传染病预警指标体系及三种预测模型的研究
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摘要
以重大传染病疫情为主的突发公共卫生事件不仅严重危害人民的生命财产安全,还极易造成恐慌,引起社会动荡,影响社会生活的方方面面,甚至阻滞经济的发展。建立和发展传染病预测预警技术,提高预测预警的及时性和准确性,对于传染病控制工作意义重大。实践证明,开展预测预警研究在传染病防制中具有良好的卫生经济学指标,具有低投入、高回报的特征。
良好的预测是制定预防和控制传染病的近期或长远应对策略的前提。疾病的预测可以及早发现疾病的发展趋势,为深入开展疾病的预警奠定基础,也为制定防制策略及措施提供理论依据。在我国,传染病的预测方法研究起步较晚,90年代后期才得到较快发展。用于传染病预测的模型大多以传统的线性模型为主,误差偏移较大,在实际运用中效果不太理想。因此,针对当前传染病的发病情况,建立新的预测模型开展科学预测研究迫在眉睫。
预测是对疾病未来的发生、发展和流行趋势开展分析;预警则不仅需要掌握疾病的发生发展趋势,更要求能及时识别早期的异常情况并发出警报,启动应急反应。预警必须建立一套指标体系,通过综合运用指标体系的方法对某一传染病的情况进行分析和评价,确认发生危机的可能性和严重程度,决定是否发出危机报警,并提出必要的措施以寻求最低损失。确立一套灵敏、有效的预警指标体系是预警系统建设成功的前提和基础。
本文首先探讨传染病预警指标体系的建立,确定适合早期预警的数据源,为发展和完善我国传染病预警监测网络提供依据。其次以预警指标体系中,最常见、目前可获得性最高的法定传染病报告数据为基础开展新预测模型的研究,比较不同模型的预测效果,建立适合传染病发病率预测的新数学模型,以期为疾病预测工作提供新的技术手段。
第一篇传染病预警指标体系的研究
目的:构建适合我国国情的传染病应急预警指标体系,提出建设和保障该指标体系有效运行的建议,为我国传染病预警系统的建设提供思路和参考。
研究内容:(1)通过文献学习和评阅,了解国外预警系统的建设和预警指标的组成情况;(2)结合文献学习和现场调查,个人深入访谈和小组访谈等形式,对我国传染病预警现状进行分析;(3)提出我国传染病预警指标体系框架。通过组织两次专家咨询会议、两轮德尔菲法咨询、以及开展小组讨论等方法,确定我国传染病疫情预警指标体系的组成;(4)提出建设和保障预警指标体系有效运行的建议。
研究方法:采用文献评阅、现有资料整理分析、现场调查、半结构化访谈/个人深入访谈等方法构建指标体系框架,使用德尔菲法与专家会议法相结合构建指标体系的组成,使用小组讨论和个别专家咨询法对指标体系进一步修正和完善。
主要研究结果:(1)指标体系的框架:结合传染病疫情发生、发展的不同时间阶段性特点和预警理论,提出传染病疫情预警指标应包括3大类:暴发或流行前期指标、非典型症状期指标和典型症状期指标;(2)指标体系的设置:通过文献学习构建109项备选指标,根据预警指标的设置原则和结合专家咨询会议进行讨论、咨询,筛选89项指标形成指标体系雏形;(3)德尔菲法咨询专家构成:主要来自传染病防制、流行病学教学科研、突发公共卫生事件应急处理、卫生行政管理、健康教育等领域。其中89%的专家具有副高以上职称,92%的专家专业年限在10年以上;(4)指标筛选结果:两轮德尔菲法咨询专家的积极系数分别为78%和100%,在咨询中有70%的专家对指标体系提出了书面的改进建议,说明专家对本研究比较支持和关心;专家对指标熟悉程度均在0.7以上,权威系数在0.8以上,说明专家咨询所得的结果具有权威性;两轮咨询后的专家意见协调系数为0.782 (P<0.05),说明专家意见协调性好;最终的指标体系共包括三大类25项指标,其中权重系数较高的指标均为目前疫情监测、预警工作中较为重视、应用较多的指标;(5)不同级别机构对各个指标的获得难易程度不一,在指标体系的应用中存在差异。
主要结论:(1)已建立的预警指标体系共包括3大类25项指标,可作为传染病预测预警的基本指标;(2)指标体系的构建结合了传染病发生、发展过程中的不同特点和预警理论,具有一定的理论基础;(3)预警病例的出现、传染性疾病病例/疑似病例报告数/死亡数、其它地区发生特定疫情、人群疫苗接种率、发生重大的灾害/灾难这5项指标在预警指标体系中相对重要性排列居前五位,与实际情况相符;(4)目前建立的预警指标体系是一个总体的、基本指标体系。具体应用到特定疾病时存在着总体和个别的关系,需根据具体疾病和地区的特点进行指标的取舍和修订。
建议:建设预警指标体系并保障其有效运行,有以下建议(1)完善现有的疾病监测系统;(2)加强症状监测的试点研究,建立和发展症状监测系统;(3)加大对基层卫生机构建设的投入;(4)与相关部门共建信息交流平台;(5)健全相关的政策,法律法规建设;(6)开发、建设数据实时采集、传递和存储系统;(7)提高数据整合、分析的技术水平;(8)加强多学科领域专家的协力合作;(9)与他国积极开展相关领域的合作,与国际接轨;(10)应用和完善预警指标体系需要分阶段、分步骤的完成。
第二篇三种传染病预测模型的研究
目的:由于传染病的月发病率数据呈现出线性和非线性的特征,而既往预测多以传统线性模型为主。本篇拟采用传统的线性ARIMA模型,非线性的神经网络径向基函数(RBF)模型和采取串联的方法,将线性和非线性模型进行组合,建立组合模型对不同传染病发病率开展预测,比较不同模型的预测效果,探讨适合传染病发病率预测的新数学模型。
研究资料和内容:以宜昌市1997-2006年法定传染病报告数据为对象,采用ARIMA模型,RBF神经网络模型和ARIMA-GRNN组合模型分别对宜昌市的甲乙类传染病合计报告发病率,肺结核报告发病率和细菌性痢疾报告发病率开展预测分析。通过比较不同模型的拟和效果和预测效果对模型进行评估。
研究方法:应用EXCEL软件进行一般统计描述;SPSS 12.0和SAS 8.1实现ARIMA模型的参数估计、模型拟合及其检验;应用Matlab7.1的神经网络工具箱开展RBF和GRNN神经网络模型的分析和预测研究。
主要研究结果:
(1)甲乙类传染病月报告发病率预测:以宜昌市1997-2005年的甲乙类传染病合计报告发病率数据建模,对2006年1-6月的发病率开展预测,以2006年1-6月的实际月报告发病率作为预测的参照值,以验证建模的可靠性。其中ARIMA模型表达式为:(1 ? B ) xt = 1 + 0.243 Bε4 t+ 0.281B6,拟和误差MSE=20.004,MAE=3.113,MAPE=0.172;预测误差MSE=19.637, MAE=3.553, MAPE=0.166。RBF神经网络模型的预测误差MSE=13.389, MAE=3.177, MAPE=0.127;ARIMA-GRNN组合模型的拟和误差MSE=2.304,MAE=0.943,MAPE=0.053;预测误差MSE=3.402,MAE=1.595,MAPE=0.068。可见组合模型的拟和误差明显小于ARIMA模型。预测准确性表现为组合模型的最好,其次为RBF网络模型,预测准确性最低的为ARIMA模型。
(2)肺结核月报告发病率预测:以宜昌市1997-2005年的肺结核报告发病率数据建模,对2006年1-6月的发病率开展预测。确定ARIMA模型的最优模型为ARIMA(1,1,1),表达式为(1 )( 1 - 0.889 B),模型拟和误差MSE=4.316,MAE=1.547,MAPE=0.227;预测误差MSE=9.748,MAE=2.661,MAPE=0.199。RBF神经网络模型的预测误差MSE=2.867, MAE=1.140, MAPE=0.091;ARIMA-GRNN组合模型的拟和误差MSE=0.535,MAE=0.472,MAPE=0.074;预测误差MSE=3.580,MAE=1.563,MAPE=0.124。可见组合模型的拟和误差明显小于ARIMA模型。预测准确性表现为RBF网络模型>组合模型>ARIMA模型。
(3)细菌性痢疾月报告发病率预测:以宜昌市2000-2005年的细菌性痢疾报告发病率数据建模,对2006年1-6月的发病率开展预测。经筛选,确定模型为SARIMA (0, 1, 1) (1, 1, 0)12,模型表达式如下: (1 + 0.389 B1 2 )(1 ? B )(1 ? B1 2) X t = (1 ? 0.822 B )εt,模型的拟和误差MSE=0.263,MAE=0.406,MAPE=0.185;预测误差MSE=0.088,MAE=0.286,MAPE=0.182。RBF神经网络模型的预测误差MSE=0.084, MAE=0.222, MAPE=0.136;ARIMA-GRNN组合模型的拟和误差MSE=0.051,MAE=0.177,MAPE=0.079;预测误差MSE=0.026,MAE=0.139,MAPE=0.083。可见组合模型的拟和误差明显小于SARIMA模型。预测准确性表现为组合模型>RBF网络模型>SARIMA模型。
主要结论:(1)基于历史发病序列的趋势外推法可用于传染病发病率预测;(2)RBF神经网络模型为非线性建模法,预测效果优于ARIMA模型;(3)组合模型兼有线性和非线性建模的优点,拟和效果和预测效果优于线性的ARIMA模型法;(4)神经网络方法不必建立复杂的数学模型,不需要了解模型的数学结构、输入和输出变量之间的关系,建模方法较传统数学模型更为简单;(5)应用时间序列进行趋势外延分析仅适用于短期预测。
Emergent public health events, of which mainly are grave infectious diseases epidemic, don’t only influence the safety of life and property greatly, but also cause panic and turbulence, almost affect every aspect of social life, and even block the economic development. It is important for infectious diseases control to establish and develop the technology of forecasting and early warning. It has been proved that conducting forecasting and early warning in infectious diseases control practice is of great health economic benefits.
Accurate forecasting is the premise for establishing short or long term strategies for infectious disease prevention and control. Forecasting can be used for the infectious diseases epidemic trends analysis, establishing foundation for early warning and providing theory basis for combating strategies and measures. Establishing appropriate prediction models and improving the forecasting accuracy can be applied by management departments to learn about the current condition and make plan for the future.
In China, late as the start was, the forecasting methods for infectious diseases had demonstrated a rapid development in the late 1990s. Most of the forecasting methods are traditional linear prediction models with great error, and it is inappropriate for application in practice. Thus, it is urgent for studying new models for infectious diseases forecasting. The forecasting research works for the analysis of diseases epidemic trends in the future and mainly focus on various mathematical models. Besides learning about the trends of diseases in the future, early warning required to identify the early abnormal events timely, send out alarm signals and start out an emergency response action. For early warning system establishment, a sensitive and effective early warning indicators system is the premise and foundation. According to indicators system, data can be collected, analyzed and investigated on purpose, which can ensure the production of effective alarm signals and reduction of the resource waste.
Searching for sensitive and effective early warning indicators includes two aspects. One is collecting data from current communicable disease reporting network, and the other aspect refers to exploit and search for new data source. These new data source will have better values in early detection of diseases epidemic and outbreak.
At first, this study established an early warning indictors system, determined the data source which can be used for early warning and provided theory basis for the development of the alarming and surveillance network. And then, this study focused on the establishment of forecasting models, with the legal infectious diseases reporting data which were very common and available in early warning indicators system. Three types of forecasting models were constructed, compared and evaluated.
Part I The early warning indicators system for infectious diseases
[Objectives] Establishing early warning indicators system for emergent public health events, especially for infectious disease outbreak in China and putting forward effective measures and suggestions that can ensure the system’s implementation.
[Methods]
1 Using literature review, existing data analysis, field investigation, semi-structured interview and focus group interview to learn about the current condition of early detection for infectious disease outbreak in China;
2 Using literature review, existing data analysis, group discussion and expert consulting meeting to build the rudiment of the indicator system;
3 Applying expert consulting meeting and Delphi methods to construct the indicator system;
4 Using group discussion and some experts’consultations to revise the indicator system and to analyze its establishment and application.
[Results]
1 Framework of indicator system: according to the early warning theory in other fields and the natural history of infectious disease outbreak, the framework was set up which included 3 categories: pre-outbreak indicators, early-symptom-period indicators and specific-syndrome-period indicators:
2 The rudiment of indicator system: it consisted of three categories and 89 indicators that were filtered from 109 indicators according to the indicator building principle and suggestions from experts in the related fields.
3 The composing of consultants: consultants came from the areas of epidemiology, infectious disease prevention and control, health management and health education, etc. Researchers, CDC staff members and decision-makers were all included. 92 percent of all consultants had over ten-year working experience and 89 percent were in senior position.
4 The results of Delphi consulting: positive coefficients of two rounds of consultations were 78% and 100% respectively, and 70% consultants put forward written suggestions for improving indicator system, which meant consultants were very concerned about this project; the acquaintance grades to indicators were above 0.7 and authority coefficients beyond 0.8, which proved the consultation result was credible; after two consultations, harmonious coefficient was 0.782 and was of statistics significance, which proved the opinions from experts were harmonious; the final indicator system included 3 categories and 25 indicators.
5 The availability of indicators: the capability of obtaining the data for those indicators was different for different-level CDC.
[Conclusions]
1 The established indicator system included 3 categories and 25 indicators, which covers the most scope of early warning for outbreak and can be used as basic indicators for early warning.
2 The construction of indicator system combined the related opinions of early warning indicators in other fields (early warning indicators should include warning source, warning sign and warning situation indicator) with the timeline of epidemic development.
3 The weighted coefficients of the emergence of early warning case, the number of reported cases, the epidemic in other areas, immunization coverage rate and the occurrence of disasters or calamities were ranked in the first 5 place. These indicators with relatively higher weighted coefficients were the ones that were usually paid more attention and applied in practice, so the result was in accordance with the practice.
4 The established indicator system is a basic prototype system of indicators for early warning, for a specific disease, the application of indicators may be revised, customized according to the features of different diseases and local circumstance at that time.
[Suggestions]
In order to ensure the system effective implementation, recommendations were put forward as follows:
1 Improving and perfecting the current disease surveillance systems;
2 Establishing and developing syndromic surveillance gradually;
3 Increasing investments on construction of grassroots health care institutions;
4 Establishing information exchange platform with other related units;
5 Strengthening the construction of related policies, laws and regulations;
6 Building and developing real-time data collection, transmission and storage system;
7 Improving the technical level of data (from different sources) synthesis and analysis;
8 Enhancing collaboration with experts from different fields such as information technology, mathematics, computer science and so on;
9 Increasing cooperation with other countries in the related fields and learning experiences and lessons from other countries’practice;
10 Establishing and implementing early warning indicators system should be carried out step by step.
Part II Three types of mathematical models for infectious diseases forecasting [Objectives] The monthly incidence data of infectious diseases showed linear and nonlinear characteristics, but previous forecasting models were mostly based on traditional linear models. In this study, linear ARIMA model, nonlinear RBF neural network and combined model which included linear and nonlinear models were constructed for infectious diseases forecasting. The three types of mathematical models were constructed, compared and evaluated in order to search for new models for infectious diseases forecasting.
[Materials and contents] With the legal notifiable communicable disease data from 1997- 2005 in Yichang city, ARIMA model, RBF neural network and ARIMA-GRNN combined model were constructed to predict the reporting incidence rate of A and B communicable diseases, pulmonary tuberculosis and bacillary dysentery in the first six months of 2006 in Yichang city. The models were evaluated with the comparison of the fitting and prediction effects.
[Methods] Statistical descriptions were conducted with EXCEL software; ARIMA model was constructed with SPSS 12.0 and SAS 8.1 package; the construction of RBF and GRNN neural network was completed with the neural network toolbox in Matlab 7.1.
[Results]:
(1) The forecasting of monthly reporting incidence rate of A and B communicable diseases Based on the legal notifiable A and B communicable diseases incidence data from 1997-2005 in Yichang city, models were constructed to predict the incidence data in the first six months of 2006. The actual incidence rates were applied as reference values to evaluate the accuracy of the models. The ARIMA model expression was: (1 ? B ) xt = 1 + 0.243 Bε4 t+ 0.281B6, the fitting error: MSE=20.004, MAE=3.113, MAPE=0.172;the prediction error: MSE=19.637, MAE=3.553, MAPE=0.166. The prediction error of RBF neural network: MSE=13.389, MAE=3.177, MAPE=0.127;the simulation error of combined model: MSE=2.304, MAE=0.943, MAPE=0.053;and the prediction error: MSE=3.402, MAE=1.595, MAPE=0.068. It is found that the simulation error of the combined model was less than the ARIMA model. Among the three models, the forecasting accuracy of the combined model was the best, and then was the RBF neural network and ARIMA model.
(2) The forecasting of monthly reporting incidence rate of pulmonary tuberculosis Based on the monthly reporting incidence rates of pulmonary tuberculosis from 1997 Jan. to 2005 Dec. in Yichang city, the incidence rates between Jan. and Jun. in 2006 were forecasted. The optimal model of ARIMA model was ARIMA(1,1,1),and the expression was The simulation error of the model were represented as follows: MSE=4.316, MAE=1.547, MAPE=0.227;the prediction error: MSE=9.748,MAE=2.661,MAPE=0.199. The prediction error of RBF neural network: MSE=2.867, MAE=1.140, MAPE=0.091; the simulation error of the combined model: MSE=0.535, MAE=0.472, MAPE=0.074; and the prediction error: MSE=3.580,MAE=1.563,MAPE=0.124. The simulation error of combined model was less than the traditional ARIMA model. The accuracy of forecasting models represented as: RBF neural network >combined model >ARIMA model.
(3) The forecasting of monthly reporting incidence rate of bacillary dysentery Based on the monthly reporting incidence rates of bacillary dysentery from 2000 Jan. to 2005 Dec. in Yichang city, the incidence rates for the first six months in 2006 were forecasted. After simulation and selection, SARIMA (0, 1, 1) (1, 1, 0)12 was determined and its expression was (1 + 0.389 B1 2 )(1 ? B )(1 ? B1 2) X t = (1 ? 0.822 B )εt. The simulation error of the model could be described as: MSE=0.263, MAE=0.406, MAPE=0.185;for prediction error, MSE was 0.088, MAE was 0.286 and MAPE was 0.182. For the prediction error of RBF neural network, the MSE was 0.084, MAE was 0.222 and MAPE was 0.136. For SARIMA-GRNN hybrid model, the simulation error represented as: MSE=0.051, MAE=0.177, MAPE=0.079, for prediction error of this model, MSE was 0.026, MAE was 0.139 and MAPE was 0.083. Obviously, the simulation error of SARIMA model was greater than the hybrid model. The accuracy of the hybrid model was better than the RBF model and SARIMA model.
[Conclusions]:
(1) Trend extrapolation, which was based on the historical incidence rates, could be used for the forecasting of communicable diseases; (2) The prediction accuracy of RBF neural network, which was a nonlinear model, was better than the ARIMA model; (3) The ARIMA-GRNN combined model, which integrated linear and nonlinear models, represented better simulation and prediction effects than traditional ARIMA model; (4) For neural network, it is unnecessary to build complex mathematical models, learn about the structure of models and the relationship between input and output variables, so it was more easy to be applied in practice; (5) Trend extrapolation based on time series data can only be applied for short-term forecasting.
良好的预测是制定预防和控制传染病的近期或长远应对策略的前提。疾病的预测可以及早发现疾病的发展趋势,为深入开展疾病的预警奠定基础,也为制定防制策略及措施提供理论依据。在我国,传染病的预测方法研究起步较晚,90年代后期才得到较快发展。用于传染病预测的模型大多以传统的线性模型为主,误差偏移较大,在实际运用中效果不太理想。因此,针对当前传染病的发病情况,建立新的预测模型开展科学预测研究迫在眉睫。
预测是对疾病未来的发生、发展和流行趋势开展分析;预警则不仅需要掌握疾病的发生发展趋势,更要求能及时识别早期的异常情况并发出警报,启动应急反应。预警必须建立一套指标体系,通过综合运用指标体系的方法对某一传染病的情况进行分析和评价,确认发生危机的可能性和严重程度,决定是否发出危机报警,并提出必要的措施以寻求最低损失。确立一套灵敏、有效的预警指标体系是预警系统建设成功的前提和基础。
本文首先探讨传染病预警指标体系的建立,确定适合早期预警的数据源,为发展和完善我国传染病预警监测网络提供依据。其次以预警指标体系中,最常见、目前可获得性最高的法定传染病报告数据为基础开展新预测模型的研究,比较不同模型的预测效果,建立适合传染病发病率预测的新数学模型,以期为疾病预测工作提供新的技术手段。
第一篇传染病预警指标体系的研究
目的:构建适合我国国情的传染病应急预警指标体系,提出建设和保障该指标体系有效运行的建议,为我国传染病预警系统的建设提供思路和参考。
研究内容:(1)通过文献学习和评阅,了解国外预警系统的建设和预警指标的组成情况;(2)结合文献学习和现场调查,个人深入访谈和小组访谈等形式,对我国传染病预警现状进行分析;(3)提出我国传染病预警指标体系框架。通过组织两次专家咨询会议、两轮德尔菲法咨询、以及开展小组讨论等方法,确定我国传染病疫情预警指标体系的组成;(4)提出建设和保障预警指标体系有效运行的建议。
研究方法:采用文献评阅、现有资料整理分析、现场调查、半结构化访谈/个人深入访谈等方法构建指标体系框架,使用德尔菲法与专家会议法相结合构建指标体系的组成,使用小组讨论和个别专家咨询法对指标体系进一步修正和完善。
主要研究结果:(1)指标体系的框架:结合传染病疫情发生、发展的不同时间阶段性特点和预警理论,提出传染病疫情预警指标应包括3大类:暴发或流行前期指标、非典型症状期指标和典型症状期指标;(2)指标体系的设置:通过文献学习构建109项备选指标,根据预警指标的设置原则和结合专家咨询会议进行讨论、咨询,筛选89项指标形成指标体系雏形;(3)德尔菲法咨询专家构成:主要来自传染病防制、流行病学教学科研、突发公共卫生事件应急处理、卫生行政管理、健康教育等领域。其中89%的专家具有副高以上职称,92%的专家专业年限在10年以上;(4)指标筛选结果:两轮德尔菲法咨询专家的积极系数分别为78%和100%,在咨询中有70%的专家对指标体系提出了书面的改进建议,说明专家对本研究比较支持和关心;专家对指标熟悉程度均在0.7以上,权威系数在0.8以上,说明专家咨询所得的结果具有权威性;两轮咨询后的专家意见协调系数为0.782 (P<0.05),说明专家意见协调性好;最终的指标体系共包括三大类25项指标,其中权重系数较高的指标均为目前疫情监测、预警工作中较为重视、应用较多的指标;(5)不同级别机构对各个指标的获得难易程度不一,在指标体系的应用中存在差异。
主要结论:(1)已建立的预警指标体系共包括3大类25项指标,可作为传染病预测预警的基本指标;(2)指标体系的构建结合了传染病发生、发展过程中的不同特点和预警理论,具有一定的理论基础;(3)预警病例的出现、传染性疾病病例/疑似病例报告数/死亡数、其它地区发生特定疫情、人群疫苗接种率、发生重大的灾害/灾难这5项指标在预警指标体系中相对重要性排列居前五位,与实际情况相符;(4)目前建立的预警指标体系是一个总体的、基本指标体系。具体应用到特定疾病时存在着总体和个别的关系,需根据具体疾病和地区的特点进行指标的取舍和修订。
建议:建设预警指标体系并保障其有效运行,有以下建议(1)完善现有的疾病监测系统;(2)加强症状监测的试点研究,建立和发展症状监测系统;(3)加大对基层卫生机构建设的投入;(4)与相关部门共建信息交流平台;(5)健全相关的政策,法律法规建设;(6)开发、建设数据实时采集、传递和存储系统;(7)提高数据整合、分析的技术水平;(8)加强多学科领域专家的协力合作;(9)与他国积极开展相关领域的合作,与国际接轨;(10)应用和完善预警指标体系需要分阶段、分步骤的完成。
第二篇三种传染病预测模型的研究
目的:由于传染病的月发病率数据呈现出线性和非线性的特征,而既往预测多以传统线性模型为主。本篇拟采用传统的线性ARIMA模型,非线性的神经网络径向基函数(RBF)模型和采取串联的方法,将线性和非线性模型进行组合,建立组合模型对不同传染病发病率开展预测,比较不同模型的预测效果,探讨适合传染病发病率预测的新数学模型。
研究资料和内容:以宜昌市1997-2006年法定传染病报告数据为对象,采用ARIMA模型,RBF神经网络模型和ARIMA-GRNN组合模型分别对宜昌市的甲乙类传染病合计报告发病率,肺结核报告发病率和细菌性痢疾报告发病率开展预测分析。通过比较不同模型的拟和效果和预测效果对模型进行评估。
研究方法:应用EXCEL软件进行一般统计描述;SPSS 12.0和SAS 8.1实现ARIMA模型的参数估计、模型拟合及其检验;应用Matlab7.1的神经网络工具箱开展RBF和GRNN神经网络模型的分析和预测研究。
主要研究结果:
(1)甲乙类传染病月报告发病率预测:以宜昌市1997-2005年的甲乙类传染病合计报告发病率数据建模,对2006年1-6月的发病率开展预测,以2006年1-6月的实际月报告发病率作为预测的参照值,以验证建模的可靠性。其中ARIMA模型表达式为:(1 ? B ) xt = 1 + 0.243 Bε4 t+ 0.281B6,拟和误差MSE=20.004,MAE=3.113,MAPE=0.172;预测误差MSE=19.637, MAE=3.553, MAPE=0.166。RBF神经网络模型的预测误差MSE=13.389, MAE=3.177, MAPE=0.127;ARIMA-GRNN组合模型的拟和误差MSE=2.304,MAE=0.943,MAPE=0.053;预测误差MSE=3.402,MAE=1.595,MAPE=0.068。可见组合模型的拟和误差明显小于ARIMA模型。预测准确性表现为组合模型的最好,其次为RBF网络模型,预测准确性最低的为ARIMA模型。
(2)肺结核月报告发病率预测:以宜昌市1997-2005年的肺结核报告发病率数据建模,对2006年1-6月的发病率开展预测。确定ARIMA模型的最优模型为ARIMA(1,1,1),表达式为(1 )( 1 - 0.889 B),模型拟和误差MSE=4.316,MAE=1.547,MAPE=0.227;预测误差MSE=9.748,MAE=2.661,MAPE=0.199。RBF神经网络模型的预测误差MSE=2.867, MAE=1.140, MAPE=0.091;ARIMA-GRNN组合模型的拟和误差MSE=0.535,MAE=0.472,MAPE=0.074;预测误差MSE=3.580,MAE=1.563,MAPE=0.124。可见组合模型的拟和误差明显小于ARIMA模型。预测准确性表现为RBF网络模型>组合模型>ARIMA模型。
(3)细菌性痢疾月报告发病率预测:以宜昌市2000-2005年的细菌性痢疾报告发病率数据建模,对2006年1-6月的发病率开展预测。经筛选,确定模型为SARIMA (0, 1, 1) (1, 1, 0)12,模型表达式如下: (1 + 0.389 B1 2 )(1 ? B )(1 ? B1 2) X t = (1 ? 0.822 B )εt,模型的拟和误差MSE=0.263,MAE=0.406,MAPE=0.185;预测误差MSE=0.088,MAE=0.286,MAPE=0.182。RBF神经网络模型的预测误差MSE=0.084, MAE=0.222, MAPE=0.136;ARIMA-GRNN组合模型的拟和误差MSE=0.051,MAE=0.177,MAPE=0.079;预测误差MSE=0.026,MAE=0.139,MAPE=0.083。可见组合模型的拟和误差明显小于SARIMA模型。预测准确性表现为组合模型>RBF网络模型>SARIMA模型。
主要结论:(1)基于历史发病序列的趋势外推法可用于传染病发病率预测;(2)RBF神经网络模型为非线性建模法,预测效果优于ARIMA模型;(3)组合模型兼有线性和非线性建模的优点,拟和效果和预测效果优于线性的ARIMA模型法;(4)神经网络方法不必建立复杂的数学模型,不需要了解模型的数学结构、输入和输出变量之间的关系,建模方法较传统数学模型更为简单;(5)应用时间序列进行趋势外延分析仅适用于短期预测。
Emergent public health events, of which mainly are grave infectious diseases epidemic, don’t only influence the safety of life and property greatly, but also cause panic and turbulence, almost affect every aspect of social life, and even block the economic development. It is important for infectious diseases control to establish and develop the technology of forecasting and early warning. It has been proved that conducting forecasting and early warning in infectious diseases control practice is of great health economic benefits.
Accurate forecasting is the premise for establishing short or long term strategies for infectious disease prevention and control. Forecasting can be used for the infectious diseases epidemic trends analysis, establishing foundation for early warning and providing theory basis for combating strategies and measures. Establishing appropriate prediction models and improving the forecasting accuracy can be applied by management departments to learn about the current condition and make plan for the future.
In China, late as the start was, the forecasting methods for infectious diseases had demonstrated a rapid development in the late 1990s. Most of the forecasting methods are traditional linear prediction models with great error, and it is inappropriate for application in practice. Thus, it is urgent for studying new models for infectious diseases forecasting. The forecasting research works for the analysis of diseases epidemic trends in the future and mainly focus on various mathematical models. Besides learning about the trends of diseases in the future, early warning required to identify the early abnormal events timely, send out alarm signals and start out an emergency response action. For early warning system establishment, a sensitive and effective early warning indicators system is the premise and foundation. According to indicators system, data can be collected, analyzed and investigated on purpose, which can ensure the production of effective alarm signals and reduction of the resource waste.
Searching for sensitive and effective early warning indicators includes two aspects. One is collecting data from current communicable disease reporting network, and the other aspect refers to exploit and search for new data source. These new data source will have better values in early detection of diseases epidemic and outbreak.
At first, this study established an early warning indictors system, determined the data source which can be used for early warning and provided theory basis for the development of the alarming and surveillance network. And then, this study focused on the establishment of forecasting models, with the legal infectious diseases reporting data which were very common and available in early warning indicators system. Three types of forecasting models were constructed, compared and evaluated.
Part I The early warning indicators system for infectious diseases
[Objectives] Establishing early warning indicators system for emergent public health events, especially for infectious disease outbreak in China and putting forward effective measures and suggestions that can ensure the system’s implementation.
[Methods]
1 Using literature review, existing data analysis, field investigation, semi-structured interview and focus group interview to learn about the current condition of early detection for infectious disease outbreak in China;
2 Using literature review, existing data analysis, group discussion and expert consulting meeting to build the rudiment of the indicator system;
3 Applying expert consulting meeting and Delphi methods to construct the indicator system;
4 Using group discussion and some experts’consultations to revise the indicator system and to analyze its establishment and application.
[Results]
1 Framework of indicator system: according to the early warning theory in other fields and the natural history of infectious disease outbreak, the framework was set up which included 3 categories: pre-outbreak indicators, early-symptom-period indicators and specific-syndrome-period indicators:
2 The rudiment of indicator system: it consisted of three categories and 89 indicators that were filtered from 109 indicators according to the indicator building principle and suggestions from experts in the related fields.
3 The composing of consultants: consultants came from the areas of epidemiology, infectious disease prevention and control, health management and health education, etc. Researchers, CDC staff members and decision-makers were all included. 92 percent of all consultants had over ten-year working experience and 89 percent were in senior position.
4 The results of Delphi consulting: positive coefficients of two rounds of consultations were 78% and 100% respectively, and 70% consultants put forward written suggestions for improving indicator system, which meant consultants were very concerned about this project; the acquaintance grades to indicators were above 0.7 and authority coefficients beyond 0.8, which proved the consultation result was credible; after two consultations, harmonious coefficient was 0.782 and was of statistics significance, which proved the opinions from experts were harmonious; the final indicator system included 3 categories and 25 indicators.
5 The availability of indicators: the capability of obtaining the data for those indicators was different for different-level CDC.
[Conclusions]
1 The established indicator system included 3 categories and 25 indicators, which covers the most scope of early warning for outbreak and can be used as basic indicators for early warning.
2 The construction of indicator system combined the related opinions of early warning indicators in other fields (early warning indicators should include warning source, warning sign and warning situation indicator) with the timeline of epidemic development.
3 The weighted coefficients of the emergence of early warning case, the number of reported cases, the epidemic in other areas, immunization coverage rate and the occurrence of disasters or calamities were ranked in the first 5 place. These indicators with relatively higher weighted coefficients were the ones that were usually paid more attention and applied in practice, so the result was in accordance with the practice.
4 The established indicator system is a basic prototype system of indicators for early warning, for a specific disease, the application of indicators may be revised, customized according to the features of different diseases and local circumstance at that time.
[Suggestions]
In order to ensure the system effective implementation, recommendations were put forward as follows:
1 Improving and perfecting the current disease surveillance systems;
2 Establishing and developing syndromic surveillance gradually;
3 Increasing investments on construction of grassroots health care institutions;
4 Establishing information exchange platform with other related units;
5 Strengthening the construction of related policies, laws and regulations;
6 Building and developing real-time data collection, transmission and storage system;
7 Improving the technical level of data (from different sources) synthesis and analysis;
8 Enhancing collaboration with experts from different fields such as information technology, mathematics, computer science and so on;
9 Increasing cooperation with other countries in the related fields and learning experiences and lessons from other countries’practice;
10 Establishing and implementing early warning indicators system should be carried out step by step.
Part II Three types of mathematical models for infectious diseases forecasting [Objectives] The monthly incidence data of infectious diseases showed linear and nonlinear characteristics, but previous forecasting models were mostly based on traditional linear models. In this study, linear ARIMA model, nonlinear RBF neural network and combined model which included linear and nonlinear models were constructed for infectious diseases forecasting. The three types of mathematical models were constructed, compared and evaluated in order to search for new models for infectious diseases forecasting.
[Materials and contents] With the legal notifiable communicable disease data from 1997- 2005 in Yichang city, ARIMA model, RBF neural network and ARIMA-GRNN combined model were constructed to predict the reporting incidence rate of A and B communicable diseases, pulmonary tuberculosis and bacillary dysentery in the first six months of 2006 in Yichang city. The models were evaluated with the comparison of the fitting and prediction effects.
[Methods] Statistical descriptions were conducted with EXCEL software; ARIMA model was constructed with SPSS 12.0 and SAS 8.1 package; the construction of RBF and GRNN neural network was completed with the neural network toolbox in Matlab 7.1.
[Results]:
(1) The forecasting of monthly reporting incidence rate of A and B communicable diseases Based on the legal notifiable A and B communicable diseases incidence data from 1997-2005 in Yichang city, models were constructed to predict the incidence data in the first six months of 2006. The actual incidence rates were applied as reference values to evaluate the accuracy of the models. The ARIMA model expression was: (1 ? B ) xt = 1 + 0.243 Bε4 t+ 0.281B6, the fitting error: MSE=20.004, MAE=3.113, MAPE=0.172;the prediction error: MSE=19.637, MAE=3.553, MAPE=0.166. The prediction error of RBF neural network: MSE=13.389, MAE=3.177, MAPE=0.127;the simulation error of combined model: MSE=2.304, MAE=0.943, MAPE=0.053;and the prediction error: MSE=3.402, MAE=1.595, MAPE=0.068. It is found that the simulation error of the combined model was less than the ARIMA model. Among the three models, the forecasting accuracy of the combined model was the best, and then was the RBF neural network and ARIMA model.
(2) The forecasting of monthly reporting incidence rate of pulmonary tuberculosis Based on the monthly reporting incidence rates of pulmonary tuberculosis from 1997 Jan. to 2005 Dec. in Yichang city, the incidence rates between Jan. and Jun. in 2006 were forecasted. The optimal model of ARIMA model was ARIMA(1,1,1),and the expression was The simulation error of the model were represented as follows: MSE=4.316, MAE=1.547, MAPE=0.227;the prediction error: MSE=9.748,MAE=2.661,MAPE=0.199. The prediction error of RBF neural network: MSE=2.867, MAE=1.140, MAPE=0.091; the simulation error of the combined model: MSE=0.535, MAE=0.472, MAPE=0.074; and the prediction error: MSE=3.580,MAE=1.563,MAPE=0.124. The simulation error of combined model was less than the traditional ARIMA model. The accuracy of forecasting models represented as: RBF neural network >combined model >ARIMA model.
(3) The forecasting of monthly reporting incidence rate of bacillary dysentery Based on the monthly reporting incidence rates of bacillary dysentery from 2000 Jan. to 2005 Dec. in Yichang city, the incidence rates for the first six months in 2006 were forecasted. After simulation and selection, SARIMA (0, 1, 1) (1, 1, 0)12 was determined and its expression was (1 + 0.389 B1 2 )(1 ? B )(1 ? B1 2) X t = (1 ? 0.822 B )εt. The simulation error of the model could be described as: MSE=0.263, MAE=0.406, MAPE=0.185;for prediction error, MSE was 0.088, MAE was 0.286 and MAPE was 0.182. For the prediction error of RBF neural network, the MSE was 0.084, MAE was 0.222 and MAPE was 0.136. For SARIMA-GRNN hybrid model, the simulation error represented as: MSE=0.051, MAE=0.177, MAPE=0.079, for prediction error of this model, MSE was 0.026, MAE was 0.139 and MAPE was 0.083. Obviously, the simulation error of SARIMA model was greater than the hybrid model. The accuracy of the hybrid model was better than the RBF model and SARIMA model.
[Conclusions]:
(1) Trend extrapolation, which was based on the historical incidence rates, could be used for the forecasting of communicable diseases; (2) The prediction accuracy of RBF neural network, which was a nonlinear model, was better than the ARIMA model; (3) The ARIMA-GRNN combined model, which integrated linear and nonlinear models, represented better simulation and prediction effects than traditional ARIMA model; (4) For neural network, it is unnecessary to build complex mathematical models, learn about the structure of models and the relationship between input and output variables, so it was more easy to be applied in practice; (5) Trend extrapolation based on time series data can only be applied for short-term forecasting.
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