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地球信息科学学报 >

2017 , Vol. 19 >Issue 8: 1036 - 1048

DOI: https://doi.org/10.3724/SP.J.1047.2017.01036

地理空间分析综合应用

利用空间聚集的贝叶斯网络评估手足口病发病风险

  • 丘文洋 ,
  • 李连发 , * ,
  • 张杰昊 ,
  • 王劲峰
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  • 1. 中国科学院地理科学与资源研究所 资源与环境信息系统国家重点实验室,北京 100101;2. 中国科学院大学,北京 100049
*通讯作者：李连发（1978-）,男,副研究员,硕士生导师,研究方向为空间数据分析、空间数据挖掘、风险分析。E-mail: lilf@lreis.ac.cn

作者简介：丘文洋（1991-）,男,硕士,研究方向为空间分析与空间统计。E-mail:

收稿日期: 2017-02-01

  要求修回日期: 2017-05-06

  网络出版日期: 2017-08-20

基金资助

国家自然科学基金项目（41471376、41171344）

上海市大气颗粒物污染防治重点实验室开放课题资助

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A Bayesian Network Method Considering Spatial Cluster to Evaluate Health Risk of Hand, Foot and Mouth Disease

  • QIU Wenyang ,
  • LI Lianfa , * ,
  • ZHANG Jiehao ,
  • WANG Jinfeng
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  • 1. State Key Laboratory of Resources and Environmental Information System, Beijing 100101, China;2. University of Chinese Academy of Sciences, Beijing 100049, China
*Corresponding author: LI Lianfa, E-mail:

Received date: 2017-02-01

  Request revised date: 2017-05-06

  Online published: 2017-08-20

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《地球信息科学学报》编辑部 所有
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摘要

手足口病是一种常见的传染病,以往的研究表明该疾病与气象、环境和社会经济等因素相关联,其影响关系复杂,而疾病本身体现出较强的区域聚集性,采用普通的线性风险建模方法无法捕捉影响因素的复杂性及空间聚集性。因此,本文以山东省为例,在前人研究的基础上,提出了采用贝叶斯网络综合风险建模方法研究手足口病的发病风险与气象、土地利用、社会经济及空气污染等要素间的关系,并通过引入空间扫描统计聚集结果,将空间聚集引入到贝叶斯网络模型加强其空间推理功能,减少模型的偏差,提高评估的精度。结果表明,本文建立的手足口病空间贝叶斯网络风险模型具有较高的估计效果,引入的空间聚集性较好地融入到贝叶斯概率推理模型中,合理建立预测因子同手足口病发病风险之间的关系。通过对建模结果的解译,分析了手足口病的发病风险影响因素,特别是气候、社会经济及空气污染的影响。本文的空间贝叶斯建模方法及研究结果对手足口病暴发的防控预警具有重要的意义。

关键词： 手足口病; 贝叶斯网络; 空间流行病学; 空间聚集

本文引用格式

丘文洋 , 李连发 , 张杰昊 , 王劲峰 . 利用空间聚集的贝叶斯网络评估手足口病发病风险[J]. 地球信息科学学报, 2017 , 19(8) : 1036 -1048 . DOI: 10.3724/SP.J.1047.2017.01036

Abstract

Hand, foot and mouth disease (HFMD) is a common infectious disease. Previous studies showed that multiple factors, such as meteorological, geographical, environmental and socio-economic factors were associated with HFMD. The associations between these risk factors and disease are complex. HFMD incidences present strong spatial clustering and auto-correlation. It is difficult to capture such complex non-linear associations and spatial auto-correlation using ordinary linear regression. Based on the previous studies, we proposed a Bayesian network based integrated risk approach to explore the relationship between HFMD incidence risk and the influential factors, such as meteorological parameters, land-use pattern, socio-economic status and air pollution. HFMD is a typical disease of children in Shandong Province of China and it was taken as our study case. Our approach incorporated the output of spatial clusters obtained by scanning statistics to enhance spatial reasoning of the proposed Bayesian network. This could also reduce the bias and improved the performance of the prediction. The results showed that the integrated Bayesian network model proposed achieved higher accuracy than the other methods. Also, spatial hot spots incorporated well in our model. By interpreting the marginal probability of every influential factor in the model, we analyzed the effect of these risk factors, in particular meteorological parameters, socio-economic factors and air pollution on the HFMD incidence. Our spatial Bayesian network approach is useful and the results provided important information for early-warning, prevention and control of HFMD.

Key words： Hand-foot-mouth disease; Bayesian network; spatial epidemiology; spatial cluster

1 引言

手足口病是一种常见的,多发于儿童的传染病,由EV71或CoxA16等病毒引起。常见的症状包括见于患者手部、口腔或足部的发热、水疱、溃疡,少数患者还会发展出无菌性脑膜炎、脑炎、神经源性水肿等病症,病情进展较快者可重至死亡[1]。近年其在中国的暴发密度和患病程度的增加引起公众注意,卫生部自2008年5月起将手足口病纳入丙类传染病管理[2],以加强对这一流行疾病的防控。获知与手足口病发病相关的环境、气候、社会经济因素,便可以利用这些因素与发病的联系对手足口病可能引起集中暴发的区域采取预防措施。根据对不同地区的研究可知,手足口病的发病与诸多因素有关,其中包括气象因素,如气温[3]、相对湿度[4]、气压[5]、风速[6]、降雨量[7]等。Onozuka等[4]研究了日本手足口病的传播与温度和湿度的关系;Wang等[8]的研究认为降雨量对中国手足口病的传播有显著的影响;Lin等[9]发现了短期的厄尔尼诺效应与深圳市手足口病的发病和传播的联系,该研究还认为手足口病病毒可通过附着在空气颗粒物中进行传播,因而空气中的颗粒物浓度也与手足口病的发病有关,当浓度较高时,病毒附着传播的机会也较大。此外,有学者研究了空气污染物对手足口病的影响：Li等[10]采集了PM2.5及PM10的空气污染样本,通过测试表明了空气污染对手足口传染源的贡献;罗晓风等[11]对广州市越秀区手足口病发病数和空气污染指数间的关系进行分析,发现二者呈负相关;而Huang等[12]通过分析表明PM10对手足口病没有太明显影响。一些研究也关注地理环境与手足口病间的联系：Cao等[13]对深圳市手足口病发病情况与地理环境要素进行回归建模分析,这些环境要素包括NDVI、人口密度、道路密度等;Stanaway等[14]研究了中国大陆手足口病发病与NDVI及土地覆盖类型间的关系。此外,不同地区间存在经济和医疗卫生条件的差异[15],这些社会经济因素同样对手足口病的传播和发病带来影响。
在研究包括手足口病在内的流行病与各方面要素的关系的方法上,除了传统的临床和病理学研究方法外,以GIS和数据挖掘方法为主体的空间流行病学方法,将发病数据、地理要素数据和空间信息相关联,能够更直观地发现疾病传播的时空规律,得到了广泛的应用[2]。Hu等[16]的研究采用GWR（地理加权回归）探测中国手足口病与气象要素间的关系;Zhang等[17]使用回归树研究广东省气候因子对手足口病发病的影响;吴北平等[18]则采用贝叶斯时空模型探索2008年山东省手足口病同气象因素之间的关系,结果发现了发病率具有明显的时间模式,且发病率相关的气象因素依次是：周平均温度、平均风速和平均气压。手足口病的发病与气象、环境因子间的关系往往比较复杂,因子和疾病发病率之间的数学关系可能是非线性的,并且不同因子之间对发病率具有交叉作用[19],而这些关系在不同地区之间又存在差异,这都对研究具体区域内的手足口病发病风险提出了挑战。
针对手足口病本身发病影响因素的复杂性及区域差异性,本研究采用贝叶斯网络综合学习器结合域知识,再结合空间扫描统计方法探索气象和社会经济等因素与手足口病发病间的关系。贝叶斯网络是一种结合不同的发病影响因素进行概率推理的模型,以变量之间的有向无环图和联合概率分布表的形式揭示要素与发病率之间的联系。与其他风险建模方法相比,贝叶斯网络可融合域知识与数据学习进行建模,网络可融合多种不同种类的解释变量建立复杂的概率关联性进行推理,同时可处理缺失数据。以往的研究[20-21]将贝叶斯风险建模方法应用在自然灾害及环境健康风险分析中,取得很好的评估结果。本研究将综合各种贝叶斯学习方法,提取学习网络结构的共同连接,采用域知识微调,从而达到优化的学习效果。
另外,传统的贝叶斯网络其结构决定了本身很难直接加入空间相关/聚集性变量,极大地限制了其空间建模及推理的功能。因此,本研究在前期的模型[20]中创造性地加入空间的相关统计量,将疾病发病率的空间聚集性作为可能影响发病的空间要素,融入到模型中,从而增强贝叶斯网络的空间推理的功能。空间扫描统计源自时空扫描方法,时空扫描统计量是一种能够探测事件在时间和空间2个维度上的变化情况,找到并在时空中“定位”其中的聚集事件的时空数据统计方法。该方法由Kulldorff针对时空聚集问题提出[22],如果所研究的事件在时间或空间上有异常增加的行为,此方法能够探测出发生此类行为的时间和空间位置。时空扫描统计还可以对多个聚集的“热点”进行聚集程度的估算和排序,能够看到哪些“热点”更“热”。这使此方法相当适合流行病学的研究,对于一系列发病时空数据,时空扫描统计能够探测出哪些区域何时暴发了该种疾病。徐敏等[23]用时空扫描统计的方法,通过研究2009年深圳市甲流感病例的时空热点,进行疫情防控预警;Deng等[24]对广东省2008-2011年手足口病病例数据进行时空扫描统计,探测出4个主要的发病聚集簇。本研究通过建立模型,更全面与综合评估影响发病率的气象、空气污染、环境和社会经济等要素,而有效地将空间聚集信息融入到网络模型加强网络的空间推理功能,估算热点区域对发病率估计的影响,探索了手足口病的空间分布的规律,研究成果可为手足口病的预防及控制传播提供相关的辅助决策信息。

2 研究区概况与数据源

2.1 研究区概况

山东省位于中国东部沿海,西邻华北平原,东部为山东半岛并伸入黄海。山东省总面积15.8万km2,以近9800万人口成为中国的第二大人口大省。山东属温带大陆性季风气候,雨热同季,年均温度13 ℃,降雨集中于夏季,全年降雨量在550~950 mm之间[6]。山东省是手足口病的多发省份,自2000年起烟台、泰安、临沂等地均有暴发流行报告,2008年山东省全省手足口病发病数居全国第三[25]。图1展示了研究区域山东省及其发病率分布图。
Fig. 1 Study area

图1 研究区域

2.2 数据源

（1）发病率数据。自2008年5月起,手足口病被卫生部列入丙类传染病管理,各级医疗机构需按照有关法律进行网络直报。本研究从中国疾病预防控制中心获取了自2008年5月起山东省共138个区县的每周发病率数据,共47周,将此时间段内各区县的总发病率作为发病风险预测的目标变量。
（2）预测变量数据。研究表明气象、社会经济、空气污染及土地利用[10,26]等与手足口病发病率有重要影响,本文在前人研究的基础上选择了以下的预测变量。
① 气象站点数据
本研究从中国气象数据网（http://data.cma.cn/）获取与手足口病发病数据同期的气数据,为全国677个气象站点的观测数据,包括日均温度、日最高温、日最低温、相对湿度、气压、风速等观测值。这些数据在ArcGIS软件中,采取IDW（反距离权重法）和分区统计方法计算出山东省各区县相应气象平均值,作为气象因子数据,探索这些气象因素在山东手足口病发病的影响。
② 社会经济数据
根据社会经济要素对手足口病发病的影响,研究通过统计年鉴（http://www.stats-sd.gov.cn/）收集并整理了2008年山东省各区县的社会经济数据,涵盖经济发展状况（如各产业生产总值、人均收入等）、社会及人口状况（如在岗职工及中小学生在校人数）、公共设施建设（如医疗卫生、学校建设）等要素。本研究依照手足口病主要在儿童间传播的特点,选取GDP、在校小学生人数比例和人均医院床位数等变量作为社会经济要素,以分析经济与社会发展对手足口病发病与传播的影响
③ 空气污染监测数据
研究表明空气污染可能会对手足口病产生重要影响[10],但有关这方面的研究很少。本研究首次采用空间统计方法结合机理探索PM2.5对手足口病的影响,获取了2013年7月以来的山东省内监测站点PM2.5数据,考虑到手足口病发病与空气污染均具有明显的季节性,因而可忽略年份不同造成的数据偏差。山东省共有96个站点具备较完备的监测记录,提取其中的根据监测PM2.5数据估算暴露度作为空气污染变量,使用前期PM2.5建模的结果进行分析建模。
④ NDVI数据
NDVI（Normalized Difference Vegetation Index）,即归一化植被指数是从遥感影像数据中提取的反映地表植被覆盖度的一项数据,是间接反映影响手足口病的环境因素[14]。本研究采用的数据源为2009年MODIS影像,分辨率为1000 m×1000 m,在ENVI 5.0软件中提取研究区域内的NDVI值,以各区县范围内的NDVI均值作为该区县NDVI值,加入模型参与分析。
⑤ 土地覆盖数据
研究表明土地类型对手足口病有重要影响[14],本研究获取来自GlobCover的2009年全球土地覆盖栅格数据集,分辨率为230 m×230 m,裁剪出研究区域数据并进行分类,分为水体、人造区域和自然区域,以表示水体覆盖、人工建造物为主的覆盖以及自然植被或荒地覆盖。对于各区县,计算每种覆盖在该区县所占比例,将该比例作为该区县土地覆盖因子加入模型。
⑥ 交通路网数据
交通路网状况可以从不同的角度影响一个地区的流行病发病率[13]。密集的道路通常意味着更高的人口流动和更高的经济水平,而稀疏的路网密度则反映出地区地理位置偏远和经济欠发达。开放地图OpenStreetMap（http://www.openstreetmap.org/）提供了全国交通路网信息作为矢量数据下载,包括道路名称、道路长度、道路分级等信息。本研究对研究区域内的交通路网信息数据进行处理,计算主要道路和次要道路在各区县内的道路密度,作为交通路网因素探测对手足口病发病影响。

3 研究方法

本研究采用了扩展性强、结构灵活的贝叶斯网络作为建模架构,在贝叶斯网络的基础上融入了空间聚集性聚类结果,通过空间聚集（相关性）的概率推理,进一步加强贝叶斯网络的风险建模能力。

3.1 贝叶斯网络

贝叶斯网络由一组节点V和连接这些节点的有向边构成的有向无环图,每个节点V表示一个随机变量（代表影响手足口病影响因素或风险水平）,每条边表示变量间的概率影响/依赖关系。每个节点V对应着一条件概率表P（Conditional Probability Table,CPT）,用于定量描述该影响因素节点与父节点之间概率依赖的数量关系,如果某个节点没有父节点,则其条件概率表为给定的先验概率分布。
考虑到手足口病影响因素复杂,数据有限,本文们采用综合集成的贝叶斯网络评估手足口病健康风险。该方法的主要优势是采用了多种结构及参数学习法,并结合领域知识微调网络结构,从多方面提高网络模型的可靠性,可减少建模过程中由于单一学习方法导致的偏差。其具体包含4个步骤：确定变量集和变量域、数据预处理、数据学习建立初步网络结构、通过域知识微调网络结构及估计参数（条件概率）。
图2展示了结合空间聚集性的手足口病风险建模的结构图。图中列出了贝叶斯网络模型需处理的目标变量,相关的变量域及其下面的具体要素,包括空间聚集的输出。该结构在朴素贝叶斯网络基础上构建网络,加入空间聚集信息随机变量节点,增强贝叶斯网络的空间推理功能,提高网络模型的推理预测功能,是对贝叶斯网络方法的改进之处。在实际学习时,不采用朴素贝叶斯的结构,而通过爬山、Tan、模拟退火及遗传算法等得到精细的网络结构,并在领域知识的的基础上调整得到最优的网络结构,从而从多方面优化手足口病风险评估模型,提高结果的可靠性。
（1）确定变量及变量域。根据领域知识我们列出了手足口病的传播介质及相关的影响因素（图2）,传播介质包括：土地/水等,其代理变量包括所提取的土地覆盖百分比、NDVI;空气,提取了PM2.5的估算结果作为空气污染的代理变量;交通,通过交通路网展示交通密集程度。影响因素包括气象及社会经济,气象则包括温度、湿度、气压、风速,社会经济包括GDP、在校学生比例及人均医院床位数。如果数据允许,将采用更多的变量。
（2）数据预处理。我们需要对目标变量及连续的解释变量进行离散化处理,并根据其对手足口病发病风险贡献率的大小进行变量的选择,减少风险评估模型中的噪音。目标变量（手足口发病率的高低）可根据领域知识按照一定规律得的域值将发病率分成高/低2类;而对解释变量的离散化方法可采用Fayyad and Irani的算法[27]选择对目标变量分类最优的离散化区间。根据最优的离散化方案,计算解释变量对目标变量分类的贡献度,采用了常用的Quinlan信息获取比率作为划分的依据。
（3）数据学习建立初步的网络结构。其可以采用爬山、模拟退火及遗传算法通过学习建立初步的网络结构,在此基础上提取共同点连接,同时下一步通过域知识对网络结构进行调优。表1展示了网络结构学习、调整及参数学习方法及在手足口病风险建模中的适用性。
（3）通过域知识微调网络结构及估计参数。由于数据学习网络结构受到数据本身的样本测量及误差的影响,所以学习的结构不一定符合要求。此时,需要根据几种学习得到的网络结构,提取其中共同的连接,再结合气象及环境影响因素对手足口病影响的域知识对网络结构调优,包括移除不合域知识的概率依赖连接,增加合理的连接,通过人工干预使得建立的网络模型更符合机理。在网络结构调优的基础上,通过概率统计、EM或Gibbs抽样计算连接参数（条件概率表）,从而完成网络模型的建立。考虑到建模数据缺失情况,本研究采用了EM算法。

3.2 空间聚集性信息及其风险概率推理

本研究采用空间扫描统计识别手足口病的高及低风险聚集区,输入到贝叶斯风险评估模型之中,以提高评估的精度。由于本研究只涉及到处理空间信息,所以只采用空间扫描统计对所采集的山东省手足口病发病数据聚集分析,发现疾病聚集性暴发的区域。虽然时空扫描统计不是直接的空间相关性测量,但其本身具有明显的空间特征（空间上的强聚集划分为一类）。因此,其聚集的结果可作为一个空间相关性的间接的随机变量节点连接到贝叶斯网络模型中,加强风险分析的估计能力。
空间扫描方法采用移动窗口法,在研究区域内建立活动圆形窗口对疾病发生率进行扫描统计。窗口的位置和大小处于动态改变中,每次变动,将计算窗口内与窗口外区域疾病发生数之间的差异,并采用对数似然比检验该差异是否由随机变异造成。空间扫描统计的目的是寻找所有位置、所有大小窗口中的最大对数似然比值,该处即为最可能存在聚集性的区域,也就是最不可能由随机变异造成的。本研究中疾病发病数采用泊松分布模型作为空间扫描统计的概率模型,提取高发病率的热点（聚集）区域。该方法通过最大似然及统计假设检验[20]获得手足口病空间聚集的结果。
因空间扫描统计获得了空间上聚集性强的高风险/低风险区域,该结果可输入到贝叶斯网络中作为空间聚集性因子。通过概率依赖关系建立条件概率表：
p ( r = r i c = c k ) = P ( r = r i , c = c k ) P ( c = c k ) = sum ( r = r i , c = c k ) sum ( c = c k ) （1）
式中：p（…）表示概率;r表示手足口发病率“高” （r1）或“低”（r0）风险水平;c表示是否＂热点＂（ck=1）或非聚集区（ck=6）,可以通过频数统计得到条件依赖关系。如果数据有缺失,采用EM算法;而数据量大,则通过Gibbs抽样得到条件概率表（表1）。
在前期的贝叶斯网络模型[20]中,空间性只是间接地通过自变量本身的空间变异来体现,没有明显的空间自相关性特征。而本研究方法融入了空间聚集结果,作为空间自相关性的间接的随机变量节点加入了模型之中（图2）。通过空间扫描获取区域聚集信息的加入,进一步加强贝叶斯风险探测方法的空间推理功能,取得更好的效果。
Fig. 2 Bayesian network topology of HFMD with spatial correlation

图2 结合空间聚集性的手足口病贝叶斯风险建模结构图

Tab. 1 Methods of Bayesian network topology and parameter learning

表1 贝叶斯网络结构建立及参数的学习方法[21]

主要算法 主要方法 在手足口病风险评估中的适用性
结构学习 K2 通过变量固定拓扑排序得到节点间连接[28] 初始变量顺序是基于朴素贝叶斯模型 局部优化算法,计算速度快,适用于处理海量数据查找各影响因素同手足口病发病风险的关系
爬山算法 通过迭代最终选择得分最高的结构模型[29]
Tabu 一种最优爬山法,在学好的结构中加Markov Blanket连接[30]
TAN 设计算法来计算极大权重扩展树[31]
模拟退火 在上一模型基础上随机生成备选网络模型BS',如果该模型比上一个模型更好,则使用这个备选模型[30] 局部优化算法,但算法较为复杂,搜索较慢,不适用于处理大数据量,但算法实施可较好地搜寻各种影响因素同手足口病发病风险的关系
遗传算法 通过遗传算法找到最优的网络结构[32]
结构微调 结合域知识 根据手足口病的传播源及影响因素领域知识[2,8,16],移除无实质意义的连接,增加新的有意义的 连接 结合特别适合于手足口病影响因素复杂情况,根域知识,可移除关系学习中的偏差,纠正网络
参数学习 简单贝叶斯 根据Dirichlet分布根据数据进行概率计算[30] 基本求参数的方法
期望最大化 EM算法,基于最大似染法,可处理数据缺失的参数的估计值[33] 适用于有有自变量缺失的情况
Gibbs抽样 通过蒙特卡洛方法进行抽样计算条件概率,适合数据量大的情况[34] 适用于海量数据学习手足口病风险评估模型

3.3 结果的评估及解译

本研究采用10×10的交叉验证方法,评价贝叶斯网络建模效果。具体比较表1所列的几种典型的贝叶斯网络学习方法,以及常用的流行病风险评估方法,包括决策树J48、随机森林及逻辑斯特回归,同我们的综合了几种贝叶斯学习方法（共同结构）加上域知识调整。关于贝叶斯网络学习方法,参见表1;其他学习方法,参见文献[21]。在该验证方法里,数据被平均分成10份,其中9份用于训练模型,1份用于测试模型。如此循环10次,所有的数据都被预测到,得到1次验证结果。此过程重复10次,取得性能的平均值作为模型总的预估性能。
对模型总体性能的评价指标包括探测率,本研究选用了以下几个指标衡量模型的有效性,即真正率、精确性、基于pd及精确性的综合性指标F计 分（F score=2×（pd×precision）/（pd+ precision））和ROC area。
Pd：真正率（也称为recall）,指样本中模型预测的高风险发病率区县数与实际高发病率区县数的比值,这个比值范围为0-1。
精确性：精确性相当于命中率的概率,即在所有预测为高风险的结果中,有多少是真正高手足口病发病率的比例。
ROC area: 指ROC曲线,即受试者特征曲线（Receiver Operating Characteristic Curve）下方的面积。该曲线是在坐标轴中以每个样本的假正率为横坐标,真正率为纵坐标绘制的曲线,越好的模型,ROC曲线越趋向左上方。
此外,根据网络的连接及参数,计算贝叶斯网络模型中各个影响因素的对目标变量（高发病率的可能性（概率））的边际概率,衡量各主要影响因素对高发病风险的影响,结合机理及领域知识进行解译。

4 结果分析

4.1 山东省手足口病发病率的总体规律

2008年5月至2009年3月,山东省共有37 945起手足口病病例,全省发病率为40.32×10-5。全年发病率最高的区县为济南槐荫区,达到638.33×10-5,而最低的则是聊城冠县,为0.283×10-5。2008年5月第二周济南槐荫的发病率达到89.71×10-5,该周临沂兰山的发病数达到558例,均为全年最高。
从全年趋势上看,手足口病发病率在2008年5-6月时最高,全省每周发病率维持2×10-5以上, 7月过后逐渐下降,在冬季约11月有轻微的上涨趋势,但发病率仅在1×10-5左右,随后一直平稳直至2009年春季。与过往的相关研究结果类似[35],山东省手足口病的高发季节为夏季,且在冬季11月出现一个次高峰（图3）。
Fig. 3 Weekly incidence rates of HFMD

图3 山东省手足口病发病率时间变化趋势

鉴于辅助数据变量数据所限,目前只是对全年的发病率平均值进行空间上的贝叶斯风险建模,所以分析结果也是基于年平均的值,暂时没有考虑时间方面的变化。

4.2 山东省手足口病发病的空间扫描统计及聚集 等级

本研究使用Satscan软件进行分析,采用空间泊松（Poisson）模型对全部47周的区县发病率数据进行高发病率扫描统计,最终探测出5个聚集热点,按照发病聚集程度从高至低,中心区分别在菏泽市曹县、莱芜市莱城区、莱阳市、枣庄市中心、德州市德城区。图4为空间扫描统计得到的山东省各区县空间聚集等级图,1表示具有最显著的发病聚集,数字递增聚集程度递减,6为无明显聚集的区域。在贝叶斯建模中,空间聚集等级将作为一个变量加入模型,其取值为各区县的聚集等级,即1至5表示热点的聚集等级且程度递减,6表示该区县不在聚集 热点中。
Fig. 4 Spatial clusters of HFMD in Shandong Province

图4 山东省手足口病发病空间聚集等级图

4.3 手足口病发病风险的贝叶斯网络建模分析

4.3.1 解释变量选择和处理
从所获取的数据中选择用于贝叶斯网络的解释变量,既需尽可能地涵盖影响手足口病的各发病要素,也需考虑数据质量以及建模时解释变量的多重共线性问题。最终根据属性重要性测量指标选取了以下因子作为贝叶斯网络的解释变量（表2）。
Tab. 2 Variable selection of HFMD Bayesian network risk model

表2 手足口病贝叶斯网络风险模型变量的选择

类别 解释变量 属性重要性（Gain Ratio）
气象 日均气温
日最高气温
日最低气温
风速
相对湿度
气压		 0.022
0.213
0.016
0.101
0.114
0.027
社会经济 GDP（生产总值）
人均医院床位数
小学在校生比例		 0.227
0.152
0.190
空气污染数据 PM2.5浓度 0.125
NDVI 区县NDVI均值 0.017
土地覆盖 人工覆盖比例 0.086
交通路网 主要及次要道路密度 0.168
空间聚集 空间聚集等级 0.219
这些解释变量在建模前均进行离散化处理,划分为若干等级,以便进行概率推理。
4.3.2 发病风险的等级划分
除了解释变量以外,目标变量,亦即手足口病发病率,也需离散化为不同等级,同时也能更直观地将发病风险和各影响因素相关联。山东省各区县中共有107个区县全年发病率在50×10-5以下,在全省全年（40.32）以下的有98个,本研究将全省全年发病率为高低风险的划分标准,全年发病率高于或等于40.32×10-5的区县为高风险区,其余则为低风险区,从而划分出49个高风险区和98个低风险区。
4.3.3 气象、环境和社会经济因素与手足口病发病风险的贝叶斯网络建模
结构学习采用数据学习结合域知识方法选择最优网络结构[20]。首先对包含了各气象、环境和社会经济要素而没有考虑时空聚集性变量的解释变量与发病风险进行建模。所学习的网络结构经过域知识验证基本符合要求,最终风险模型的贝叶斯网络结构如图5所示。
Fig. 5 Bayesian network topology of HFMD risk and predictors

图5 手足口病发病风险与各解释变量的贝叶斯网络结构图

根据所学习的网络结构,相对湿度、土地覆盖、GDP、人均医院床位数、日最低温、NDVI、交通路网等要素与发病风险直接相关,反映手足口病的发病风险与气象、地理环境和社会经济等要素综合相关。将此网络结构和其他网络结构学习算法习得的结构及其他推理方法进行交叉验证,高风险等级的真正率值达到0.57,ROC面积为0.78,低风险等级真正率为0.85,ROC面积为0.78。表3为贝叶斯综合风险评估模型和其他网络结构及机器学习算法（表1）的比较结果,表明本文的综合风险评估取得最好的效果。
Tab. 3 Performance comparison of different Bayesian network without spatial clusters

表3 无空间聚集性贝叶斯网络风险不同模型的建模结果

学习算法 真正率（风险:高/低） 假正率（风险:高/低） 精确度（风险:高/低） 准确度 ROC面积
综合BN+域知识 0.57/0.85 0.15/0.43 0.63/0.82 0.77 0.78
BN K2 0.52/0.82 0.17/0.48 0.56/0.80 0.74 0.79
BN 爬山 0.52/0.88 0.12/0.48 0.67/0.80 0.76 0.79
BN Tabu 0.52/0.87 0.13/0.48 0.65/0.80 0.76 0.78
BN 模拟退火 0.45/0.90 0.10/0.55 0.68/0.79 0.77 0.68
决策树：J48 0.38/0.98 0.02/0.62 0.84/0.78 0.80 0.62
随机森林 0.48/0.85 0.15/0.52 0.59/0.79 0.74 0.78
逻辑斯特回归 0.48/0.91 0.10/0.52 0.59/0.80 0.77 0.70
4.3.4 考虑时空聚集性后的贝叶斯网络建模
在已有的各影响因子的基础上,将时空扫描统计的结果,即每个区县的手足口病发病聚集等级作为一个新的变量参与建模。在综合各网络结构共同连接及域知识的调整之后,最终风险模型的网络结构如图6所示。
Fig. 6 Bayesian network topology of HFMD risk and predictors

图6 结合空间聚集性后的贝叶斯网络结构图

将聚集等级作为一个解释因子加入后,在网络结构中对发病风险产生了直接影响,可见该因素对手足口病发病有重要的关系。交叉验证结果上,高风险等级的真正率值达到0.64,ROC面积0.79;低风险等级真正率值为0.85,ROC面积为0.79。与表3的无空间聚集性建模结果相比,在考虑了空间聚集后,高风险的建模真正率提高了7%,与其他算法的各项评估指标比较结果见表4。结果表明了贝叶斯综合风险评估模型取得最优的学习效果。
Tab. 4 Performance comparison of different Bayesian network with spatial clusters

表4 有空间聚集性贝叶斯网络风险不同模型建模结果

学习算法 真正率（风险:高/低） 假正率（风险:高/低） 精确度（风险:高/低） 准确度 ROC面积
BN+域知识 0.64/0.85 0.15/0.36 0.70/0.83 0.80 0.79
BN K2 0.62/0.85 0.15/0.38 0.65/0.84 0.78 0.78
BN 爬山 0.54/0.87 0.12/0.45 0.60/0.80 0.78 0.79
BN Tabu 0.52/0.87 0.14/0.48 0.71/0.81 0.76 0.79
BN 模拟退火 0.43/0.93 0.06/0.58 0.75/0.79 0.78 0.71
决策树：J48 0.40/0.95 0.05/0.60 0.77/0.78 0.77 0.62
随机森林 0.52/0.84 0.15/0.50 0.78/0.79 0.74 0.78
逻辑斯特回归 0.50/0.86 0.15/0.52 0.60/0.80 0.74 0.69
本研究计算了在贝叶斯网络结构中与发病风险直接联系的各解释变量与发病风险的边际条件概率（表5）,即对于一个区域,某个主要解释变量按离散化结果取不同等级时,模型推理该地区为手足口病高风险或低风险的边际条件概率。结果反映了这些变量对手足口病发病风险的贡献和影响,相对湿度、日最低气温等变量为高等级的地区有超过70%概率在模型中被推测为高发风险,而高等级的NDVI则有80%的概率使该地区推测为低风险。结合机理可以分析不同变量与发病风险间的相关性,在诸多变量的混合作用下,发现山东省手足口病发病最重要的影响因素。
Tab. 5 Conditional probability table of risk factors and HFMD incidence risk

表5 解释变量与发病风险的边际条件概率表

解释变量 等级 范围 发病风险
高 低
相对湿度/% 高 71.04~73.52 0.736 0.264
低 60.58~71.04 0.304 0.696
日最低气温/℃ 高 17.05~20.03 0.747 0.253
低 13.44~17.05 0.291 0.709
GDP（元/人） 高 42 146~176 826 0.553 0.447
中 20 847~42 146 0.386 0.614
低 2200~20 847 0.252 0.748
人均医院床位 高 62.15~72.23 0.752 0.248
中 28.30~62.15 0.325 0.675
低 10.81~28.30 0.172 0.828
小学在校人数比例/% 高 0.831~1.082 0.103 0.897
低 0.416~0.831 0.317 0.683
道路网密度/（km/km2） 高 0.56~2.60 0.481 0.519
低 0.21~0.56 0.223 0.777
NDVI 高 0.43~0.61 0.160 0.840
低 0.18~0.43 0.358 0.642
土地覆盖（人工用地比例/%） 高 26.18~99.05 0.944 0.056
中 10.29~26.18 0.677 0.323
低 1.16~10.29 0.210 0.780

5 讨论

手足口病作为一种常见的传染病,其传播、发病与地理、环境、气候、社会经济要素密切相关。以往的研究往往针对某种要素的某几个指标（如气象要素的温度与湿度）来探讨其对手足口病发病的影响,但将不同类别的要素相结合,综合分析这些要素与疾病的联系的研究较少,而同空间聚集性结合的更为少见。Bo等[36]结合气象因子和社会经济因子对中国手足口病发病风险的空间模式进行建模分析;Cao等[13]则利用遥感数据和医院密度等数据进行研究。本研究收集气象、空气污染、土地利用、社会经济要素等较全面的数据及空间聚集结果,建立贝叶斯网络综合风险评估模型分析手足口病发病与这些要素之间的关系。建立的模型同传统的分析方法如逻辑斯特回归相比提高了风险探测的精度（高风险探测率提高了14%,综合评价指标ROC提高了10%,表4）。结果发现,与山东省手足口病发病风险密切相关的各要素包括相对湿度、GDP、人均医院床位数等。研究将空间聚集结果加入模型中,也提高了模型高风险探测率的精度。
贝叶斯网络因为其灵活的网络结构,可将先验知识同数据学习相结合,融入多种优化算法,同传统的逻辑斯特模型相比,其高风险的探测比例有大幅的提高（14%）,模型精度的提高有助于模型更客观地展示影响因素同目标变量之间的关联关系,同时有助于区域风险评估精度的提高。严格的10×10的交叉验证的验证也从统计学上验证了本文方法在实际预测中相比其他方法如逻辑斯特、随机森林、决策树及单一的贝叶斯学习方法好。此外,本文模型通过加入空间聚集性,交叉验证揭示了本文方法对发病风险等级预测精确度的贡献显著提高（探测率7%的提高）。贝叶斯网络方法在风险分析中有广泛应用[20],通过融入不同来源的数据和域知识提高风险预测率,但在流行病学分析中应用较少。此外,贝叶斯网络通过计算主要的影响因子与发病风险间的边际条件概率,分析在多个混淆因子作用下,各变量与发病风险的关系,结合相关的机理探测影响发病风险的主要因素,对揭示手足口病的传播规律和疾病防控有重要意义。贝叶斯网络是不同于贝叶斯时空模型[18]的方法,二者具有不同的模型结构及机制,贝叶斯时空模型采用基于logit的线性回归拟合影响因素同发病率的关系,探索通过回归及先验知识探索时空模式;而本研究中的贝叶斯网络则是预测发病的风险,该模型具有更灵活的网络结构,可融入更全面的变量,并捕捉变量之间的非线性关系,提高预测的精度。而本文的创新之处在于,在经典贝叶斯模型基础上加入了明显的空间推理功能,极大增强了贝叶斯网络的空间推理功能,提高了预测精度,更有助于对结果的解译。
气象因素是影响手足口病发病的重要要素,以往的研究对不同的气象指标与手足口病发病间的关系进行了探讨[3,5]。本研究选取了气温、相对湿度、风速、气压等指标参与建模,在贝叶斯网络结构中,日最低温和相对湿度与手足口病发病率有直接的联系,通过边际概率表可以发现,当相对湿度较高时,发病风险概率提高。Onozuka等[4]的研究结果表明相对湿度和气温上升时,手足口病的发病显著增加。Chen等[3]也发现相对湿度的增加在一定的滞 没后期内会导致疾病发病的增加,该研究还发现温度在1-3 d的滞后期内与手足口病发病的变化呈负相关,在5-9 d的滞后期内呈正相关。吴北平等[18]则发现了发病率相关的气象因素依次是：周平均温度、平均风速和平均气压。尽管这些研究是在时间尺度上进行的,本研究发现日最低温及相对湿度的高低与手足口病发病的关系在空间尺度上也具有相似的规律,即根据边际概率表,日最低温和相对湿度较高的地区,具有更高的患病风险。在潮湿的地区,空气中的水汽为病毒的传播提供了便利。日最低温而不是日均气温或最高温能够更明显地影响发病,本研究认为是人体对最低温的变化可能较为敏感导致的,但具体的机理仍需要深入研究。
对于GDP、人均医院床位数和小学在校人数比例等社会经济因子,本研究发现GDP和人均医院床位数与发病风险密切联系。而在加入空间聚集要素后,小学在校人数比例也与发病风险有关联,可能与人口集中流动增加热点区域的传染性相关,结果也表明了社会经济因素对山东省手足口病发病在空间上的差异有较大的影响。例如,GDP较高、人均医院床位数较多的地区具有较高的高发病风险概率,研究发现济南、青岛、临沂等经济发达的地区发病率也偏高。一方面,在这些发达的地区,尽管儿童作为主要的发病群体在学校、幼儿园活动的时间较长,集中管理降低了他们的发病几率,然而对于散居儿童而言,密集的人口与高流动性增加了发病的风险。根据胡跃华等[36]研究,这些散居儿童占发病儿童的多数。另一方面,发达地区的医疗卫生条件丰富,病人患病后在医院接受检查治疗,对病例的收集和报告也较欠发达地区积极[15],这些因素导致了经济发达地区具有了更高的患病风险。目前,极少有相关的研究报道土地利用同手足口病的关系,本研究中人工土地利用比例为高等级的地区有94.4%的概率为发病高风险区,进一步说明城市中的发病风险较农村地区高,支持经济条件与手足口发病之间的联系。
一些研究关注空气污染与手足口病发病间的关系。Lin等[9]认为空气中颗粒物的增加使病毒更易附着其上,助长了病毒的传播;Bo等[36]提出空气污染物可以降低人体免疫力,使暴露人群患病风险升高。本研究发现在山东省PM2.5与手足口病发病间的联系并不明显,2个变量在贝叶斯网络中没有直接关系。本文在研究中计算了PM2.5作为预测变量时与发病风险间的边际条件概率,也显示高污染与高发病的关联性不高。考虑到东部沿海如威海、烟台等地区空气污染相对较轻而发病风险较重,空气污染对发病的贡献可能存在与其他变量之间的混淆效应,从而存在估计偏差,需要进一步研究。
研究表明手足口病发病具有空间聚集性[24],时空扫描统计方法能够寻找发病聚集的区域,并按照聚集程度划分主要和次要聚集簇。Liu等[37]对2007-2011年山东省手足口病发病率进行时空扫描统计分析,发现了7个不同的聚集簇,且聚集区域随时间移动;Wang等[38]利用扫描统计方法,研究以区县为单位的全国手足口病发病聚集情况,结果显示空间聚集簇大多位于中国东部和南部。有关手足口病空间聚集的研究通常旨在探测出热点区域,很少将其与其他发病风险因素结合分析。本研究对2008年山东省手足口病发病数据进行空间扫描统计,共得到5个聚集簇,并将空间聚集等级信息作为一项解释因子加入贝叶斯网络建模。所建立的网络在预测精度上得到提高,10×10的交叉验证说明高风险预测真正率增加7%,这一结果表明考虑空间聚集性这一重要的手足口病流行病学特征,与发病的地理环境、社会经济要素结合能更全面地刻画手足口病的传播规律,从而提高模型的预测精度,体现出空间聚集性的重要意义;同时,能更合理地解释人口经济因素（如人均医院床位数）同发病源的关系。
本研究仍有一些局限性：① 研究所采用的手足口病发病数据是以区县为空间单位,以周为时间单位的数据,缺乏更为精准的个案数据来揭示各影响要素,特别是社会经济要素对发病的影响;② 限于各因子数据不统一的时间尺度,本研究没有考虑时间变化,将全年数据一并进行建模分析,而手足口病发病数据及气象要素数据均具有明显的季节性变化,时间尺度上的影响未能在模型中体现。而我们也即将开展与时空相结合的方法研究山东省的手足口病时空分异规律。

6 结论

本研究采用贝叶斯网络综合考虑多方面发病风险因子及空间聚集性,经过多种学习优化算法与域知识修正网络,交叉验证表明所建立的模型同传统逻辑斯特模型等比较预测精度有较大的提高,客观地反映了山东省手足口病发病与气象、土地利用、社会经济要素及空间聚集性的关系。研究结果说明加入空间聚集性增强贝叶斯网络空间推理功能及显著提高模型精度情况同时,对环境因素同手足口发病风险的关系产生一定的影响,空间聚集热点（高风险）的地理分布有助于解释环境影响因素的来源或其空间分布同高风险的关联性;研究也探索了土地利用、交通及空气污染同手足口病间的关系,结果表明具有高土地利用率的城市比低土地利用率农村具有更高发病风险,研究也发现交通用地及关联的空气污染同手足口病风险呈现显著的正相关性。本文研究方法及结果对手足口病的预防与监控提供可靠的方法参考及多方面因素的影响。

The authors have declared that no competing interests exist.

参考文献

原文顺序 | 文献年度倒序 | 文中引用次数倒序
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别芹芹,邱冬生,胡辉,等.我国手足口病时空分布特征的GIS分析[J].地球信息科学学报, 2010,12(3):380-384. ]手足口病是一种常见传染病。近几年在我国多次暴发且发病人数显著增加,引起了我国政府和社会各界的广泛关注。目前,对手足口病的研究主要集中在医学领域,而在宏观尺度上的时空分布特征研究及其重点地区分布研究等方面均较少。本文探索应用地理信息系统(GIS)的工具和方法,对2008-2009年中国疾病预防控制信息系统收集的手足口病监测数据进行统计计算、空间可视化和空间分析,得到我国手足口病疫情的时空分布与动态变化特征。研究表明:(1)尽管全国均有手足口病的报告病例,但各省之间发病情况差异较大,且区域内的发病情况也存在较显著差异,一般在人口密度和人口流动性均较大的城市疫情较严重;(2)手足口病在我国的流行高峰期为4-7月,比国外相关研究中的描述提前了一个月;(3)5-6月,我国手足口病的高发区分布明显由南向北移动。(4)2008-2009年,我国手足口病患者98%以上为托幼儿童、散居儿童和学生。鉴此分析,本文提出了具有时间、空间和人群针对性的防控手足口病暴发流行的科学建议。

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[3]
Chen C, Lin H, Li X, et al.Short-term effects of meteorological factors on children hand, foot and mouth disease in Guangzhou, China[J]. International journal of biometeorology, 2014,58(7):1605-1614.Hand, foot and mouth disease (HFMD) is a contagious viral illness that commonly affects infants and children. The underlying risk factors have not yet been systematically examined. This study analyzed the short-term effects of meteorological factors on children HFMD in Guangzhou, China. Daily count of HFMD among children younger than 15years and meteorological variables from 2009 to 2011 were collected to construct the time series. A generalized additive model was applied to estimate the effects of meteorological factors on HFMD occurrence, after adjusting for long-term trend, seasonal trend, day of week, and public holidays. A negative association between temperature and children HFMD occurrence was observed at lag days 1–3, with the relative risk (RR) for a 1°C increase on lag day 2 being 0.983 (95% confidence intervals (CI) 0.977 to 0.989); positive effect was found for temperature at lag days 5–9, with the highest effect at lag day 6 (RR65=651.014, 95% CI 1.006 to 1.023). Higher humidity was associated with increased HFMD at lag days 3–10, with the highest effect at lag day 8 (RR65=651.009 for 1% increase in relative humidity, 95% CI 1.007 to 1.010). And we also observed significant positive effect for rainfall at lag days 4 and 8 (RR65=651.001, 95% CI 1.000 to 1.002) for 1-mm increase. Subgroup analyses showed that the positive effects of temperature were more pronounced among younger children. This study suggests that meteorological factors might be important predictors of children HFMD occurrence in Guangzhou.

DOI PMID

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Onozuka D, Hashizume M. The influence of temperature and humidity on the incidence of hand, foot,mouth disease in Japan[J]. The Science of The Total Environment, 2011,410-411:119-125.Abstract BACKGROUND: The increasing evidence for rapid global climate change has highlighted the need for investigations examining the relationship between weather variability and infectious diseases. However, the impact of weather fluctuations on hand, foot, and mouth disease (HFMD), which primarily affects children, is not well understood. METHODS: We acquired data related to cases of HFMD and weather parameters of temperature and humidity in Fukuoka, Japan between 2000 and 2010, and used time-series analyses to assess the possible relationship of weather variability with pediatric HFMD cases, adjusting for seasonal and interannual variations. RESULTS: Our analysis revealed that the weekly number of HFMD cases increased by 11.2% (95% CI: 3.2-19.8) for every 1掳C increase in average temperature and by 4.7% (95% CI: 2.4-7.2) for every 1% increase in relative humidity. Notably, the effects of temperature and humidity on HFMD infection were most significant in children under the age of 10 years. CONCLUSIONS: Our study provides quantitative evidence that the number of HFMD cases increased significantly with increasing average temperature and relative humidity, and suggests that preventive measures for limiting the spread of HFMD, particularly in younger children, should be considered during extended periods of high temperature and humidity. Copyright 脗漏 2011 Elsevier B.V. All rights reserved.

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[5]
Li T, Yang Z, Di B, et al.Hand-foot-and-mouth disease and weather factors in Guangzhou, southern China[J]. Epidemiology and Infection, 2014,142(8):1741-1750.Abstract Hand-foot-and-mouth disease (HFMD) is becoming one of the common airborne and contact transmission diseases in Guangzhou, southern China, leading public health authorities to be concerned about its increased incidence. In this study, we aimed to examine the effect of weather patterns on the incidence of HFMD in the subtropical city of Guangzhou for the period 2009-2012, and assist public health prevention and control measures. A negative binomial multivariable regression was used to identify the relationship between meteorological variables and HFMD. During the study period, a total of 166,770 HFMD-confirmed cases were reported, of which 11 died, yielding a fatality rate of 000·66/10,000. Annual incidence rates from 2009 to 2012 were 13200·44, 31100·40, 40200·76, and 46800·59/100,000 respectively. Each 100°C rise in temperature corresponded to an increase of 900·38% (95% CI 800·17-1000·51) in the weekly number of HFMD cases, while a 1 hPa rise in atmospheric pressure corresponded to a decrease in the number of cases by 600·80% (95% CI -600·99 to -600·65), having an opposite effect. Similarly, a 1% rise in relative humidity corresponded to an increase of 000·67% or 000·51%, a 1 m/h rise in wind velocity corresponded to an increase of 400·01% or 200·65%, and a 1 day addition in the number of windy days corresponded to an increase of 2400·73% or 2500·87%, in the weekly number of HFMD cases, depending on the variables considered in the model. Our findings revealed that the epidemic status of HFMD in Guangzhou is characterized by high morbidity but low fatality. Weather factors had a significant influence on occurrence and transmission of HFMD.

DOI PMID

[6]
Liao Y, Ouyang R, Wang J, et al.A study of spatiotemporal delay in hand, foot and mouth disease in response to weather variations based on SVD: A case study in Shandong Province, China[J]. BMC Public Health, 2015,15(1):71.Abstract BackgroundA large number of hand, foot and mouth disease (HFMD) outbreaks was reported during 2008 in China. However, little is known about the effects of meteorological conditions on different temporal and spatial scales on HFMD incidence in children. The aim of this study was to explore the relationship between meteorological data on various temporal and spatial scales and HFMD incidence among children in Shandong Province, China.MethodsThe association between weekly HFMD cases and meteorological data on different temporal and spatial scales in Shandong Province from May 2008 to July 2008 and September 2008 to October 2008 was analyzed, using buffer analysis and the singular value decomposition method.ResultsWind speed within a 50-km buffer circle of counties in Shandong Province with two-week lag and RH within a 10-km buffer circle of counties with eight-week lag were significantly associated with HFMD incidence. We found a positive correlation between wind speed within the 50-km buffer circle in the prior two weeks and wind speed within the province in the prior one week.ConclusionsThis study revealed strong associations between HFMD incidence in children and wind speed and RH. Thus, meteorological anomalies in the prior two or eight weeks could be used as a valid tool for detecting anomalies during the peak periods of infectious disease.

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[7]
Hii Y L, Rocklov J, Ng N.Short term effects of weather on hand, foot and mouth disease[J]. PloS one, 2011,6(2):e16796.Hand, foot, and mouth disease (HFMD) outbreaks leading to clinical and fatal complications have increased since late 1990s; especially in the Asia Pacific Region. Outbreaks of HFMD peaks in the warmer season of the year, but the underlying factors for this annual pattern and the reasons to the recent upsurge trend have not yet been established. This study analyzed the effect of short-term changes in weather on the incidence of HFMD in Singapore.The relative risks between weekly HFMD cases and temperature and rainfall were estimated for the period 2001-2008 using time series Poisson regression models allowing for over-dispersion. Smoothing was used to allow non-linear relationship between weather and weekly HFMD cases, and to adjust for seasonality and long-term time trend. Additionally, autocorrelation was controlled and weather was allowed to have a lagged effect on HFMD incidence up to 2 weeks.Weekly temperature and rainfall showed statistically significant association with HFMD incidence at time lag of 1-2 weeks. Every 1°C increases in maximum temperature above 32°C elevated the risk of HFMD incidence by 36% (95% CI66=661.341-1.389). Simultaneously, one mm increase of weekly cumulative rainfall below 75 mm increased the risk of HFMD by 0.3% (CI66=661.002-1.003). While above 75 mm the effect was opposite and each mm increases of rainfall decreased the incidence by 0.5% (CI66=660.995-0.996). We also found that a difference between minimum and maximum temperature greater than 7°C elevated the risk of HFMD by 41% (CI66=661.388-1.439).Our findings suggest a strong association between HFMD and weather. However, the exact reason for the association is yet to be studied. Information on maximum temperature above 32°C and moderate rainfall precede HFMD incidence could help to control and curb the up-surging trend of HFMD.

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[8]
Wang J F, Guo Y S, Christakos G, et al.Hand, foot and mouth disease: spatiotemporal transmission and climate[J]. International Journal of Health Geographics, 2011,10(1):25.pAbstract/p pBackground/p pThe Hand-Foot-Mouth Disease (HFMD) is the most common infectious disease in China, its total incidence being around 500,000 ~1,000,000 cases per year. The composite space-time disease variation is the result of underlining attribute mechanisms that could provide clues about the physiologic and demographic determinants of disease transmission and also guide the appropriate allocation of medical resources to control the disease./p pMethods and Findings/p pHFMD cases were aggregated into 1456 counties and during a period of 11 months. Suspected climate attributes to HFMD were recorded monthly at 674 stations throughout the country and subsequently interpolated within 1456 脳 11 cells across space-time (same as the number of HFMD cases) using the Bayesian Maximum Entropy (BME) method while taking into consideration the relevant uncertainty sources. The dimensionalities of the two datasets together with the integrated dataset combining the two previous ones are very high when the topologies of the space-time relationships between cells are taken into account. Using a self-organizing map (SOM) algorithm the dataset dimensionality was effectively reduced into 2 dimensions, while the spatiotemporal attribute structure was maintained. 16 types of spatiotemporal HFMD transmission were identified, and 3-4 high spatial incidence clusters of the HFMD types were found throughout China, which are basically within the scope of the monthly climate (precipitation) types./p pConclusions/p pHFMD propagates in a composite space-time domain rather than showing a purely spatial and purely temporal variation. There is a clear relationship between HFMD occurrence and climate. HFMD cases are geographically clustered and closely linked to the monthly precipitation types of the region. The occurrence of the former depends on the later./p

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[9]
Lin H, Zou H, Wang Q, et al.Short-term effect of El Nino-Southern Oscillation on pediatric hand, foot and mouth disease in Shenzhen, China[J]. PloS one, 2013,8(7):e65585.Hand, foot and mouth disease (HFMD) was an emerging viral infectious disease in recent years in Shenzhen. The underlying risk factors have not yet been systematically examined. This study analyzed the short-term effect of El Ni09o-Southern Oscillation on pediatric HFMD in Shenzhen, China. Daily count of HFMD among children aged below 15 years old, Southern Oscillation Index (SOI), and weather variables were collected to construct the time series. A distributed lag non-linear model was applied to investigate the effect of daily SOI on pediatric HFMD occurrence during 2008–2010. We observed an acute effect of SOI variation on HFMD occurrence. The extremely high SOI (SOI66=6645, with 0 as reference) was associated with increased HFMD, with the relative risk (RR) being 1.66 (95% Confidence Interval [CI]: 1.34–2.04). Further analyses of the association between HFMD and daily mean temperature and relative humidity supported the correlation between pediatric HFMD and SOI. Meteorological factors might be important predictors of pediatric HFMD occurrence in Shenzhen.

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[10]
Li P, Li T, Gu Q, et al.Children's caregivers and public playgrounds: Potential reservoirs of infection of Hand-foot-and-mouth disease[J]. Scientific Reports, 2016,6:36375.Hand-foot-and-mouth disease (HFMD) is a common infectious disease, which has led to millions of clinical cases and hundreds of deaths every year in China.

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[11]
罗晓风,湛柳华,周文,等.2010-2011年广州市越秀区手足口病发例数与气象因素和空气污染指数的相关性分析[J].中国药物经济学,2013(S3):182-184.

[ Luo X, Zhan L, Zhou W, et al.Correlation Analysis of 2010-2011 in Guangzhou City,Yuexiu District hand foot and mouth disease incidence and meteorological factors and air pollution index[J]. China Journal of Pharmaceutical Economics, 2013,S3:182-184. ]

[12]
Huang R, Bian G, He T, et al.Effects of meteorological parameters and PM10 on the incidence of hand, foot, and mouth disease in children in China[J]. International Journal of Environmental Research and Public Health, 2016,13(5):481.Abstract Hand, foot, and mouth disease (HFMD) is a globally-prevalent infectious disease. However, few data are available on prevention measures for HFMD. The purpose of this investigation was to evaluate the impacts of temperature, humidity, and air pollution, particularly levels of particulate matter with an aerodynamic diameter 10 micrometers (PM10), on the incidence of HFMD in a city in Eastern China. Daily morbidity, meteorological, and air pollution data for Ningbo City were collected for the period from January 2012 to December 2014. A total of 86,695 HFMD cases were enrolled in this study. We used a distributed lag nonlinear model (DLNM) with Poisson distribution to analyze the nonlinear lag effects of daily mean temperature, daily humidity, and found significant relationships with the incidence of HFMD; in contrast, PM10 level showed no relationship to the incidence of HFMD. Our findings will facilitate the development of effective preventive measures and early forecasting of HFMD outbreaks.

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[13]
Cao C, Li G, Zheng S, et al.editors. Research on the environmental impact factors of Hand-Foot-Mouth disease in Shenzhen, China using RS and GIS technologies[C]. 2012 IEEE International Geoscience and Remote Sensing Symposium, 2012.

[14]
Stanaway J D.Insights from disease ecology: Focus on hand, foot and mouth disease in China[D]. Washington: University of Washington, 2013.

[15]
朱琦,郝元涛,于石成.广东省2008-2010年手足口病流行特征分析及时空聚集性研究[J].现代预防医学,2011(10):1824-1826,1831.目的] 描述手足口病在广东省的流行特征,寻找手足口病在广东省可能存在的时空聚集区,为广东省手足口病的预防控制工作提供依据.[方法] 利用国家相关卫生部门公布的2008～2010年手足口病监测数据,广东省2009年人口统计数据,描述手足口病在广东省的三闻分布情况,并基于离散型泊 松分布模型,同时从时间和空间二维角度寻找手足口病在广东的高发时空聚集区.[结果] 2008年5月～2010年4月,广东省报告的总手足口病病例数为209 712例,两年手足口病总的发病率为21.97/10 000,男性的发病率高于女性,所有病例中,5岁以下儿童所占的比例为90.56%;珠三角地区手足口病的发病率较高;手足口病每年的流行期从3月底4月 初开始,一直持续到7月底8月初.手足口病时空聚集区的时间起点均在4、5月份,珠海地区存在手足口病的长期流行趋势.[结论] 广东省(特别是珠三角地区)手足口病的流行情况较为严重,控制手足口病流行的关键时段是3月底和4月初.

[ Zhu Q, Hao Y T, Yu S C.Epidemiological characteristics and Space-time analysis of Hand-Foot-Mouth disease in Guangdong Province from 2008 to 2010[J]. Modern Preventive Medicine, 2011,10:1824-1826,1831. ]

[16]
Hu M, Li Z, Wang J, et al.Determinants of the incidence of hand, foot and mouth disease in China using geographically weighted regression models[J]. PloS one, 2012,7(6):e38978.Over the past two decades, major epidemics of hand, foot, and mouth disease (HFMD) have occurred throughout most of the West-Pacific Region countries, causing thousands of deaths among children. However, few studies have examined potential determinants of the incidence of HFMD. Reported HFMD cases from 2912 counties in China were obtained for May 2008. The monthly HFMD cumulative incidence was calculated for children aged 9 years and younger. Child population density (CPD) and six climate factors (average-temperature [AT], average-minimum-temperature [ATmin], average-maximum-temperature [ATmax], average-temperature-difference [ATdiff], average-relative-humidity [ARH], and monthly precipitation [MP]) were selected as potential explanatory variables for the study. Geographically weighted regression (GWR) models were used to explore the associations between the selected factors and HFMD incidence at county level. There were 176,111 HFMD cases reported in the studied counties. The adjusted monthly cumulative incidence by county ranged from 0.26 cases per 100,000 children to 2549.00 per 100,000 children. For local univariate GWR models, the percentage of counties with statistical significance (p<0.05) between HFMD incidence and each of the seven factors were: CPD 84.3%, ATmax54.9%, AT 57.8%, ATmin61.2%, ARH 54.4%, MP 50.3%, and ATdiff51.6%. TheR2for the seven factors- univariate GWR models are CPD 0.56, ATmax0.53, AT 0.52, MP 0.51, ATmin0.52, ARH 0.51, and ATdiff0.51, respectively. CPD, MP, AT, ARH and ATdiffwere further included in the multivariate GWR model, withR20.62, and all counties show statistically significant relationship. Child population density and climate factors are potential determinants of the HFMD incidence in most areas in China. The strength and direction of association between these factors and the incidence of HFDM is spatially heterogeneous at the local geographic level, and child population density has a greater influence on the incidence of HFMD than the climate factors.

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[17]
Zhang W, Du Z, Zhang D, et al.Boosted regression tree model-based assessment of the impacts of meteorological drivers of hand, foot and mouth disease in Guangdong, China[J]. The Science of the total environment, 2016,553:366-371.This study indicated significantly facilitating effects of five meteorological factors within some range on the epidemic of HFMD. Results from the current study were particularly important for developing early warning and response system on HFMD in the context of global climate change.

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[18]
吴北平,杨典,王劲峰,等.利用贝叶斯时空模型分析山东省手足口病时空变化及影响因素[J].地球信息科学学报,2016,18(12):1645-1652.手足口病是一种常见的传染病,多见于5岁以下儿童。近年来,中国手足口病发病人数逐年上升,疾病疫情也越来越受到公共卫生部门与社会大众的关注。虽然已有不少手足口病相关的研究,但对其时空变化及影响因素驱动效应的研究仍然较少。本文采用贝叶斯时空模型,对2008年山东省手足口病高发时间段(5-8月)的发病时空演变特征进行系统分析,并探究影响手足口病发病风险的气象因素。结果表明:1空间上不同区县的手足口病发病风险存在一定差异,且区县间的发病风险随时间变化趋势也各不相同;2 5月和6月手足口病发病风险明显高于整个研究阶段(5-8月)平均发病风险;3对手足口病发病风险影响较大的气象因素依次是:周平均温度、平均风速和平均气压。本文针对山东省手足口病时空演化特征及气象影响因素的研究,能为高发时间段内手足口病的区域化防控提供科学依据。

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[ Wu B P, Yang D, Wang J, et al.Space-time variability and determinants of Hand, Foot and Mouth in Shandong Province: A bayesian spatio-temporal modeling approach[J]. Journal of Geo-Information Science, 2016,18(12):1645-1652. ]

[19]
Zhang Z, Xie X, Chen X, et al.Short-term effects of meteorological factors on hand, foot and mouth disease among children in Shenzhen, China: Non-linearity, threshold and interaction[J]. The Science of the Total Environment, 2016,539:576-582.This study suggests that mean temperature, relative humidity and wind speed might be risk factors of children HFMD in Shenzhen, and the interaction analysis indicates that these meteorological factors might have played their roles individually.

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[20]
Li L, Wang J, Leung H.Using spatial analysis and bayesian network to model the vulnerability and make insurance pricing of catastrophic risk[J]. International Journal of Geographical Information Science, 2010,24(12):1759-1784.NSFC [40601077/D0120, 40471111/D0120]; MOST [2007AA12Z233, O88RA204SA]; PolyU [H-ZG20]

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Li L, Wang J, Leung H, et al.A Bayesian method to mine spatial data sets to evaluate the vulnerability of human beings to catastrophic risk[J]. Risk analysis : An Official Publication of the Society for Risk Analysis, 2012,32(6):1072-1092.Abstract Vulnerability of human beings exposed to a catastrophic disaster is affected by multiple factors that include hazard intensity, environment, and individual characteristics. The traditional approach to vulnerability assessment, based on the aggregate-area method and unsupervised learning, cannot incorporate spatial information; thus, vulnerability can be only roughly assessed. In this article, we propose Bayesian network (BN) and spatial analysis techniques to mine spatial data sets to evaluate the vulnerability of human beings. In our approach, spatial analysis is leveraged to preprocess the data; for example, kernel density analysis (KDA) and accumulative road cost surface modeling (ARCSM) are employed to quantify the influence of geofeatures on vulnerability and relate such influence to spatial distance. The knowledge- and data-based BN provides a consistent platform to integrate a variety of factors, including those extracted by KDA and ARCSM to model vulnerability uncertainty. We also consider the model's uncertainty and use the Bayesian model average and Occam's Window to average the multiple models obtained by our approach to robust prediction of the risk and vulnerability. We compare our approach with other probabilistic models in the case study of seismic risk and conclude that our approach is a good means to mining spatial data sets for evaluating vulnerability. 漏 2012 Society for Risk Analysis.

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[22]
Kulldorff M, Nagarwalla N.Spatial disease clusters: detection and inference[J]. Statistics in Medicine, 1995,14(8):799-810.

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[23]
徐敏,曹春香,程锦泉,等.甲流感疫情时空聚集性的GIS分析[J].地球信息科学学报,2010,12(5):707-712.2009年肆虐全球的甲流感疫情是由一种突变的猪流感病毒引发的流感,故又被称为猪流感。自2009年5月11日发现首例甲流感病例传入我国以来,在短短几个月的时间里,疫情迅速蔓延并呈现全国大爆发的态势。深圳因地理位置特殊,流动人口众多,一直是我国流行病的高发地区。本文以深圳市为例,对2009年5月26日至2009年11月15日间通过传染病疫情信息网络直报系统所上报的甲型H1N1流感确诊病例,分别依据患者的性别、年龄、职业等属性进行了统计,同时以日发病数为基本单位对这期间的甲流感疫情进行了时序与特征分析;并将病例数据输入地理信息系统进行地理空间定位,选取病例患者的家庭住址作为地理空间定位的基本单元,利用回顾性时空重排扫描统计量的方法对这期间深圳市的甲流感疫情进行时空聚集性分析。结果显示,深圳市的甲流感疫情的时空聚集性重点表现在9月份上旬与香港接壤的南部地区,对深圳市疫情的防控要重点布置在与香港往来的几个通关口岸处。

[ Xu M, Cao C, Cheng J, et al.Space-time cluster detection of pandemic H1N1 influenza a using GIS[J]. Journal of Geo-Information Science, 2010,12(5):707-712. ]

[24]
Deng T, Huang Y, Yu S, et al.Spatial-temporal clusters and risk factors of hand, foot, and mouth disease at the district level in Guangdong Province, China[J]. PloS one, 2013,8(2):e56943.Hand, foot, and mouth disease (HFMD) has posed a great threat to the health of children and become a public health priority in China. This study aims to investigate the epidemiological characteristics, spatial-temporal patterns, and risk factors of HFMD in Guangdong Province, China, and to provide scientific information for public health responses and interventions.HFMD surveillance data from May 2008 to December 2011were provided by the Chinese Center for Disease Control and Prevention. We firstly conducted a descriptive analysis to evaluate the epidemic characteristics of HFMD. Then, Kulldorff scan statistic based on a discrete Poisson model was used to detect spatial-temporal clusters. Finally, a spatial paneled model was applied to identify the risk factors.A total of 641,318 HFMD cases were reported in Guangdong Province during the study period (total population incidence: 17.51 per 10,000). Male incidence was higher than female incidence for all age groups, and approximately 90% of the cases were children [Formula: see text] years old. Spatial-temporal cluster analysis detected four most likely clusters and several secondary clusters (P<0.001) with the maximum cluster size 50% and 20% respectively during 2008-2011. Monthly average temperature, relative humidity, the proportion of population [Formula: see text] years, male-to-female ratio, and total sunshine were demonstrated to be the risk factors for HFMD.Children [Formula: see text] years old, especially boys, were more susceptible to HFMD and we should take care of their vulnerability. Provincial capital city Guangzhou and the Pearl River Delta regions had always been the spatial-temporal clusters and future public health planning and resource allocation should be focused on these areas. Furthermore, our findings showed a strong association between HFMD and meteorological factors, which may assist in predicting HFMD incidence.

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[ Wang L S, Bi Z, Fang Y, et al.Epidemiological analysis of hand, foot and mouth disease in Shandong Province during 2008[J]. Shandong Medical Journal, 2009,49(19):45-47. ]

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[ A Study on the spread model and spatial distribution of HFMD based on GIS[D].A Study on the spread model and spatial distribution of HFMD based on GIS[D]. Ningbo: Ningbo University, 2010. ]

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[35]
胡跃华,肖革新,郭莹,等. 2008-2011年中国大陆手足口病流行特征分析[J].中华疾病控制杂志,2014(8):693-697,747.目的 分析2011年中国大陆手足口病流行特征,探讨手足口病流行规律,为制定防控策略和措施提供依据.方法 采用描述性流行病学方法对2011年国家《疾病监测信息报告管理系统》网络直报的手足口病监测资料进行分析.结果 2011年全国共计报告手足口病1 619 706例,报告发病率为120.79/10万;死亡509例,死亡率为0.038/10万,病死率为0.031％.全年呈现夏季和秋冬季两个高峰,主高峰 集中在夏季(5-7月),次高峰集中在秋冬季(10- 12月).重症病例和死亡病例也相应呈现两个高峰.在主高峰(5-7月)中,重症和死亡病例占总病例的比例为1.1％ ～1.2％,在次高峰(10- 12月)中,重症和死亡病例占总病例的比例降到0.7％ ～0.8％.报告病例以5岁及以下儿童为主(占90％),其中重症病例和死亡病例集中在3岁及以下儿童(均占83％).实验室病原监测显示肠道病毒71型 (EV71)和柯萨奇病毒A组16型(Cox A16)仍为主要病原(合计占79％),各月份均以EV71为主,但10- 12月Cox A16和其他肠道病毒所占比例较前期略有升高.结论 2011年中国大陆手足口病发病流行强度与2010年相近,呈现夏季和秋冬季双峰模式;在秋冬季次高峰中重症及死亡病例比例低于在夏季高峰中的比例.

[ Hu Y H, Xiao G X, Guo Y, et al.The epidemic features of the hand,foot,and mouth disease during 2008-2011 in China[J]. Chinese Journal of Disease Control & Prevention, 2014,8:693-697,747. ]

[36]
Bo Y C, Song C, Wang J F, et al.Using an autologistic regression model to identify spatial risk factors and spatial risk patterns of hand, foot and mouth disease (HFMD) in Mainland China[J]. BMC public health, 2014,14:358.Background There have been large-scale outbreaks of hand, foot and mouth disease (HFMD) in Mainland China over the last decade. These events varied greatly across the country. It is necessary to identify the spatial risk factors and spatial distribution patterns of HFMD for public health control and prevention. Climate risk factors associated with HFMD occurrence have been recognized. However, few studies discussed the socio-economic determinants of HFMD risk at a space scale. Methods HFMD records in Mainland China in May 2008 were collected. Both climate and socio-economic factors were selected as potential risk exposures of HFMD. Odds ratio (OR) was used to identify the spatial risk factors. A spatial autologistic regression model was employed to get OR values of each exposures and model the spatial distribution patterns of HFMD risk. Results Results showed that both climate and socio-economic variables were spatial risk factors for HFMD transmission in Mainland China. The statistically significant risk factors are monthly average precipitation (OR = 1.4354), monthly average temperature (OR = 1.379), monthly average wind speed (OR = 1.186), the number of industrial enterprises above designated size (OR = 17.699), the population density (OR = 1.953), and the proportion of student population (OR = 1.286). The spatial autologistic regression model has a good goodness of fit (ROC = 0.817) and prediction accuracy (Correct ratio = 78.45%) of HFMD occurrence. The autologistic regression model also reduces the contribution of the residual term in the ordinary logistic regression model significantly, from 17.25 to 1.25 for the odds ratio. Based on the prediction results of the spatial model, we obtained a map of the probability of HFMD occurrence that shows the spatial distribution pattern and local epidemic risk over Mainland China. Conclusions The autologistic regression model was used to identify spatial risk factors and model spatial risk patterns of HFMD. HFMD occurrences were found to be spatially heterogeneous over the Mainland China, which is related to both the climate and socio-economic variables. The combination of socio-economic and climate exposures can explain the HFMD occurrences more comprehensively and objectively than those with only climate exposures. The modeled probability of HFMD occurrence at the county level reveals not only the spatial trends, but also the local details of epidemic risk, even in the regions where there were no HFMD case records.

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[37]
Liu Y, Wang X, Liu Y, et al.Detecting spatial-temporal clusters of HFMD from 2007 to 2011 in Shandong Province, China[J]. PloS One, 2013,8(5):e63447.Abstract BACKGROUND: Hand, foot, and mouth disease (HFMD) has caused major public health concerns worldwide, and has become one of the leading causes of children death. China is the most serious epidemic area with a total of 3,419,149 reported cases just from 2008 to 2010, and its different geographic areas might have different spatial epidemiology characteristics at different spatial-temporal scale levels. We conducted spatial and spatial-temporal epidemiology analysis to HFMD at county level in Shandong Province, China. METHODS: Based on the China National Disease Surveillance Reporting and Management System, the spatial-temporal database of HFMD from 2007 to 2011 was built. The global autocorrelation statistic (Moran's I) was first used to detect the spatial autocorrelation of HFMD cases in each year. Purely Spatial scan statistics combined with Space-time scan statistic were used to detect epidemic clusters. RESULTS: The annual average incidence rate was 93.70 per 100,000 in Shandong Province. Most HFMD cases (93.94%) were aged within 0-5 years old with an average male-to-female sex ratio 1.71, and the incidence seasonal peak was between April and July. The dominant pathogen was EV71 (47.35%), and CoxA16 (26.59%). HFMD had positive spatial autocorrelation at medium spatial scale level (county level) with higher Moran's I from 0.31 to 0.62 (P<0.001). Seven spatial-temporal clusters were detected from 2007 to 2011 in the landscape of the whole Shandong, with EV71 or CoxA16 as the dominant pathogen for most hotspots areas. CONCLUSIONS: The spatial-temporal clusters of HFMD wandered around the whole Shandong Province during 2007 to 2011, with EV71 or CoxA16 as the dominant pathogen. These findings suggested that a real-time spatial-temporal surveillance system should be established for identifying high incidence region and conducting prevention to HFMD timely.

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[38]
Wang C, Li X, Zhang Y, et al.Spatiotemporal cluster patterns of hand, foot, and mouth disease at the county level in mainland China, 2008-2012[J]. PloS One, 2016,11(1):e0147532.Hand, foot, and mouth disease (HFMD) is known to be a highly contagious childhood illness. In recent years, the number of reported cases of HFMD has significantly increased in mainland China. This study aims at the epidemiological features, spatiotemporal patterns of HMFD at the county/district level in mainland China. Data on reported HFMD cases for each county from 1 January 2008 to 31 December 2012 were obtained from the Chinese Center for Disease Control and Prevention. Cluster analysis, spatial autocorrelation, and retrospective scan methods were used to explore the spatiotemporal patterns of the disease. The annual incidences varied greatly among the counties, ranging from 0 to 74.31‰ with the median of 5.42‰ (interquartile range: 1.54‰–13.55‰) during 2008–2012 in mainland China. Counties close to provincial capital cities generally had higher incidences than rural counties. A seasonal distribution was observed between the northern and southern China, of which dual epidemic were shown in southern China and usually only one in northern China. Based on the global and local spatial autocorrelation analysis, we found that the spatial distribution of HFMD was presented a significant clustering pattern for each year (P<0.001), and hotspots of the disease were mostly distributed in coastal provinces of China. The retrospective scan statistic further identified the dynamics of spatiotemporal clustering areas of the disease, which were mainly distributed in the counties of eastern and southern China, as well as provincial capitals and their surrounding counties. The spatiotemporal clustering areas of the disease identified in this way were relatively stable, and imminent public health planning and resource allocation should be focused within those areas.

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