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Article(id=1321169965399519635, tenantId=1146029695717560320, journalId=1319373219989389464, issueId=1321169924697993338, articleNumber=null, orderNo=null, doi=10.11847/zgggws1145990, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1730304000000, receivedDateStr=2024-10-31, revisedDate=1731859200000, revisedDateStr=2024-11-18, acceptedDate=1739721600000, acceptedDateStr=2025-02-17, onlineDate=1792921065901, onlineDateStr=2026-10-25, pubDate=1746806400000, pubDateStr=2025-05-10, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1792921065901, onlineIssueDateStr=2026-10-25, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1792921065901, creator=13701087609, updateTime=1792921065901, updator=13701087609, issue=Issue{id=1321169924697993338, tenantId=1146029695717560320, journalId=1319373219989389464, year='2025', volume='41', issue='5', pageStart='513', pageEnd='640', issueExtLink='null', onlineDate='null', pubDate='1746806400000', pubDateStr='2025-05-10', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1792921056198, creator='13701087609', updateTime=1792921056198, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=592, endPage=598, ext={EN=ArticleExt(id=1321169965613429140, articleId=1321169965399519635, tenantId=1146029695717560320, journalId=1319373219989389464, language=EN, title=Projected changes and burden of type 2 diabetes in China from 1990 to 2021: an analysis of GBD 2021 data, columnId=1320427686514770171, journalTitle=Chinese Journal of Public Health, columnName=Survey and Report, runingTitle=null, highlight=null, articleAbstract=
Objective

To analyze the disease burden and trends of type 2 diabetes mellitus (T2DM) in China from 1990 to 2021, and to predict the T2DM disease burden from 2022 to 2026, providing data support and a scientific basis for the development and evaluation of diabetes prevention and control strategies.

Methods

Data on the disease burden of T2DM in China were obtained from the Global Burden of Disease Study 2021 database. The trends in the prevalence, mortality, and disability-adjusted life years (DALYs) rates of T2DM in China from 1990 to 2021 were analyzed. Autoregressive integrated moving average (ARIMA) models, neural network autoregression (NNAR) models, and combined ARIMA-NNAR models for the prevalence, mortality, and DALYs rates of T2DM in China were established based on data from 1990 to 2016 (training set). Model evaluation was performed using data from 2017 to 2021 (test set). The mean absolute percentage error (MAPE), mean absolute error (MAE), and root mean square error (RMSE) were used to compare the fitting and prediction performance of the models, and the best model was selected to predict the disease burden of T2DM in China from 2022 to 2026.

Results

By calculating the rate of change of T2DM in China from 1990 to 2021, the prevalence, mortality, and DALYs rates of T2DM in China in 2021 showed a significant upward trend compared with 1990, and the disease burden was higher in males than in females. The dynamic trends of the predicted values of the ARIMA model, NNAR model, and combined ARIMA-NNAR model were basically consistent with the actual situation, but the values of each evaluation index of the combined prediction model showed that the prediction effect was better than that of the single prediction model. The prevalence, mortality, and DALYs rates of T2DM in China from 2022 to 2026 predicted by the ARIMA-NNAR model were 8 353.71/105, 8 565.00/105, 8 776.30/105, 8 987.60/105, and 9 198.90/105; 12.55/105, 12.78/105, 12.99/105, 13.20/105, and 13.41/105; and 826.79/105, 846.22/105, 864.49/105, 881.86/105, and 898.54/105, respectively.

Conclusions

The combined ARIMA-NNAR model has a good effect in predicting the disease burden of T2DM in China and can provide a reference for short-term prediction of the T2DM disease burden. The prevalence, mortality, and DALYs rates of T2DM in China will continue to increase from 2022 to 2026, indicating that the disease burden of T2DM in China will continue to increase, and the situation of disease prevention and control remains severe.

, authors=Junhao MA1, Guangqiang MIAO2, Guixiao WANG2, Shen LI2, Liping YANG2, 3, authorsList=Junhao MA, Guangqiang MIAO, Guixiao WANG, Shen LI, Liping YANG, authorCompany=null, correspAuthors=Liping YANG, authorNote=null, correspAuthorsNote=
YANG Liping, E-mail:
, copyrightStatement=Copyright © 2025 Chinese Journal of Public Health. All rights reserved., copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1321169973096067529, articleId=1321169965399519635, tenantId=1146029695717560320, journalId=1319373219989389464, language=CN, title=1990—2021年中国2型糖尿病疾病负担及未来变化趋势预测, columnId=1320427686770622717, journalTitle=中国公共卫生, columnName=调查报告与分析, runingTitle=null, highlight=null, articleAbstract=
目的

分析1990—2021年中国2型糖尿病（T2DM）的疾病负担和变化趋势，预测2022—2026年的T2DM疾病负担，为制定和评估糖尿病防治策略提供数据支持和科学依据。

方法

从全球疾病负担2021数据库中获取中国T2DM疾病负担数据，分析1990—2021年中国T2DM患病率、死亡率和DALYs率的变化趋势；基于1990—2016年数据（训练集）建立中国T2DM患病率、死亡率及DALYs率的自回归整合移动平均（ARIMA）模型、神经网络自回归（NNAR）模型和ARIMA-NNAR组合模型，利用2017—2021年数据（测试集）进行模型评价；采用平均绝对百分误差（MAPE）、平均绝对误差（MAE）和均方根误差（RMSE）比较模型的拟合和预测效果，选择最佳模型预测2022—2026年中国T2DM疾病负担。

结果

通过计算1990—2021年中国T2DM的变化率，2021年中国T2DM患病率、死亡率、DALYs率相较1990年均具有明显上升趋势，且男性疾病负担高于女性。ARIMA模型、NNAR模型和ARIMA-NNAR组合模型预测值的动态趋势与实际情况基本一致，但组合预测模型各评价指标的值均显示预测效果好于单预测模型。经ARIMA-NNAR模型预测得到2022—2026年中国T2DM患病率分别为8 353.71/10万、8 565.00/10万、8 776.30/10万、8 987.60/10万、9 198.90/10万，死亡率分别为12.55/10万、12.78/10万、12.99/10万、13.20/10万、13.41/10万，DALYs率分别为826.79/10万、846.22/10万、864.49/10万、881.86/10万、898.54/10万。

结论

ARIMA-NNAR组合模型在预测中国T2DM疾病负担应用中具有良好的效果，可为T2DM疾病负担短期预测提供借鉴与参考。中国T2DM疾病患病率、死亡率和DALYs率在2022—2026年仍会增长，表明中国T2DM疾病负担将持续加重，疾病防控形势依然严峻。

, authors=马军豪1, 苗广强2, 王贵骁2, 李燊2, 杨立平2, 3, *, *, authorsList=马军豪, 苗广强, 王贵骁, 李燊, 杨立平, authorCompany=null, correspAuthors=杨立平, authorNote=

马军豪（2001—），硕士在读，研究方向：预防医学、生物医学数据分析

, correspAuthorsNote=
杨立平， E-mail：
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figureFileBig=Ebi0Z4YvkTJ5fS65zrRpqg==, tableContent=null), ArticleFig(id=1321169977722384892, tenantId=1146029695717560320, journalId=1319373219989389464, articleId=1321169965399519635, language=CN, label=图3, caption=基于NNAR模型的T2DM患病率、死亡率、DALYs率拟合预测, figureFileSmall=SBGO3/OUqUEdU6IXQYPMMw==, figureFileBig=Ebi0Z4YvkTJ5fS65zrRpqg==, tableContent=null), ArticleFig(id=1321169977785299453, tenantId=1146029695717560320, journalId=1319373219989389464, articleId=1321169965399519635, language=EN, label=Fig.4, caption=Fitted and predicted prevalence, mortality, and DALY rates of type 2 diabetes mellitus based on the ARIMA-NNAR combined model, figureFileSmall=V/rjYYyKU+jbiIJP7a5Q5A==, figureFileBig=s9jYW29LsfoOw3xiElQruw==, tableContent=null), ArticleFig(id=1321169977864991230, tenantId=1146029695717560320, journalId=1319373219989389464, articleId=1321169965399519635, language=CN, label=图4, caption=基于ARIMA-NNAR组合模型的T2DM患病率、死亡率、DALYs率拟合预测, figureFileSmall=V/rjYYyKU+jbiIJP7a5Q5A==, 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(middle), and the total population (right) based on the combined model, figureFileSmall=BOFUCfE/mz6QlGAV7smSTg==, figureFileBig=lBUAAnUbwJAHbs7U8OJ/Tw==, tableContent=null), ArticleFig(id=1321169978301198850, tenantId=1146029695717560320, journalId=1319373219989389464, articleId=1321169965399519635, language=CN, label=图6, caption=基于组合模型的T2DM男性（左）、女性（中）以及总人群死亡率（右）拟合预测, figureFileSmall=BOFUCfE/mz6QlGAV7smSTg==, figureFileBig=lBUAAnUbwJAHbs7U8OJ/Tw==, tableContent=null), ArticleFig(id=1321169978364113411, tenantId=1146029695717560320, journalId=1319373219989389464, articleId=1321169965399519635, language=EN, label=Fig.7, caption=Fitted and predicted DALYs rates of T2DM in males (left), females (middle), and the total population (right) based on the combined model, figureFileSmall=N3ZBYZCAFwqLTOht2s+eOA==, figureFileBig=fmGirirsCpADohqxLw1rYg==, tableContent=null), ArticleFig(id=1321169978439610884, tenantId=1146029695717560320, journalId=1319373219989389464, articleId=1321169965399519635, language=CN, label=图7, caption=基于组合模型的T2DM男性（左）、女性（中）以及总人群（右）DALYs率拟合预测, figureFileSmall=N3ZBYZCAFwqLTOht2s+eOA==, figureFileBig=fmGirirsCpADohqxLw1rYg==, tableContent=null), ArticleFig(id=1321169978502525445, tenantId=1146029695717560320, journalId=1319373219989389464, articleId=1321169965399519635, language=EN, label=Tab.1, caption=

Changes in the disease burden of T2DM in China from 1990 to 2021 (1/105) in male and female

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组别患病率标化
患病率		死亡率标化
死亡率		DALYs率标化
DALYs率
男性19902 963.773 571.204.629.04316.96429.18
20218 545.256 554.5011.829.97830.09620.06
变化率/%188.3283.54155.8410.29161.8944.48
女性19902 921.273 454.116.749.84357.54450.10
20217 720.165 532.6712.748.08780.41523.52
变化率/%164.2760.1889.02–17.89118.2716.32
总计19902 943.193 519.815.659.29336.61438.68
20218 142.416 055.5112.278.74805.84569.84
变化率/%176.6572.04117.17–5.92139.4029.90
), ArticleFig(id=1321169978582217222, tenantId=1146029695717560320, journalId=1319373219989389464, articleId=1321169965399519635, language=CN, label=表1, caption=

1990—2021中国T2DM疾病负担变化情况（1/10万）

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组别患病率标化
患病率		死亡率标化
死亡率		DALYs率标化
DALYs率
男性19902 963.773 571.204.629.04316.96429.18
20218 545.256 554.5011.829.97830.09620.06
变化率/%188.3283.54155.8410.29161.8944.48
女性19902 921.273 454.116.749.84357.54450.10
20217 720.165 532.6712.748.08780.41523.52
变化率/%164.2760.1889.02–17.89118.2716.32
总计19902 943.193 519.815.659.29336.61438.68
20218 142.416 055.5112.278.74805.84569.84
变化率/%176.6572.04117.17–5.92139.4029.90
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Comparison of prediction effects of different models in the prevalence, mortality, and DALYs rates

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特征模型训练集测试集
MAPE/%MAERMSEMAPE/%MAERMSE
患病率ARIMA0.43417.91823.8542.372186.370221.665
NNAR1.19148.48665.2193.763295.837354.048
ARIMA-NNAR0.39716.78422.3492.369185.662221.752
死亡率ARIMA0.8220.0690.1010.8640.1010.110
NNAR1.2570.1080.1596.4580.7660.866
ARIMA-NNAR0.8200.0690.1000.8590.1010.110
DALYs率ARIMA0.4512.1633.0282.26217.58020.194
NNAR0.9664.6086.0127.74659.91966.083
ARIMA-NNAR0.4072.0002.8622.24317.43320.089
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不同模型预测效果比较

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特征模型训练集测试集
MAPE/%MAERMSEMAPE/%MAERMSE
患病率ARIMA0.43417.91823.8542.372186.370221.665
NNAR1.19148.48665.2193.763295.837354.048
ARIMA-NNAR0.39716.78422.3492.369185.662221.752
死亡率ARIMA0.8220.0690.1010.8640.1010.110
NNAR1.2570.1080.1596.4580.7660.866
ARIMA-NNAR0.8200.0690.1000.8590.1010.110
DALYs率ARIMA0.4512.1633.0282.26217.58020.194
NNAR0.9664.6086.0127.74659.91966.083
ARIMA-NNAR0.4072.0002.8622.24317.43320.089
), ArticleFig(id=1321169978787738121, tenantId=1146029695717560320, journalId=1319373219989389464, articleId=1321169965399519635, language=EN, label=Tab.3, caption=

Predicted burden of type 2 diabetes mellitus from 2022 to 2026 based on the ARIMA-NNAR combined model (1/105)

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年份患病率死亡率DALYs率
20228 347.1812.55826.91
20238 569.8612.78846.34
20248 781.1512.99864.60
20258 992.4513.20881.98
20269 203.7513.41898.66
), ArticleFig(id=1321169978867429898, tenantId=1146029695717560320, journalId=1319373219989389464, articleId=1321169965399519635, language=CN, label=表3, caption=

基于ARIMA-NNAR组合模型的2022—2026年T2DM疾病负担预测情况（1/10万）

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年份患病率死亡率DALYs率
20228 347.1812.55826.91
20238 569.8612.78846.34
20248 781.1512.99864.60
20258 992.4513.20881.98
20269 203.7513.41898.66
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1990—2021年中国2型糖尿病疾病负担及未来变化趋势预测
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马军豪 1 , 苗广强 2 , 王贵骁 2 , 李燊 2 , 杨立平 2, 3, *, *
中国公共卫生 | 调查报告与分析 2025,41(5): 592-598
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中国公共卫生 |调查报告与分析 2025 , 41 (5) : 592 -598
1990—2021年中国2型糖尿病疾病负担及未来变化趋势预测
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马军豪1, 苗广强2, 王贵骁2, 李燊2, 杨立平2, 3, *, *
作者信息
  • 1杭州医学院公共卫生学院，杭州 310053
  • 2新疆医科大学医学工程技术学院，乌鲁木齐 830017
  • 3新疆医科大学医工交叉研究所，乌鲁木齐市 830017
通讯作者:
杨立平， E-mail：
作者简介:

马军豪（2001—），硕士在读，研究方向：预防医学、生物医学数据分析

Projected changes and burden of type 2 diabetes in China from 1990 to 2021: an analysis of GBD 2021 data
Junhao MA1, Guangqiang MIAO2, Guixiao WANG2, Shen LI2, Liping YANG2, 3
Affiliations
  • 1School of Public Health, Hangzhou Medical College, Hangzhou 310053, China
  • 2Department of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830017, China
  • 3Institute of Medical Engineering Interdisciplinary Research, Xinjiang Medical University, Urumqi 830017, China
    • Corresponding Author:
    YANG Liping, E-mail:
出版时间: 2025-05-10 doi: 10.11847/zgggws1145990
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摘要
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目的

分析1990—2021年中国2型糖尿病（T2DM）的疾病负担和变化趋势，预测2022—2026年的T2DM疾病负担，为制定和评估糖尿病防治策略提供数据支持和科学依据。

方法

从全球疾病负担2021数据库中获取中国T2DM疾病负担数据，分析1990—2021年中国T2DM患病率、死亡率和DALYs率的变化趋势；基于1990—2016年数据（训练集）建立中国T2DM患病率、死亡率及DALYs率的自回归整合移动平均（ARIMA）模型、神经网络自回归（NNAR）模型和ARIMA-NNAR组合模型，利用2017—2021年数据（测试集）进行模型评价；采用平均绝对百分误差（MAPE）、平均绝对误差（MAE）和均方根误差（RMSE）比较模型的拟合和预测效果，选择最佳模型预测2022—2026年中国T2DM疾病负担。

结果

通过计算1990—2021年中国T2DM的变化率，2021年中国T2DM患病率、死亡率、DALYs率相较1990年均具有明显上升趋势，且男性疾病负担高于女性。ARIMA模型、NNAR模型和ARIMA-NNAR组合模型预测值的动态趋势与实际情况基本一致，但组合预测模型各评价指标的值均显示预测效果好于单预测模型。经ARIMA-NNAR模型预测得到2022—2026年中国T2DM患病率分别为8 353.71/10万、8 565.00/10万、8 776.30/10万、8 987.60/10万、9 198.90/10万，死亡率分别为12.55/10万、12.78/10万、12.99/10万、13.20/10万、13.41/10万，DALYs率分别为826.79/10万、846.22/10万、864.49/10万、881.86/10万、898.54/10万。

结论

ARIMA-NNAR组合模型在预测中国T2DM疾病负担应用中具有良好的效果，可为T2DM疾病负担短期预测提供借鉴与参考。中国T2DM疾病患病率、死亡率和DALYs率在2022—2026年仍会增长，表明中国T2DM疾病负担将持续加重，疾病防控形势依然严峻。

2型糖尿病  /  疾病负担  /  ARIMA模型  /  NNAR模型  /  组合预测模型
Objective

To analyze the disease burden and trends of type 2 diabetes mellitus (T2DM) in China from 1990 to 2021, and to predict the T2DM disease burden from 2022 to 2026, providing data support and a scientific basis for the development and evaluation of diabetes prevention and control strategies.

Methods

Data on the disease burden of T2DM in China were obtained from the Global Burden of Disease Study 2021 database. The trends in the prevalence, mortality, and disability-adjusted life years (DALYs) rates of T2DM in China from 1990 to 2021 were analyzed. Autoregressive integrated moving average (ARIMA) models, neural network autoregression (NNAR) models, and combined ARIMA-NNAR models for the prevalence, mortality, and DALYs rates of T2DM in China were established based on data from 1990 to 2016 (training set). Model evaluation was performed using data from 2017 to 2021 (test set). The mean absolute percentage error (MAPE), mean absolute error (MAE), and root mean square error (RMSE) were used to compare the fitting and prediction performance of the models, and the best model was selected to predict the disease burden of T2DM in China from 2022 to 2026.

Results

By calculating the rate of change of T2DM in China from 1990 to 2021, the prevalence, mortality, and DALYs rates of T2DM in China in 2021 showed a significant upward trend compared with 1990, and the disease burden was higher in males than in females. The dynamic trends of the predicted values of the ARIMA model, NNAR model, and combined ARIMA-NNAR model were basically consistent with the actual situation, but the values of each evaluation index of the combined prediction model showed that the prediction effect was better than that of the single prediction model. The prevalence, mortality, and DALYs rates of T2DM in China from 2022 to 2026 predicted by the ARIMA-NNAR model were 8 353.71/105, 8 565.00/105, 8 776.30/105, 8 987.60/105, and 9 198.90/105; 12.55/105, 12.78/105, 12.99/105, 13.20/105, and 13.41/105; and 826.79/105, 846.22/105, 864.49/105, 881.86/105, and 898.54/105, respectively.

Conclusions

The combined ARIMA-NNAR model has a good effect in predicting the disease burden of T2DM in China and can provide a reference for short-term prediction of the T2DM disease burden. The prevalence, mortality, and DALYs rates of T2DM in China will continue to increase from 2022 to 2026, indicating that the disease burden of T2DM in China will continue to increase, and the situation of disease prevention and control remains severe.

type 2 diabetes mellitus  /  disease burden  /  ARIMA model  /  NNAR model  /  combined forecasting model
马军豪, 苗广强, 王贵骁, 李燊, 杨立平. 1990—2021年中国2型糖尿病疾病负担及未来变化趋势预测. 中国公共卫生, 2025 , 41 (5) : 592 -598 . DOI: 10.11847/zgggws1145990
Junhao MA, Guangqiang MIAO, Guixiao WANG, Shen LI, Liping YANG. Projected changes and burden of type 2 diabetes in China from 1990 to 2021: an analysis of GBD 2021 data[J]. Chinese Journal of Public Health, 2025 , 41 (5) : 592 -598 . DOI: 10.11847/zgggws1145990
正文
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糖尿病（diabetes mellitus，DM）是一种慢性代谢性疾病，其特征是胰岛素分泌和/或作用缺陷导致高血糖水平[1]。根据病理生理学，糖尿病分1型糖尿病和2型糖尿病（type 2 diabetes mellitus, T2DM）两种形式[2]。据统计，2017年全球约有糖尿病患者 4.25 亿人，其中大约 90 %～95% 患者为T2DM[3]。国际糖尿病联盟（International Diabetes Federation, IDF）发布的《2021 IDF全球糖尿病地图（第10版）》[4]显示，2021年中国 20 ～ 79岁成人糖尿病患者约1.41亿，位居全球第一，年龄调整后的患病率为 10.6%，相关卫生支出约1 653亿美元；预计到2030年和2045年我国将分别约有1.64亿和1.74亿糖尿病患者，年龄调整后的患病率将分别达到11.8%和12.5%。这些数据表明，糖尿病给国家及家庭带来了沉重的经济负担，且中国糖尿病患者数量庞大，防治形势严峻，糖尿病防控工作仍面临巨大挑战。本研究基于最新发布的2021全球疾病负担（Global Burden of Disease 2021, GBD 2021）数据库中1990—2021年中国T2DM疾病负担数据，运用时间序列分析方法，分析流行现状及发展趋势，并建立组合模型预测未来5年T2DM疾病负担，旨在为降低中国T2DM的疾病负担提供科学依据和决策支撑。
1　资料与方法
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1.1　数据来源
本研究所用的数据来源于华盛顿大学健康指标与评估研究所（IHME）发布的GBD 2021数据库。GBD提供了有关发病率，死亡率，残疾调整生命年（DALYs）和年龄标准化率（ASRs）等指标的详细数据，旨在量化1990—2021年204个国家和地区的371种疾病和伤害以及88种风险因素的年龄和性别健康损失[5–7]。根据《国际疾病分类第10版》（International Classification of Diseases Version 10, ICD-10）[8]，T2DM 疾病编码为：E14、E11。
1.2　方法
1.2.1　指标定义
对T2DM 疾病负担在全人群及不同性别人群中的变化趋势进行描述性分析，同时探究了 T2DM 疾病负担在不同年龄段的变化趋势，其中，变化率[9]=（2021年指标值–1990年指标值）/1990年指标值×100%。DALYs是描述疾病负担最重要的综合性指标之一，由YLL和YLD相加得出[10]。
1.2.2　ARIMA模型
ARIMA（$ p $，$ d $，$ q $）模型是一种广泛应用于时间序列分析的统计模型，其中 $ p $ 代表自回归项的阶数，$ d $ 代表使序列平稳所需的差分次数，而 $ q $ 代表移动平均项的阶数。在R语言中，可以利用“forecast”和“tseries”包提供的“auto.arima”函数来自动识别和构建最优的ARIMA模型。这一过程通常基于赤池信息准则（AIC）和贝叶斯信息准则（BIC）来选择最佳的模型参数，从而实现对时间序列数据的良好拟合。构建模型后，评估模型拟合优度的一个重要步骤是对残差序列进行Ljung-Box检验，若残差序列的Ljung-Box检验的P值>0.05，表明残差序列近似为白噪声，意味着ARIMA模型对数据的拟合度较好。反之，若P值<0.05，则表明残差序列中存在可检测的自相关性，提示模型需要重新构建或调整。
1.2.3　NNAR模型
NNAR模型是一种基于人工神经网络的时间序列预测方法，能够捕捉数据中的复杂非线性动态。该模型通过模拟生物神经网络的结构，由输入层、隐藏层和输出层组成。输入层接收时间序列的滞后值，隐藏层包含一定数量的神经元（或节点），这些神经元的数量（用 $ k $ 表示），决定了模型捕捉非线性关系的能力。NNAR模型的滞后输入数由 $ p $ 确定，而模型的复杂性和预测能力则由隐藏层的节点数 $ k $ 决定。在R语言中，可以通过“forecast”包提供的“nnetar”函数来实现NNAR模型的自动拟合和预测。
1.2.4　ARIMA-NNAR组合模型
ARIMA-NNAR组合模型将ARIMA模型与NNAR模型结合起来，形成一种新的预测模型，即ARIMA-NNAR组合模型，该模型首先基于ARIMA模型对时间序列数据进行平稳化处理，然后基于NNAR模型对平稳序列进行非线性建模。使用ARIMA对中国T2DM疾病负担进行预测，设预测结果为$ \widehat{{L}_{t}} $，原序列和ARIMA模型预测结果的残差为$ {e}_{t} $，即$ {e}_{t}= {P}_{t}-\widehat{{L}_{t}} $，序列$ \left\{{e}_{t}\right\} $隐含了原序列中的非线性关系，$ {e}_{t}=f\left({e}_{t-1},{e}_{t-2},\cdots ,{e}_{t-n}\right)+\varepsilon $，其中，$ \mathrm{\varepsilon } $为随机误差。对上一步的残差序列进行输入向量构造，得到NNAR样本集$ \left\{e\left({t}_{i}\right)e\left({t}_{i}-s\right)\cdots ,e\left({t}_{i}-{\tau }_{s}\right)\right\} $，利用NNAR对残差进行预测，设预测结果为$ \widehat{{e}_{t}} $。最终的预测结果$ \widehat{{P}_{t}} $，则$ \widehat{{P}_{t}}=\widehat{{L}_{t}}+\widehat{{e}_{t}} $。
1.2.5　模型比较
采用平均绝对百分误差（MAPE）、平均绝对误差（MAE）及均方根误差（RMSE）对模型的拟合和预测效果进行评价。MAPE、MAE、RMSE 值越小，模型拟合精度越高，MAPE<15%时提示预测精度较好[11]。
1.3　统计分析
所有数据均采用Excel 2019录入整理，使用 R 4.3.3 进行统计分析及可视化。
2　结　果
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2.1　T2DM患病率、死亡率和DALYs率（表1）
1990—2021年中国T2DM的患病率和标化患病率均呈现上升趋势，男性的增长速度高于女性。患病率从2 943.19/10万增至8 142.41/10万，标化患病率从3 519.81/10万增至6 055.51/10万。同时，T2DM的死亡率整体上升了117.17%，但标化死亡率略有下降（5.92%），男性死亡率的增长高于女性。DALYs率显著增长139.40%，标化DALYs率增长29.89%，男性的DALYs率和标化DALYs率的增长均超过女性。
2.2　2021年不同年龄段、不同性别患病率、死亡率和DALYs率及其数量变化趋势（图1）
由图1可以看出，男性、女性患病人数和患病率均随年龄增长呈现先升高后降低的趋势，患病人数在55～59岁达到高峰。85～89岁之前男性患病率高于女性，之后女性反超。死亡人数在70～74岁达到最高，男性死亡率在90～94岁后呈现下降趋势，女性死亡率随着年龄的增加不断上升。DALYs数在65～69岁达到峰值，之后女性DALYs数超过男性。男性DALYs率在75～79岁后显著上升，女性则持续下降，男性在90～94岁后呈现下降趋势。
2.3　基于ARIMA、NNAR和组合模型的T2DM疾病负担预测研究（图2～4）
以 1990 —2016年的中国T2DM疾病负担数据为训练集，分别采用 ARIMA、NNAR、ARIMA-NNAR 方法进行模型拟合，用2017— 2021年的T2DM疾病负担数据作为验证集检验模型的预测效果。基于各预测模型对中国T2DM总人群的疾病负担拟合结果如下：由“auto.arima”函数得到最小的AIC和BIC对应的ARIMA模型，即总人群患病率最优模型为ARIMA（2，1，0）（AIC=150.66，BIC=155.2）、死亡率最优模型为ARIMA（0，1，1）（AIC=71.7，BIC=75.1）和DALYs率最优模型为ARIMA（0，1，1）（AIC=202.75，BIC=206.16）。由图2可知，ARIMA模型对于训练集的患病率、死亡率还是DALYs率的拟合程度均较好，并预测得到2017—2021年中国T2DM总人群的患病率、死亡率和DALYs率均呈现上升趋势。由“nnetar”函数得到的最优模型为NNAR（1,1），由图3可知，NNAR模型对于训练集的患病率、死亡率及DALY率的拟合程度相对较差。最后，使用ARIMA模型对时间序列数据进行初步拟合，并利用NNAR模型对残差进行进一步的非线性建模，以捕捉数据中的非线性特征和剩余的动态变化。由图4可知，ARIMA-NNAR组合模型对于训练集的患病率、死亡率及DALYs率的拟合程度较好，并预测得到2017—2021年中国T2DM总人群患病率、死亡率和DALYs率呈上升趋势。
2.4　模型比较（表2）
无论训练集还是测试集，ARIMA-NNAR组合模型的中国T2DM患病率、死亡率、DALYs率的各评价指标的值均低于ARIMA模型和NNAR模型，即ARIMA-NNAR组合模型在预测中国T2DM患病率、死亡率和DALYs率的性能优于单预测模型。最终选择使用ARIMA-NNAR组合模型预测2022—2026年中国T2DM的患病率、死亡率和DALYs率。
2.5　基于ARIMA-NNAR组合模型的中国T2DM疾病负担预测（图5～7、表3）
由组合模型预测结果可知，2022—2026年中国T2DM男性、女性以及总人群的患病率、死亡率和DALYs率均呈现上升趋势，即中国T2DM的疾病负担依然在不断加重，防控形势依旧严峻。经ARIMA-NNAR组合模型预测得到2022—2026年中国T2DM患病率分别为8 347.18/10万、8 569.86/10万、8 781.15/10万、8 992.45/10万、9 203.75/10万；死亡率分别为12.55/10万、12.78/10万、12.99/10万、13.20/10万、13.41/10万；DALYs率分别为826.91/10万、846.34/10万、864.60/10万、881.98/10万、898.66/10万。
3　讨　论
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本研究利用GBD 2021数据库分析了1990—2021年中国T2DM的患病率、死亡率和DALYs率，并用ARIMA-NNAR组合模型预测了2022—2026年的疾病负担变化趋势。结果显示，1990—2021年中国T2DM疾病负担整体呈现上升趋势，预计未来5年将继续增长，防控形势十分严峻。
本研究结果显示，1990—2021年中国总人群 T2DM 患病率、死亡率和DALYs率整体呈上升趋势，且男性患病率和DALYs率略高于女性，死亡率则低于女性。目前，中国糖尿病患病率急剧上升，成为导致失明、肾衰竭和截肢的主要原因[12]。糖尿病不仅与癌症[13]、认知功能障碍[14]紧密相关，还受性别、年龄和居住地等因素的影响，城市及经济发达地区的居民患病风险较高[15–16]。环境因素如空气污染[17]，特别是PM10、PM2.5、NO2和NO等[18]，与糖尿病的高发有显著关联。另外，肥胖也是2型糖尿病的主要诱因[19]。1990—2021年中国T2DM的疾病负担显著增加，这一趋势可能与中国经济的持续发展、饮食结构的变化以及人口老龄化的加速密切相关。目前糖尿病的发病人群倾向于年轻化，尤其是男性的患病和死亡风险更高[20]。而定期中等强度的运动可以有效预防T2DM，降低患病风险[21]。
此外，本研究发现，中国T2DM的疾病负担在不同性别和年龄段间存在显著差异。T2DM患病人数在55～59岁达到高峰，之后随年龄增长而减少，可能因为年长者更注重健康和改善生活习惯；65～69岁之前男性T2DM患者数量多于女性，可能与男性更高的吸烟和饮酒比例、社会环境因素、经济水平以及工作压力有关[22–24]。65～69岁后的女性患病人数超过男性，这可能与女性更年期后，激素变化和代谢功能下降有关[25]。男性死亡率在75～79岁后显著上升，这可能与共病如心血管疾病的高比例有关，这些共病增加了死亡风险。有研究显示，≥75岁人群中，不健康睡眠成为最主要的生活方式风险因素[26]。男性在75～79岁可能面临更多生活方式风险因素，如长期吸烟和饮酒，导致病情加重，DALYs率上升并超过女性。女性DALYs率在更年期后略有下降，可能因为某些激素在特定阶段对心血管等器官具有保护作用，减轻了糖尿病并发症的严重程度[27]。
本研究比较了ARIMA、NNAR和ARIMA-NNAR组合模型在中国T2DM患病率、死亡率和DALYs率预测中的应用效果。结果显示，ARIMA-NNAR组合模型在预测中国T2DM疾病负担方面表现最佳，其在训练集和测试集上的MAPE、MAE、RMSE等拟合参数均优于单独的ARIMA和NNAR模型，即组合模型具有更高的预测精度。
ARIMA模型[28]是一种经典的时间序列模型，可以很好地捕捉时间序列数据的稳定趋势[29]，由于ARIMA模型假设时间序列是线性的，并且模型要求时间序列数据满足平稳性和同方差性的条件，这就限制了它对于非线性关系的建模能力以及对于非平稳性或异方差的数据不适用性。NNAR模型是一种以时间序列为基础的神经网络模型，具有逼近非线性不平稳时间序列的优势，模型泛化能力较强[30–31]，但由于 NNAR 神经网络中的延时阶数及隐藏的神经元个数无法用科学的方法得出，只能依靠经验获取，即 NNAR 模型依旧是“黑盒”模型[32]。ARIMA-NNAR 组合模型结合了ARIMA模型与NNAR模型的优势，具有更好的预测性能。这种组合方法的性能在疾病趋势预测等领域也得到了验证，如陈登建等人[33]将ARIMA与支持向量机（SVR）结合用于股票数据预测，孙存浩等人[34]提出BP神经网络与LSTM神经网络的组合模型，王颖等人[35]采用ARIMA-GM组合模型预测涌水量，王仕鸿等人[36]则分别使用ARIMA和NNAR模型预测慢性肾病的发病率和患病率，这些研究表明，组合模型在提高预测精度和鲁棒性方面具有显著优势。
针对未来5年中国T2DM疾病负担仍呈现不断上升的趋势，本研究结合世界卫生组织（WHO）对于糖尿病防治策略提出以下建议：个人应保持健康生活方式，如理想体重、规律运动、健康饮食、戒烟，并定期检测血糖；社会层面应重视预防，控制风险因素，增加筛查，早期干预高危人群，提高农村慢性病管理，关注男性和老年人群，以提高治疗和控制率。
本研究的局限性：（1）本研究仅探究ARIMA-NNAR组合模型对于中国T2DM疾病负担的拟合精度和预测效果，对于其他组合模型的性能还有待验证；（2）预测是在限定条件中模拟的，而疾病发生的不可控因素较多，包括人口、环境、卫生、经济等多方面因素，故本研究的预测结果与实际发生情况会有偏差，且预测结果准确度会随着预测时间的增加而下降，需要进一步完善模型，提高预测的准确性。尽管存在局限，但本研究仍从全国层面分析了糖尿病疾病负担情况及不同性别、年龄段患者的疾病负担特点及变化趋势，为我国糖尿病精准防治提供了重要依据。

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doi: 10.11847/zgggws1145990
  • 接收时间：2024-10-31
  • 首发时间：2026-10-25
  • 出版时间：2025-05-10
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  • 收稿日期：2024-10-31
  • 修回日期：2024-11-18
  • 录用日期：2025-02-17
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    1杭州医学院公共卫生学院，杭州 310053
    2新疆医科大学医学工程技术学院，乌鲁木齐 830017
    3新疆医科大学医工交叉研究所，乌鲁木齐市 830017

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