自回归移动平均模型; TBATS:具有 Box-Cox变换、ARMA误差、趋势和季节性分量的指数平滑状态空间模型; NNETAR:时间序列神经网络模型; NNETAR-REG:带回归变量的时间序列神经网络模型; TSLM:线性回归时间序列模型; SPLINEF:三次样条预测模型。

, figureFileSmall=4wlpECRdw4wbs0hQbJEDgg==, figureFileBig=+ATKY/9YSMBJtiE5QHfeOQ==, tableContent=null), ArticleFig(id=1240651457091916163, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240651445805044497, language=EN, label=Fig.4, caption=Fitting and prediction performance of the combined SARIMA, TBATS, and SPLINEF model, figureFileSmall=3xU8lkItmDC//5/FSWf+/w==, figureFileBig=e6IaBUbNf8x+troT1ty6Og==, tableContent=null), ArticleFig(id=1240651457179996557, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240651445805044497, language=CN, label=图4, caption=SARIMA-TBATS-SPLINEF的组合模型拟合及预测效果, figureFileSmall=3xU8lkItmDC//5/FSWf+/w==, figureFileBig=e6IaBUbNf8x+troT1ty6Og==, tableContent=null), ArticleFig(id=1240651457276465557, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240651445805044497, language=EN, label=Table 1, caption=

Ljung-Box Q test was conducted on the residuals of the fitted models of ETS and 8 other models for the monthly incidence rate of HFRS in Hubei from 2005 to 2021

, figureFileSmall=null, figureFileBig=null, tableContent=
模型表达式Q统计量P值
ETSETS(A,N,A)12.9080.045
SARIMASARIMA(2,1,2)(2,1,1)[12]3.1540.790
SARIMA-REGSARIMA(2,1,1)(1,1,1)[12]带回归项2.5360.864
TBATSTBATS(0.288,{0,0},0.856,{<12,4>})9.2770.158
NNETARNNAR(2,1,2)[12]20.8830.002
NNETAR-REGNNAR(2,1,3)[12]带回归项12.8940.045
TSLM-420.456<0.001
SPLINEF-104.332<0.001
), ArticleFig(id=1240651457502957983, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240651445805044497, language=CN, label=表1, caption=

ETS 等8个模型对2005—2021年湖北省肾综合征出血热逐月发病率拟合残差的Ljung-Box Q检验

, figureFileSmall=null, figureFileBig=null, tableContent=
模型表达式Q统计量P值
ETSETS(A,N,A)12.9080.045
SARIMASARIMA(2,1,2)(2,1,1)[12]3.1540.790
SARIMA-REGSARIMA(2,1,1)(1,1,1)[12]带回归项2.5360.864
TBATSTBATS(0.288,{0,0},0.856,{<12,4>})9.2770.158
NNETARNNAR(2,1,2)[12]20.8830.002
NNETAR-REGNNAR(2,1,3)[12]带回归项12.8940.045
TSLM-420.456<0.001
SPLINEF-104.332<0.001
), ArticleFig(id=1240651457612009893, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240651445805044497, language=EN, label=Table 2, caption=

The top 5 models with the minimum MAPE for fitting and forecasting among the 98 models, including 8 individual and combined models such as ETS, are as follows (%)

, figureFileSmall=null, figureFileBig=null, tableContent=
模型类型模型组合拟合预测综合
单一SPLINEF11.9837.5124.75
SARIMA-REG24.2334.4829.36
SARIMA24.4739.5031.98
TBATS27.5539.8433.70
NNETAR31.0838.9935.04
2个组合SARIMA-SPLINEF15.1429.9622.55
SARIMA-REG-SPLINEF15.3829.8422.61
SARIMA-REG-TBATS24.4222.7723.60
SARIMA-TBATS24.2123.7623.98
SARIMA-NNETAR-REG20.9727.2924.13
3个组合SARIMA-TBATS-SPLINEF18.0023.8420.92
SARIMA-REG-TBATS-SPLINEF18.3124.4221.36
ETS-SARIMA-SPLINEF17.8625.5521.71
ETS-SARIMA-REG-SPLINEF17.9525.4921.72
SARIMA-NNETAR-REG-SPLINEF16.0628.4122.23
4个组合SARIMA-SARIMA-REG-TBATS-SPLINEF19.1922.3120.75
ETS-SARIMA-SARIMA-REG-SPLINEF19.0924.1521.62
SARIMA-SARIMA-REG-NNETAR-REG-SPLINEF17.8625.8221.84
SARIMA-TBAT-NNETAR-REG-SPLINEF17.7526.5822.16
SARIMA-SARIMA-REG-TBATS-NNETAR-REG22.0922.6822.38
), ArticleFig(id=1240651457733644718, tenantId=1146029695717560320, journalId=1227665162245664772, articleId=1240651445805044497, language=CN, label=表2, caption=

ETS等8个单一和组合模型共98个模型中拟合及预测综合最小MAPE前5位（%）

, figureFileSmall=null, figureFileBig=null, tableContent=
模型类型模型组合拟合预测综合
单一SPLINEF11.9837.5124.75
SARIMA-REG24.2334.4829.36
SARIMA24.4739.5031.98
TBATS27.5539.8433.70
NNETAR31.0838.9935.04
2个组合SARIMA-SPLINEF15.1429.9622.55
SARIMA-REG-SPLINEF15.3829.8422.61
SARIMA-REG-TBATS24.4222.7723.60
SARIMA-TBATS24.2123.7623.98
SARIMA-NNETAR-REG20.9727.2924.13
3个组合SARIMA-TBATS-SPLINEF18.0023.8420.92
SARIMA-REG-TBATS-SPLINEF18.3124.4221.36
ETS-SARIMA-SPLINEF17.8625.5521.71
ETS-SARIMA-REG-SPLINEF17.9525.4921.72
SARIMA-NNETAR-REG-SPLINEF16.0628.4122.23
4个组合SARIMA-SARIMA-REG-TBATS-SPLINEF19.1922.3120.75
ETS-SARIMA-SARIMA-REG-SPLINEF19.0924.1521.62
SARIMA-SARIMA-REG-NNETAR-REG-SPLINEF17.8625.8221.84
SARIMA-TBAT-NNETAR-REG-SPLINEF17.7526.5822.16
SARIMA-SARIMA-REG-TBATS-NNETAR-REG22.0922.6822.38
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湖北省肾综合征出血热预测模型建立
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刘天 1, 2 , 吴杨 3 , 刘漫 3 , 陈琦 3 , 童叶青 3 , 赵婧 4
现代预防医学 | 临床与预防 2024,51(12): 2287-2293
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现代预防医学 | 临床与预防 2024, 51(12): 2287-2293
湖北省肾综合征出血热预测模型建立
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刘天1, 2, 吴杨3, 刘漫3, 陈琦3, 童叶青3, 赵婧4
作者信息
  • 1.荆州市疾病预防控制中心传染病防治所，湖北 荆州 434000
  • 2.长江大学公共卫生研究中心
  • 3.湖北省疾病预防控制中心传染病防治所
  • 4. 中国疾病预防控制中心卫生应急中心（传染病溯源预警与智能决策全国重点实验室，中国疾病预防控制中心

    • 刘天（1991—），男，本科，主管医师，研究方向：急性传染病防制工作

通讯作者:

赵婧，E-mail：
Establishments of a prediction model for hantavirus hemorrhagic fever with renal syndrome, Hubei
Tian LIU1, 2, Yang WU3, Man LIU3, Qi CHEN3, Ye-qing TONG3, Jing ZHAO4
Affiliations
  • Department for Infectious Disease Control and Prevention, Jingzhou Center for Disease Control and Prevention, Jingzhou, Hubei 434000, China
出版时间: 2024-06-25 doi: 10.20043/j.cnki.MPM.202312041
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摘要
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目的

探讨湖北省肾综合出血热最优预测模型，为建立湖北省肾综合征出血热监测预警模型提供依据。

方法

利用2005—2021年湖北省肾综合征出血热逐月发病率监测数据，以指数平滑模型（ETS），乘积季节自回归移动平均模型（SARIMA）及带回归变量的SARIMA-REG，具有 Box-Cox变换、ARMA误差、趋势和季节性分量的指数平滑状态空间模型（TBATS），时间序列神经网络模型（NNETAR）及带回归变量的NNETAR-REG，线性回归时间序列模型（TSLM）和三次样条预测模型（SPLINEF）8种单一时间序列模型为基础，通过1~4个模型进行组合，共建立162个模型。采用平均绝对百分比误差 (MAPE)作为评价指标，评价模型拟合及预测效果。拟合及预测综合效果通过计算拟合、预测MAPE均值评价。

结果

TSLM模型及其构建组合模型拟合及预测综合MAPE均超过100%。其它98个模型中，单一模型、2个模型的组合模型、3个模型的组合模型、4个模型的组合模型最优拟合模型分别为SPLINEF（11.98%），SARIMA-SPLINEF（15.14%），SARIMA-NNETAR-REG-SPLINEF（16.06%），SARIMA-TBAT-NNETAR-REG-SPLINEF（17.75%）。单一模型、2个模型的组合模型、3个模型的组合模型、4个模型的组合模型最优预测模型分别为SARIMA-REG（34.48%），SARIMA-REG-TBATS（22.77%），SARIMA-TBATS-SPLINEF（23.84%），SARIMA-SARIMA-REG-TBATS-SPLINEF（22.31%）。单一模型、2个模型的组合模型、3个模型的组合模型、4个模型的组合模型最优拟合及预测模型分别为SPLINEF（24.75%），SARIMA-SPLINEF（22.55%），SARIMA-TBATS-SPLINEF（20.92%），SARIMA-SARIMA-REG-TBATS-SPLINEF（20.75%）。

结论

综合模型数量、模型拟合及预测精度认为SARIMA-TBATS-SPLINEF为最优预测模型，可以用于湖北省肾综合征出血热监测预警。

肾综合征出血热  /  预测  /  组合模型  /  湖北省  /  权重
Objective

To explore the optimal prediction model for hantavirus hemorrhagic fever with renal syndrome (HFRS) in Hubei province, and to provide a basis for establishing a monitoring and early warning model for HFRS.

Methods

Using monthly surveillance data of HFRS incidence in Hubei province from 2005 to 2021, eight single time series models based on exponential smoothing (ETS), seasonal autoregressive integrated moving average (SARIMA) with and without regression variables, a state space model with Box-Cox transformation, ARMA errors, trend, and seasonal components (TBATS), a time series neural network model (NNETAR) with and without regression variables, a linear regression time series model (TSLM), and a cubic spline prediction model (SPLINEF) were used to build 162 models through 1-4 model combinations. The mean absolute percentage error (MAPE) was used as an evaluation index to evaluate the fitting and prediction performance of the models. The comprehensive fitting and prediction performance were evaluated by calculating the mean MAPE of fitting and prediction.

Results

The TSLM model and its combined models had a comprehensive MAPE of more than 100%. Among the other 98 models, the optimal fitting models for single, two, three, and four-model combinations were SPLINEF (11.98%), SARIMA-SPLINEF (15.14%), SARIMA-NNETAR-REG-SPLINEF (16.06%), and SARIMA-TBAT-NNETAR-REG-SPLINEF (17.75%), respectively. The optimal prediction models for single, two, three, and four-model combinations were SARIMA-REG (34.48%), SARIMA-REG-TBATS (22.77%), SARIMA-TBATS-SPLINEF (23.84%), and SARIMA-SARIMA-REG-TBATS-SPLINEF (22.31%), respectively. The optimal fitting and prediction models for single, two, three, and four-model combinations were SPLINEF (24.75%), SARIMA-SPLINEF (22.55%), SARIMA-TBATS-SPLINEF (20.92%), and SARIMA-SARIMA-REG-TBATS-SPLINEF (20.75%), respectively.

Conclusion

Based on the number of models, fitting and prediction accuracy, SARIMA-TBATS-SPLINEF is considered the optimal prediction model and can be used for monitoring and early warning of HFRS in Hubei.

Hemorrhagic fever with renal syndrome  /  Prediction  /  Hybrid model  /  Hubei province  /  Weights
刘天, 吴杨, 刘漫, 陈琦, 童叶青, 赵婧. 湖北省肾综合征出血热预测模型建立. 现代预防医学, 2024 , 51 (12) : 2287 -2293 . DOI: 10.20043/j.cnki.MPM.202312041
Tian LIU, Yang WU, Man LIU, Qi CHEN, Ye-qing TONG, Jing ZHAO. Establishments of a prediction model for hantavirus hemorrhagic fever with renal syndrome, Hubei[J]. Modern Preventive Medicine, 2024 , 51 (12) : 2287 -2293 . DOI: 10.20043/j.cnki.MPM.202312041
正文
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肾综合征出血热是由汉坦病毒感染引起的，以鼠类等啮齿类动物为主要传染源的自然疫源性传染病[1]。我国是肾综合征出血热的高发国家，全世界约90%病例分布在我国[2]。准确拟合及预测传染病的趋势是科学、精准实施监测预警的基础。肾综合征出血热监测预警能为识别该传染病流行特征、早期发现规模化疫情提供重要参考，为进一步采取以防鼠灭鼠、应急接种及健康教育为主的综合性干预措施提供依据。既往曾有研究建立了全国肾综合征出血热预测模型[3-4]；但华中地区，尤其是湖北省肾综合征出血热预测模型鲜有报道。湖北省是我国肾综合征出血热的老疫区[5]，2014—2019年湖北省肾综合征出血热报告发病率呈上升趋势[6]，防控形势严峻，建立拟合及预测精度高的模型对该省肾综合征出血热监测预警至关重要。本研究利用2005—2021年湖北省肾综合征出血热逐月发病率监测数据，分别建立多种模型，评价拟合及预测效果，筛选最优模型，以期为该省肾综合征出血热的防控提供科学依据。
1　资料与方法
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1.1　资料来源
中国疾病预防控制中心的《监测报告管理》系统按照发病日期为2005年1月1日—2021年12月31日，现住址为湖北省，卡片状态为“已终审”导出肾综合征出血热病例资料。湖北省人口数据来源于中国疾病预防控制中心的《综合管理系统》。通过逐月发病数与人口数计算逐月发病率。
1.2　方法
为探讨湖北省肾综合征出血热时间序列最优预测模型，本研究以6种常见单一时间序列模型为基础，通过不同组合，共建立3类共162个模型。第1类是指数平滑模型（ETS），乘积季节自回归移动平均模型（SARIMA），具有 Box-Cox变换、ARMA误差、趋势和季节性分量的指数平滑状态空间模型（TBATS），时间序列神经网络模型（NNETAR），线性回归时间序列模型（TSLM）和三次样条预测模型（SPLINEF）6个单一时间序列预测模型；第2类是带回归变量的SARIMA（SARIMA-REG）和NNETAR（NNETAR-REG）；第3类是上述8个模型分别选取2~4个进行组合的组合模型（共154个，2个组合28个，3个组合56个，4个组合70个）。所有模型建立均在R软件中实现。
1.2.1　ETS
ETS模型具有三个主要参数：误差、趋势和季节性分量，可以是加法(A)模型、乘法(M) 模型或无(N)趋势模型[7]。本文采用自动定阶方法，拟合ETS模型，基于Akaike信息准则(AIC)最小值选择最佳模型[7]。
1.2.2　SARIMA与SARIMA-REG
SARIMA模型一般表达式为SARIMA(p, d, q) (P, D, Q)s。式中，d表示时间序列的差分次数，p表示自回归阶数，q表示移动平均的阶数。D表示季节性差分次数，P表示季节性自回归阶数，Q表示季节性移动平均阶数，s表示周期性模式的长度[8]。在R软件中，auto.arima()函数根据AIC自动选择最佳SARIMA模型[9]。SARIMA-REG模型是指含回归变量的SARIMA模型。本研究回归变量包括3个：一是考虑周期性，根据该省荆州市既往研究结果，肾综合征出血热周期性升高为12年/次，最近一次发病高峰出现在2006—2007年；本研究将2005—2009年、2017—2021年赋值为1，其它年份赋值为0。二是考虑季节性，湖北省肾综合征出血热出血热发病高峰为5—6月、11月—次年1月[6]，将上述月份赋值为1，其他月份赋值为0。三是考虑新型冠状病毒疫情影响，将2020—2021年赋值为1，其它年份赋值为0。
1.2.3　TBATS
该模型是含多个成分的组合模型，T表示傅里叶三角变换，B表示Box-Cox变换，A表示ARMA模型，T是对象时间序列中的趋势特征，S表示对象时间序列中的季节性。模型一般表达式为TBATS(ω, p, q, φ, {m1, k1}, {m2, k2}, …,{mT, kT})，其中ω代表Box-Cox变换参数，p, q为ARMA模型参数，φ表示阻尼参数值，m表示季节周期，k是用于季节性特征的谐波数[10]。在R软件中，采用tbats()函数建立模型[10]。
1.2.4　NNETAR与NNETAR-REG
NNETAR是一种神经网络，是一种应用于预测问题的参数非线性模型。在NNETAR模型中，预测分两个阶段进行。首先采用自回归模型（AR）进行定阶，AIC最小原则确定自回归阶数p。第二阶段，以非季节1至p期滞后数据、P期季节性滞后数据作为输入层，k个隐藏神经元的数量，实际值作为输出层训练神经网络[11]。模型表达式为NNETAR(p, P, k)m，m表示季节周期[11]。在R软件中，采用nnetar()函数建立模型。NNETAR-REG模型为含回归变量的SARIMA模型，纳入回归变量同SARIMA-REG模型。
1.2.5　TSLM
该模型是由J Hyndman等人开发的一种时间序列回归模型，在线性回归基础上考虑季节性和趋势性变化。模型通过建立多个月份的哑变量和趋势性变量建立线性回归模型[12]。在R软件中，采用tslm()函数建立模型。
1.2.6　SPLINEF
三次样条基于随机状态空间模型，该模型允许使用似然技术估计平滑参数。三次样条模型可以被认为是ARIMA(0, 2, 2)模型的特例。它为预测提供了更好的长期趋势平滑性和线性度[13]。在R软件中，采用splinef()函数建立模型。
1.2.7　组合模型
对上述8个模型选取2~4个进行组合，模型组合按相同权重计算得到拟合（预测）最终值y，y的计算公式为：，其中n表示组合模型个数，取值为2~4，y1，y1，…，yi表示进行组合的单一模型。
1.3　模型评价及统计分析
2005年1月—2020年12月湖北省逐月肾综合征出血热发病率数据作为训练数据，用于模型训练及拟合效果评价；2021年1—12月数据作为测试数据，用于模型预测效果评价。评价指标选择平均绝对百分比误差 (MAPE)。为兼顾拟合及预测效果，以拟合及预测评价的MAPE均值（MMAPE）作为模型最终筛选指标，以MMAPE最小者为最优模型。局部回归季节分解法（STL）用于分析肾综合征出血热季节性和趋势性，在R软件中利用stl()函数进行分解[14]。Ljung-Box Q检验用于诊断残差序列是否为白噪声序列。统计分析均在R 4.1软件中进行，“ggplot2”包用于图形绘制。检验水准α=0.05。
2　结果
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2.1　肾综合征出血热发病概况
2005—2021年湖北省累计报告肾综合征出血热5 798例，年均发病率0.57/10万，月均发病率0.05/10万。湖北省肾综合征出血热存在明显长期趋势，2016年前发病率维持较低水平，2016年后发病率明显升高，至2018年达到发病高峰，随后有所下降，但较2016年前仍较高。肾综合征出血热发病存在明显季节性，呈双峰型特点；4—7月为春夏季发病高峰，11月—次年1月为秋冬季发病高峰，春夏季发病高峰（2 449例，占42.24%）略高于秋冬季发病高峰（2 127例，占36.69%）。分地区来看，除神农架林区无病例报告外，其余16个地级市（自治州、省辖县）均有病例报告；发病率最高的5个地区为潜江市（761例，4.68/10万）、天门市（578例，2.30/10万）、荆门市（695例，1.41/10万）、荆州市（1 399例，1.40/10万）、仙桃市（303例，1.37/10万）。见图1。
2.2　模型建立
分别建立8个模型，Ljung-Box Q检验显示SARIMA、SARIMA-REG、TBATS、ETS、NNETAR-REG残差为白噪声，模型对原始数据信息提取充分；NNETAR、TSLM、SPLINEF模型残差非白噪声序列，模型对原始数据信息提取不充分，残差存在明显趋势性变化，见表1、图2。对获得的8个模型选择2~4个进行组合，共获得154个组合模型。
2.3　模型拟合及预测结果比较
TSLM模型及其构建组合模型拟合及预测综合MAPE均超过100%，模型拟合及预测效果较差予以剔除。剩余98个模型中，总体来看，组合模型拟合及预测效果优于单一模型；组合模型个数越多，模型拟合及预测综合MAPE越小，精度越高。综合精度最高的模型为ARIMA，SARIMA-REG，TBATS，SPLINEF组成的组合模型，其次为SARIMA，TBATS和SPLINEF组成的组合模型。单一模型SPLINEF模型综合MAPE最小，其次为SARIMA-REG，预测MAPE均超过30%。2个模型组合的组合模型，综合考虑拟合及预测效果，SARIMA-REG和TBATS组合模型最优（拟合MAPE：24.42%，预测MAPE：22.77%）; 3个模型组合的组合模型，综合考虑拟合及预测效果，SARIMA、TBATS和SPLINEF组合模型最优（拟合MAPE：18.00%，预测MAPE：23.84%）; 4个模型组合的组合模型，综合考虑拟合及预测效果，SARIMA、SARIMA-REG、TBAT和SPLINEF组合模型最优（拟合MAPE：19.19%，预测MAPE：22.31%）。综合考虑拟合及预测效果、纳入模型数量，SARIMA、TBATS和SPLINEF组合模型为最优模型（拟合MAPE：18.00%，预测MAPE：23.84%）。见图3、4，表2。
3　讨论
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季节分解显示，湖北省肾综合征出血热2017年呈快速上升趋势。建立肾综合征出血热监测预警模型是动态监测该省肾综合征出血热趋势变化的关键，既往有关于该省肾综合征出血热未来趋势预测的报道[15]，但主要为预测应用的研究，未对模型的适用性及模型优化进行探讨。准确预测疾病未来基线水平是监测预警的关键技术。为了筛选湖北省肾综合征出血热最优预测模型，本文以6种常见时间序列模型为基础，通过不同组合共建立162个模型，采用MAPE作为模型筛选指标，综合考虑拟合及预测效果，最终筛选出最优模型为SARIMA-REG-TBATS-SPLINEF组合模型。按照Pao等[16]的分类标准，最优模型的拟合及预测精度均达到了“较好”，可以用于该省肾综合征出血热的监测预警。
既往传染病预测模型的筛选通常基于数个模型进行探讨；建立组合模型多集中在某个组合模型与单一模型比较，鲜有批量组建组合模型再筛选最优模型的研究。本文在3个方面进行创新：一是批量组建组合模型。早在1969年Bates等[17]指出组合模型预测精度往往优于单一模型。但关于组合模型组合方式-组合原则无统一标准。为了筛选最优模型，本文对单一模型及2~4个模型的组合模型自由组合，以筛选出最优模型。本文至多选择4个模型进行组合，主要考虑随着模型个数增加，模型拟合及预测精度提升不大；同时，单一模型数量过多可能导致组合模型过于冗杂，不便于解释。在本文最优模型选择中，SARIMA-SARIMA-REG-TBATS-SPLINEF组合模型总综合MAPE最小，但考虑到SARIMA与SARIMA-REG均在组合模型中，且较SARIMA-REG-TBATS-SPLINEF组合模型精度提升不大，综合认为SARIMA-REG-TBATS-SPLINEF组合模型为最优模型。二是在建立单一模型时，充分考虑其它因素，包括周期性-季节性和新冠病毒疫情的影响，结果显示SARIMA-REG综合精度高于单一SARIMA模型；最优模型将NNETAR-REG纳入，提示本文纳入的变量提升了单一模型精度。三是在模型评价方面。MAPE是最常用的模型传染病预测模型精度评价指标。预测模型往往存在拟合精度高，预测精度低。提示模型可能存在过拟合，模型泛化能力差；另一方面，预测模型有时存在模型拟合效果不好，预测精度较高的情况。2种情况的存在，不便于筛选最优模型。在本文中，本文已拟合-预测的MAPE均值作为综合MAPE，综合评价模型拟合及预测效果。在尚无综合性评价指标的情况下，不失为一种较好的处理方法。
综上，本文通过建立多种组合模型，筛选出了湖北省肾综合征出血热较好的监测预警模型，今后湖北省可利用该模型动态监测肾综合征出血热趋势变化，为该省肾综合征出血热防控提供科学指导。
基金
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  • 中国疾病预防控制中心公共卫生应急反应机制的运行(102393220020010000017)
  • 荆州市科技局2023年医疗卫生科技计划项目(2023HC38)
文献
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2024年第51卷第12期
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doi: 10.20043/j.cnki.MPM.202312041
  • 接收时间：2023-12-04
  • 首发时间：2026-03-17
  • 出版时间：2024-06-25
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  • 收稿日期：2023-12-04
基金
中国疾病预防控制中心公共卫生应急反应机制的运行(102393220020010000017)
荆州市科技局2023年医疗卫生科技计划项目(2023HC38)
作者信息
    1.荆州市疾病预防控制中心传染病防治所，湖北 荆州 434000
    2.长江大学公共卫生研究中心
    3.湖北省疾病预防控制中心传染病防治所
    4. 中国疾病预防控制中心卫生应急中心（传染病溯源预警与智能决策全国重点实验室，中国疾病预防控制中心

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赵婧，E-mail：
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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