利用人工神经网络模型预测原发性高血压的研究
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摘要
前言
原发性高血压(essential hypertension, EH)是常见的心血管疾病之一,近年来,随着我国经济发展,生活节奏明显增快,产生了一系列的不健康的生活方式,导致我国心脑血管疾病死亡率、发病率和患病率持续上升。高血压既是一种独立的疾病,又是引发心脑血管疾病的重要危险因素,发生高血压危象及高血压脑病等严重并发症时可危及生命。因此,高血压的防治工作不容忽视。
国内外研究表明,高血压是一种多因子疾病,致病因素多,各因素间关系复杂,是高血压研究的重要特点。目前疾病预测的方法以传统的Logistic回归(Logistic regression, LR)为主,Logistic回归模型要求变量满足独立性且不能处理变量之间的共线性问题。因此,应用Logistic回归模型进行预测高血压这样的复杂疾病具有一定的局限性。人工神经网络(Artificial Neural Networks,ANNs),简称为神经网络(NNs),是模拟生物神经网络进行信息处理的一种数学模型。神经网络具有强大的解决共线性效应和变量间的交互作用的能力,善于处理非线性的、模糊的、含有噪声的数据情况。目前,人工神经网络在医学上的应用还远没有传统的Logistic回归那么广泛。
本研究所选择的现场是辽宁省彰武县农村,经调查该人群高血压标化患病率高达35%，全国罕见。本研究利用这些调查数据建立BP人工神经网络(backpropagation ANNs)预测模型,并与Logistic回归模型进行比较,利用受试者工作特征曲线(receiver operator characteristic curve, ROC曲线)评价人工神经网络模型的预测性能。以探讨和评价ANNs用于疾病预测的效果和特点,为高血压等复杂疾病的预测探索新的方法,同时对农村高血压病的防治也有一定的参考价值。
研究对象与方法
一、研究对象的选择
本研究利用之前在辽宁省彰武县农村进行的EH流行病学调查的资料进行统计、预测分析。该调查采用整群多级随机抽样的方法总计调查5208人,最后30岁以上常住人群共计4126名调查对象被纳入本次研究,其中女1942人,男2184人。
二、调查内容和检测指标
在现场以问询和测量的方式填写调查表,调查内容主要包括：一般特征,吸烟史,饮酒史等；测量血压、体重、身高等
现场每人采血5ml(隔夜空腹),经离心后分离血清,分装冰冻保存用于血清指标检测。
三、诊断标准和测量方法：
高血压诊断是根据1999年WHO／ISH公布的高血压诊断标准：收缩压≥140mmHg和／或舒张压≥90 mmHg或既往确诊的原发性高血压者。血压测量及其他血清生化检测指标由专业医护人员在标准条件下进行测量。
胆固醇、甘油三酯、HDL、LDL、血清钠、血清钾、血清铁、血清钙等指标的水平采用日本第一化学提供的7150型全自动生化分析仪,用比色法进行分析。血糖水平采用美国强生公司生产的稳捷基础型血糖分析仪,用滴血法进行分析。
四、神经网络模型的建立
ANNs模型采用含有一个隐含层的三层BP神经网络模型。模型输入层的神经元为单因素分析中P<0.05的与高血压相关的因素,输出层有1个神经元(即按照诊断标准判断研究对象是否患高血压),隐含层的神经元个数通过实验根据均方误差择优确定。隐含层的激活函数为tansig,输出层的激活函数为logsig。
本研究将4126例资料按照性别、年龄进行均衡后按3：1的比例随机分为训练总集(3096例)和测试集(1030例)两部分,分别用于模型的建立和测试。为了防止ANNs过渡拟合,在ANNs模型的训练过程中,又将训练总集(3096例)按3：1的比例随机分为训练集(2334例)和检验集(762例),利用检验集时时地检查训练效果。
五、资料统计分析方法
用Matlab7.1软件编程建立ANNs预测模型。用spss13.0统计软件建立二分类非条件Logistic回归的高血压预测模型和绘制模型预测识别的ROC曲线。预测概率的判别标准为0.5,即p≥0.5时预测结果为患高血压,否则为不患高血压。统计学显著性水平规定为α=0.05。
结果
一、非条件单因素Logistic回归模型进行高血压预测
对调查数据进行高血压的单因素分析,筛选出p<0.05的因素作为预测模型的输入变量,共22个因素与高血压有关。
二、非条件多因素Logistic回归模型进行高血压预测
(一)建立非条件多因素Logistic回归模型
对训练总集的3096例样本进行非条件多因素Logistic回归分析,将单因素筛选出的指标作为自变量(身高、体重已转化为BMI故未进入模型),以研究对象是否患高血压为因变量建立多因素Logistic回归模型。模型采用最大似然估计前进法进行逐步回归分析,入选变量的标准是p<0.05,剔除变量的标准是p>0.10。经逐步回归后,共有9个因素进入模型,模型改善情况检验(x2=4.335)和整个模型检验(x2=1439.457)。整个训练总集的分类一致率为78.42%,特异度为80.45%,灵敏度为76.62%,
(二)利用非条件多因素Logistic回归模型预测
用上述Logistic回归模型预测测试集(1030例)研究对象是否患高血压。经模型预测,测试集一致率为77.48%,特异度为80%,灵敏度为74.85%。三、BP神经网络模型进行预测
(一)建立BP神经网络模型
建立一个三层的BPANNs模型,以单因素筛选出的全部22个因素作为输入变量,其隐含层设为22个神经元,输出层1个神经元(即是否患EH)。目标误差取0.01,学习速率取0.1,最大训练周期2000。经过17步训练,此时训练中均方误差MSE为0.126262,梯度Gradient为137.276／le-010,网络的训练由于检验集均方误差达到极小值而结束。测试训练好的BPANNs模型的拟合效果,训练集的分类一致率为81.06%,检验集的分类一致率为77.95%,整个训练总集的分类一致率为80.30%,特异度为84.48%,灵敏度为76.16%。
(二)利用BP神经网络模型进行预测
用上述BPANNs模型预测测试集(1030例)研究对象是否患高血压,测试结果见表5。其测试集分类一致率为78.83%,特异度为81.57%,灵敏度为76.42%。
四、BP神经网络模型与Logistic回归模型高血压预测比较
(一)预测结果的比较
神经网络模型的分类一致率、灵敏度、特异度均高于Logistic回归模型。
(二)ROC曲线面积比较
利用SSPS13.0绘出多因素Logistic回归模型和BPANNs模型的ROC曲线,多因素Logistic回归模型的ROC曲线下面积为0.782,95%可信区间为[0.768,0.797],BPANNs模型的ROC曲线下面积为0.800,95%可信区间为[0.786,0.814]。
讨论
高血压的病因复杂,影响高血压患病的危险因素是多方面的,一些危险因素之间可能存在交互作用、多重共线性,这些复杂的关系影响预测模型的拟合,严重干扰了高血压的预测和病因研究工作。因此本研究利用辽宁省彰武县农村人群的调查资料建立高血压的神经网络预测模型,并与传统方法的Logistic回归模型相比较,以探讨神经网络模型预测高血压发病的能力。
神经网络模型建立过程中各函数、参数的设置并没有统一的标准,需要针对具体问题具体分析。本研究建立的模型是以误差反向后传学习算法而得名的BP神经网络,它是医学领域应用最广泛的一种神经网络,集中体现了神经网络中最精华的部分。因为对于任何在闭区间内的一个连续函数都可以用单隐含层的BP神经网络逼近,所以本研究采用了含有一个隐含层的三层BP神经网络。考虑到输入层神经元个数过多对样本量的要求较高,所以只选择了与高血压密切相关的因素作为输入变量,即单因素分析中p<0.05的因素。对于输入变量中的多分类变量(如民族)采取设置哑变量的处理方法,以方便模型更好的利用数据信息。隐含层的神经元个数和训练函数是根据试验来确定的,试验显示,相对于其他取值,神经元个数为22训练函数为trainlm时均方误差既小又稳定,网络的初始权值取(0～1)区间的随机数,由于初始值不同建立ANNs模型也不同,所以经多次试验选出最优的模型。为了避免过度拟合,本研究利用检验集在训练过程中随时监督训练。
在本研究中,神经网络模型的分类一致率、灵敏度、特异度均高于Logistic回归模型,Logistic回归模型的分类一致率为77.48%,神经网络模型为78.83%。可以看出神经网络模型的预测能力略优于Logistic回归模型。本研究利用ROC曲线来评价两种模型的预测效果,Logistic回归模型和ANNs模型的AUC分别为0.782,0.800,同样提示,对于高血压这样的致病因素多而且各因素间关系复杂的疾病,神经网络模型的拟合效果略好一些。
神经网络尚存在一些问题有待解决。首先,神经网络的建立随着参数、函数、初始值等的设置而变化,这些设置的正确性缺乏理论依据,只能依靠经验和试验来确定；其次,神经网络不能像Logistic回归模型那样有一个公认的模型输入变量的准入和剔出原则；再次,各因素对因变量作用的医学解释尚不明确,以及其假设检验方法和可信区间等问题仍有待进一步研究。
结论
试验表明对于高血压这样的复杂疾病,神经网络预测模型的预测能力略优于Logistic回归模型。因此可以作为Logistic回归模型的必要补充,神经网络在复杂疾病的预测方面具有广阔应用前景。
Prediction using artificial neural network model of essential hypertension
Preface
Essential hypertension (EH) is one of the common cardiovascular disease, In recent years, as the economic development pace of life is significantly increased, resulting in a series of unhealthy lifestyles, leading our country mortality, morbidity and prevalence of cardiovascular disease continued to rise. Hypertension not only is an independent disease, but also is risk factors leading to important cardiovascular disease, even the event of serious complications such as hypertensive crisis and hypertensive encephalopathy may be life-threatening. Therefore, prevention and control of hypertension can not be ignored.
Research has shown that hypertension is a multifactorial disease, Large number of risk factors and complexity of relationship between various factors is an important feature of hypertension. Currently, method of disease prediction is mainly traditional Logistic regression(LR),but Logistic regression model require variables must satisfy the independence and can not deal with the problem of collinearity between the variables. Therefore, using logistic regression model to predict such a complex disease, high blood pressure, has some limitations. Artificial Neural Networks(ANNs), referred to as neural networks (NNs), is a mathematical model of simulating the biological neural network to information process. Neural network has the strong ability to solve the collinearity effect and the interaction between variables, and are good at handling non-linear, fuzzy, noisy data case. Currently, artificial neural network applications in medicine is far less widespread than the traditional Logistic regression.
The selected scene in this study is Zhangwu County in Liaoning Province. By investigation, the standardized prevalence hypertension rate was 35%, national rare. In this study, we used of these survey data set up a back propagation ANNs (BPANNs) prediction model, comparing with the Logistic regression model, and evaluated the forecast performance of ANNs by receiver operator characteristic curve(ROC curve). We also studied and evaluated the ANNs for the prediction effects and characteristics, to explore new prediction ways for the complex diseases such as high blood pressure and provide a reference for prevention and treatment of hypertension in rural areas.
Subjects and Methods
1.The selection of study subjects
This study used the survey data which came from the epidemiological investigation in Zhangwu County in Liaoning Province before to statistics and forecast analysis.Using clustering multistage sampling method 5208 people were total surveyed, at last 4126 respondents over 30 years old were enrolled in this study, of which women were 1942 people, men were 2184 people.
2.The contents of investigation and measurement indicators
Qusetionnaires were filled by means of inquiring and measurement in sites, the contents of survey included:general characteristics, smoking habits, alcohol intake and so on. Measure blood pressure, body height and weight, et al.
Five millititers blood samples were drawn after an overnight fast. After centrifugation, the serum fraction was removed and frozen in aliquots until assayed.
3.Diagnosis standard and measurement methods
The diagnosis standard of EHT:According to 1999 WHO-ISH guidelines for the management of hypertension, hypertension was defined as a systolic blood pressure (SBP)≥140mmHg and/or a diastolic blood pressure (DBP)≥90mmHg. The measurement of blood pressure should be carried out according to the unified standard under standard conditions.
Cholesterol, triglyceride, high density lipoprotein (HDL), low density lipoprotein (LDL), serum sodium, serum potassium, serum iron, serum calcium were measured by automatic biochemistry analyzer 7150 (HITACHI, Japan), the blood sugar was measured by blood sugar analyzer (Johnson & Johnson, America).
4.The establishment of ANNs
ANNs model used the three layers BP neural network model with a hidden layer. Input layer neurons of the model were the factors related to hypertension and P<0.05 by Univariate analysis, output layer had one neuron(that was studied whether hypertension according to diagnostic criteria), and number of neurons in the hidden layer through the experiment was merited to determine basing on the mean square error. The hidden layer activation function was tansig, and the output layer activation function was logsig.
The data(4126 cases) according to the ratio of 3:1 after balancing by gender and age were randomly divided into the total set of training (3096 cases) and test set(1030 cases), and were respectively used to set up and test, In order to prevent over fitting the total set of training according to the ratio of 3:1 were randomly divided into train set (2334 cases) and check set(762 cases), using check set from time to time to check the results of training.
5.Statistical methods
The ANNs prediction model of hypertension was created by Matlab7.1 software,the Logistic regression prediction model was created and ROC Curve was draw by spss13.0. Criteria for predicted probability was 0.5, that is, when p≥0.5 predicted infestation of hypertension, or high blood pressure was not. A 2-sided value ofα=0.05 was regarded as statistically significant.
Results
1. Prediction of hypertension using unconditional single factor Logistic regression model
Univariate analysis of hypertension was conducted for the survey data. The factors that is p<0.05, A total of hypertension-related factors is 22,was selected and taken as input variables predictive model.
2. Prediction of hypertension using multivariate non-conditional
Logistic regression model
(1)The establishment of multi-factor non-conditional Logistic regression model
The total set of training (3096 cases) was carried out multivariate non-conditional Logistic regression analysis.the chosen indicators by single factor analysis served as independent variables(Height, weight has been transformed into BMI, so did not enter the model), and whether subjects are suffering from high blood pressure served as the dependent variable, and in this way a multi-factor Logistic Regression Model was set up. Model used the maximum likelihood estimation method, forward stepwise regression analysis, the Access criteria selected variables is p<0.05, the Exclusion criteria selected variables was p>0.10. After stepwise regression,9 factors enter the model, in Omnibus Tests of Model Coefficients the step wasχ2=4.335, and the model test wasχ2=1439.457. the consistency rate of the total set of training was 78.42%, specificity was 80.45%, sensitivity 76.62%.
(2)The prediction Using multi-factor non-conditional Logistic regression model
The subjects of test set(1030 cases) were predicted whether they were suffering from high blood pressure by the Logistic Regression Model.The predicted results was that the consistency rate was 77.48%, specificity was 80%, sensitivity 74.85%. 3. The prediction of hypertension using BPANNs
(1)The establishment of BPANNs
BPANNs was a three-tier model, the 22 chosen indicators by single factor analysis served as input variable, there were 22 hidden layer neurons in the hidden layer, there was one neuron in output layer (whether was the risk of EH).the target error took 0.01, and learning rate took 0.1, the maximum training period took 2000. After 17-step training, then training meaned square error MSE was 0.126262, gradient Gradient was 137.276/1e-010, The network training ended, when test set to the minimum mean square error, fitting results of that test trained BPANNs model was, the consistency rate of the train set,the check set was respectively 81.06%,and 77.95%, and the consistency rate specificity and sensitivity of the total set was respectively 80.30%,84.48%, 76.16%.
(2)The prediction Using of BPANNs
The subjects of test set(1030 cases) were predicted whether they were suffering from high blood pressure using the BPANNs.The predicted results was,the consistency rate of the test set was 78.83%, specificity was 81.57%, sensitivity 76.42%.
4.The comparison between BPANNs and Logistic regression model about predictive ability of high blood pressure
(1) Comparison of predicted results
The consistency rate, sensitivity and specificity of Neural network model were higher than Logistic regression model.
(2) Comparison of ROC curve area
The ROC curve of BPANNs and Logistic regression mode were drawn, The results showed that, the area under ROC curve of Logistic regression model was 0.782,95% CI is[0.768,0.797], the area under ROC curve of BPANNs was 0.800,95% CI was [0.786,0.814].
Discussion
Causes of hypertension are complex, and the risk factors of affecting hypertension are in many aspects.Some risk factors may exist many interactions, multicollinearity. These complex relationships influence the predictive model fitting, and seriously disturb the prediction and high blood pressure research. Therefore, this study, using of these survey data from Zhangwu county in Liaoning Province,set up a back propagation ANNs (BPANNs) prediction EH model, and compared with the Logistic regression model, and evaluated the ANNs for the prediction effects and characteristics. In the process of building neural network model, there was no uniform standard to set the function and parameter, so we need to analyze specific issues. In this study, the model was the BP neural network, known as a "feed-forward back-propagation network", which was the most widely used in the medical field and embodies the essence of neural networks. Because any continuous function in closed interval could be closed by single hidden layer BP ANNs, so this study used three layers (containing a hidden layer) BP neural network. Taking into account that excessive number of neurons requires a higher sample size, so only selected factors closely related to high blood pressure as input variables, that was, p<0.05 in univariate analysis. For the multi-categorical variables in the input variables (such as national) we set the dummy variable to facilitate better use of data. Number of neurons in the hidden layer and training function was determined according to the test. Test showed that compared to other values, when the number of neurons was 22 and training functions are trainlm, the mean square error was small and stable, the initial weights of the network was set to (01) interval of random numbers.Since if the initial value of different then ANNs model was different,so after numerous experiments, the best model selected. In order to avoid over-fitting, we used chedk set to supervise training at intervals in the training process.
In this study, the consistency rate,, sensitivity and specificity of the neural network model were higher than Logistic regression model. The consistency rate of Logistic regression model and neural network model was respectively 77.48% and 78.83%, that could see the predictive ability of neural network model was better than Logistic regression model.Using ROC curve to evaluate the effectiveness of two models, AUC area under the curve of Logistic regression model and ANNs AUC were respectively 0.782,0.800. it also suggested that neural network model fitted slightly better than LR for these diseases such as hypertension of which risk factors were many and complex relationship exists between the various factors.
Neural networks were still some issues to be resolve. First of all,the establishment of neural networks changes with setting parameters, functions, initial value, etc. The correctness of these settings is still a lack of theoretical basis,so that only rely on experience and testing to determine. Second, there is no recognized principle of access and remove as a Logistic regression model about the input variables of neural network. Again, the medical explanation of the role of various factors on the dependent variable was not clear,and hypothesis testing method,confidence intervals and other issues need further study.
Conclusion
Experiments showed that such a complex disease for high blood pressure, neural network prediction model performs was better than the Logistic regression model. Therefore, ANNs could be used as a necessary complement for Logistic regression model, neural network prediction in complex diseases had broad application prospects.
原发性高血压(essential hypertension, EH)是常见的心血管疾病之一,近年来,随着我国经济发展,生活节奏明显增快,产生了一系列的不健康的生活方式,导致我国心脑血管疾病死亡率、发病率和患病率持续上升。高血压既是一种独立的疾病,又是引发心脑血管疾病的重要危险因素,发生高血压危象及高血压脑病等严重并发症时可危及生命。因此,高血压的防治工作不容忽视。
国内外研究表明,高血压是一种多因子疾病,致病因素多,各因素间关系复杂,是高血压研究的重要特点。目前疾病预测的方法以传统的Logistic回归(Logistic regression, LR)为主,Logistic回归模型要求变量满足独立性且不能处理变量之间的共线性问题。因此,应用Logistic回归模型进行预测高血压这样的复杂疾病具有一定的局限性。人工神经网络(Artificial Neural Networks,ANNs),简称为神经网络(NNs),是模拟生物神经网络进行信息处理的一种数学模型。神经网络具有强大的解决共线性效应和变量间的交互作用的能力,善于处理非线性的、模糊的、含有噪声的数据情况。目前,人工神经网络在医学上的应用还远没有传统的Logistic回归那么广泛。
本研究所选择的现场是辽宁省彰武县农村,经调查该人群高血压标化患病率高达35%，全国罕见。本研究利用这些调查数据建立BP人工神经网络(backpropagation ANNs)预测模型,并与Logistic回归模型进行比较,利用受试者工作特征曲线(receiver operator characteristic curve, ROC曲线)评价人工神经网络模型的预测性能。以探讨和评价ANNs用于疾病预测的效果和特点,为高血压等复杂疾病的预测探索新的方法,同时对农村高血压病的防治也有一定的参考价值。
研究对象与方法
一、研究对象的选择
本研究利用之前在辽宁省彰武县农村进行的EH流行病学调查的资料进行统计、预测分析。该调查采用整群多级随机抽样的方法总计调查5208人,最后30岁以上常住人群共计4126名调查对象被纳入本次研究,其中女1942人,男2184人。
二、调查内容和检测指标
在现场以问询和测量的方式填写调查表,调查内容主要包括：一般特征,吸烟史,饮酒史等；测量血压、体重、身高等
现场每人采血5ml(隔夜空腹),经离心后分离血清,分装冰冻保存用于血清指标检测。
三、诊断标准和测量方法：
高血压诊断是根据1999年WHO／ISH公布的高血压诊断标准：收缩压≥140mmHg和／或舒张压≥90 mmHg或既往确诊的原发性高血压者。血压测量及其他血清生化检测指标由专业医护人员在标准条件下进行测量。
胆固醇、甘油三酯、HDL、LDL、血清钠、血清钾、血清铁、血清钙等指标的水平采用日本第一化学提供的7150型全自动生化分析仪,用比色法进行分析。血糖水平采用美国强生公司生产的稳捷基础型血糖分析仪,用滴血法进行分析。
四、神经网络模型的建立
ANNs模型采用含有一个隐含层的三层BP神经网络模型。模型输入层的神经元为单因素分析中P<0.05的与高血压相关的因素,输出层有1个神经元(即按照诊断标准判断研究对象是否患高血压),隐含层的神经元个数通过实验根据均方误差择优确定。隐含层的激活函数为tansig,输出层的激活函数为logsig。
本研究将4126例资料按照性别、年龄进行均衡后按3：1的比例随机分为训练总集(3096例)和测试集(1030例)两部分,分别用于模型的建立和测试。为了防止ANNs过渡拟合,在ANNs模型的训练过程中,又将训练总集(3096例)按3：1的比例随机分为训练集(2334例)和检验集(762例),利用检验集时时地检查训练效果。
五、资料统计分析方法
用Matlab7.1软件编程建立ANNs预测模型。用spss13.0统计软件建立二分类非条件Logistic回归的高血压预测模型和绘制模型预测识别的ROC曲线。预测概率的判别标准为0.5,即p≥0.5时预测结果为患高血压,否则为不患高血压。统计学显著性水平规定为α=0.05。
结果
一、非条件单因素Logistic回归模型进行高血压预测
对调查数据进行高血压的单因素分析,筛选出p<0.05的因素作为预测模型的输入变量,共22个因素与高血压有关。
二、非条件多因素Logistic回归模型进行高血压预测
(一)建立非条件多因素Logistic回归模型
对训练总集的3096例样本进行非条件多因素Logistic回归分析,将单因素筛选出的指标作为自变量(身高、体重已转化为BMI故未进入模型),以研究对象是否患高血压为因变量建立多因素Logistic回归模型。模型采用最大似然估计前进法进行逐步回归分析,入选变量的标准是p<0.05,剔除变量的标准是p>0.10。经逐步回归后,共有9个因素进入模型,模型改善情况检验(x2=4.335)和整个模型检验(x2=1439.457)。整个训练总集的分类一致率为78.42%,特异度为80.45%,灵敏度为76.62%,
(二)利用非条件多因素Logistic回归模型预测
用上述Logistic回归模型预测测试集(1030例)研究对象是否患高血压。经模型预测,测试集一致率为77.48%,特异度为80%,灵敏度为74.85%。三、BP神经网络模型进行预测
(一)建立BP神经网络模型
建立一个三层的BPANNs模型,以单因素筛选出的全部22个因素作为输入变量,其隐含层设为22个神经元,输出层1个神经元(即是否患EH)。目标误差取0.01,学习速率取0.1,最大训练周期2000。经过17步训练,此时训练中均方误差MSE为0.126262,梯度Gradient为137.276／le-010,网络的训练由于检验集均方误差达到极小值而结束。测试训练好的BPANNs模型的拟合效果,训练集的分类一致率为81.06%,检验集的分类一致率为77.95%,整个训练总集的分类一致率为80.30%,特异度为84.48%,灵敏度为76.16%。
(二)利用BP神经网络模型进行预测
用上述BPANNs模型预测测试集(1030例)研究对象是否患高血压,测试结果见表5。其测试集分类一致率为78.83%,特异度为81.57%,灵敏度为76.42%。
四、BP神经网络模型与Logistic回归模型高血压预测比较
(一)预测结果的比较
神经网络模型的分类一致率、灵敏度、特异度均高于Logistic回归模型。
(二)ROC曲线面积比较
利用SSPS13.0绘出多因素Logistic回归模型和BPANNs模型的ROC曲线,多因素Logistic回归模型的ROC曲线下面积为0.782,95%可信区间为[0.768,0.797],BPANNs模型的ROC曲线下面积为0.800,95%可信区间为[0.786,0.814]。
讨论
高血压的病因复杂,影响高血压患病的危险因素是多方面的,一些危险因素之间可能存在交互作用、多重共线性,这些复杂的关系影响预测模型的拟合,严重干扰了高血压的预测和病因研究工作。因此本研究利用辽宁省彰武县农村人群的调查资料建立高血压的神经网络预测模型,并与传统方法的Logistic回归模型相比较,以探讨神经网络模型预测高血压发病的能力。
神经网络模型建立过程中各函数、参数的设置并没有统一的标准,需要针对具体问题具体分析。本研究建立的模型是以误差反向后传学习算法而得名的BP神经网络,它是医学领域应用最广泛的一种神经网络,集中体现了神经网络中最精华的部分。因为对于任何在闭区间内的一个连续函数都可以用单隐含层的BP神经网络逼近,所以本研究采用了含有一个隐含层的三层BP神经网络。考虑到输入层神经元个数过多对样本量的要求较高,所以只选择了与高血压密切相关的因素作为输入变量,即单因素分析中p<0.05的因素。对于输入变量中的多分类变量(如民族)采取设置哑变量的处理方法,以方便模型更好的利用数据信息。隐含层的神经元个数和训练函数是根据试验来确定的,试验显示,相对于其他取值,神经元个数为22训练函数为trainlm时均方误差既小又稳定,网络的初始权值取(0～1)区间的随机数,由于初始值不同建立ANNs模型也不同,所以经多次试验选出最优的模型。为了避免过度拟合,本研究利用检验集在训练过程中随时监督训练。
在本研究中,神经网络模型的分类一致率、灵敏度、特异度均高于Logistic回归模型,Logistic回归模型的分类一致率为77.48%,神经网络模型为78.83%。可以看出神经网络模型的预测能力略优于Logistic回归模型。本研究利用ROC曲线来评价两种模型的预测效果,Logistic回归模型和ANNs模型的AUC分别为0.782,0.800,同样提示,对于高血压这样的致病因素多而且各因素间关系复杂的疾病,神经网络模型的拟合效果略好一些。
神经网络尚存在一些问题有待解决。首先,神经网络的建立随着参数、函数、初始值等的设置而变化,这些设置的正确性缺乏理论依据,只能依靠经验和试验来确定；其次,神经网络不能像Logistic回归模型那样有一个公认的模型输入变量的准入和剔出原则；再次,各因素对因变量作用的医学解释尚不明确,以及其假设检验方法和可信区间等问题仍有待进一步研究。
结论
试验表明对于高血压这样的复杂疾病,神经网络预测模型的预测能力略优于Logistic回归模型。因此可以作为Logistic回归模型的必要补充,神经网络在复杂疾病的预测方面具有广阔应用前景。
Prediction using artificial neural network model of essential hypertension
Preface
Essential hypertension (EH) is one of the common cardiovascular disease, In recent years, as the economic development pace of life is significantly increased, resulting in a series of unhealthy lifestyles, leading our country mortality, morbidity and prevalence of cardiovascular disease continued to rise. Hypertension not only is an independent disease, but also is risk factors leading to important cardiovascular disease, even the event of serious complications such as hypertensive crisis and hypertensive encephalopathy may be life-threatening. Therefore, prevention and control of hypertension can not be ignored.
Research has shown that hypertension is a multifactorial disease, Large number of risk factors and complexity of relationship between various factors is an important feature of hypertension. Currently, method of disease prediction is mainly traditional Logistic regression(LR),but Logistic regression model require variables must satisfy the independence and can not deal with the problem of collinearity between the variables. Therefore, using logistic regression model to predict such a complex disease, high blood pressure, has some limitations. Artificial Neural Networks(ANNs), referred to as neural networks (NNs), is a mathematical model of simulating the biological neural network to information process. Neural network has the strong ability to solve the collinearity effect and the interaction between variables, and are good at handling non-linear, fuzzy, noisy data case. Currently, artificial neural network applications in medicine is far less widespread than the traditional Logistic regression.
The selected scene in this study is Zhangwu County in Liaoning Province. By investigation, the standardized prevalence hypertension rate was 35%, national rare. In this study, we used of these survey data set up a back propagation ANNs (BPANNs) prediction model, comparing with the Logistic regression model, and evaluated the forecast performance of ANNs by receiver operator characteristic curve(ROC curve). We also studied and evaluated the ANNs for the prediction effects and characteristics, to explore new prediction ways for the complex diseases such as high blood pressure and provide a reference for prevention and treatment of hypertension in rural areas.
Subjects and Methods
1.The selection of study subjects
This study used the survey data which came from the epidemiological investigation in Zhangwu County in Liaoning Province before to statistics and forecast analysis.Using clustering multistage sampling method 5208 people were total surveyed, at last 4126 respondents over 30 years old were enrolled in this study, of which women were 1942 people, men were 2184 people.
2.The contents of investigation and measurement indicators
Qusetionnaires were filled by means of inquiring and measurement in sites, the contents of survey included:general characteristics, smoking habits, alcohol intake and so on. Measure blood pressure, body height and weight, et al.
Five millititers blood samples were drawn after an overnight fast. After centrifugation, the serum fraction was removed and frozen in aliquots until assayed.
3.Diagnosis standard and measurement methods
The diagnosis standard of EHT:According to 1999 WHO-ISH guidelines for the management of hypertension, hypertension was defined as a systolic blood pressure (SBP)≥140mmHg and/or a diastolic blood pressure (DBP)≥90mmHg. The measurement of blood pressure should be carried out according to the unified standard under standard conditions.
Cholesterol, triglyceride, high density lipoprotein (HDL), low density lipoprotein (LDL), serum sodium, serum potassium, serum iron, serum calcium were measured by automatic biochemistry analyzer 7150 (HITACHI, Japan), the blood sugar was measured by blood sugar analyzer (Johnson & Johnson, America).
4.The establishment of ANNs
ANNs model used the three layers BP neural network model with a hidden layer. Input layer neurons of the model were the factors related to hypertension and P<0.05 by Univariate analysis, output layer had one neuron(that was studied whether hypertension according to diagnostic criteria), and number of neurons in the hidden layer through the experiment was merited to determine basing on the mean square error. The hidden layer activation function was tansig, and the output layer activation function was logsig.
The data(4126 cases) according to the ratio of 3:1 after balancing by gender and age were randomly divided into the total set of training (3096 cases) and test set(1030 cases), and were respectively used to set up and test, In order to prevent over fitting the total set of training according to the ratio of 3:1 were randomly divided into train set (2334 cases) and check set(762 cases), using check set from time to time to check the results of training.
5.Statistical methods
The ANNs prediction model of hypertension was created by Matlab7.1 software,the Logistic regression prediction model was created and ROC Curve was draw by spss13.0. Criteria for predicted probability was 0.5, that is, when p≥0.5 predicted infestation of hypertension, or high blood pressure was not. A 2-sided value ofα=0.05 was regarded as statistically significant.
Results
1. Prediction of hypertension using unconditional single factor Logistic regression model
Univariate analysis of hypertension was conducted for the survey data. The factors that is p<0.05, A total of hypertension-related factors is 22,was selected and taken as input variables predictive model.
2. Prediction of hypertension using multivariate non-conditional
Logistic regression model
(1)The establishment of multi-factor non-conditional Logistic regression model
The total set of training (3096 cases) was carried out multivariate non-conditional Logistic regression analysis.the chosen indicators by single factor analysis served as independent variables(Height, weight has been transformed into BMI, so did not enter the model), and whether subjects are suffering from high blood pressure served as the dependent variable, and in this way a multi-factor Logistic Regression Model was set up. Model used the maximum likelihood estimation method, forward stepwise regression analysis, the Access criteria selected variables is p<0.05, the Exclusion criteria selected variables was p>0.10. After stepwise regression,9 factors enter the model, in Omnibus Tests of Model Coefficients the step wasχ2=4.335, and the model test wasχ2=1439.457. the consistency rate of the total set of training was 78.42%, specificity was 80.45%, sensitivity 76.62%.
(2)The prediction Using multi-factor non-conditional Logistic regression model
The subjects of test set(1030 cases) were predicted whether they were suffering from high blood pressure by the Logistic Regression Model.The predicted results was that the consistency rate was 77.48%, specificity was 80%, sensitivity 74.85%. 3. The prediction of hypertension using BPANNs
(1)The establishment of BPANNs
BPANNs was a three-tier model, the 22 chosen indicators by single factor analysis served as input variable, there were 22 hidden layer neurons in the hidden layer, there was one neuron in output layer (whether was the risk of EH).the target error took 0.01, and learning rate took 0.1, the maximum training period took 2000. After 17-step training, then training meaned square error MSE was 0.126262, gradient Gradient was 137.276/1e-010, The network training ended, when test set to the minimum mean square error, fitting results of that test trained BPANNs model was, the consistency rate of the train set,the check set was respectively 81.06%,and 77.95%, and the consistency rate specificity and sensitivity of the total set was respectively 80.30%,84.48%, 76.16%.
(2)The prediction Using of BPANNs
The subjects of test set(1030 cases) were predicted whether they were suffering from high blood pressure using the BPANNs.The predicted results was,the consistency rate of the test set was 78.83%, specificity was 81.57%, sensitivity 76.42%.
4.The comparison between BPANNs and Logistic regression model about predictive ability of high blood pressure
(1) Comparison of predicted results
The consistency rate, sensitivity and specificity of Neural network model were higher than Logistic regression model.
(2) Comparison of ROC curve area
The ROC curve of BPANNs and Logistic regression mode were drawn, The results showed that, the area under ROC curve of Logistic regression model was 0.782,95% CI is[0.768,0.797], the area under ROC curve of BPANNs was 0.800,95% CI was [0.786,0.814].
Discussion
Causes of hypertension are complex, and the risk factors of affecting hypertension are in many aspects.Some risk factors may exist many interactions, multicollinearity. These complex relationships influence the predictive model fitting, and seriously disturb the prediction and high blood pressure research. Therefore, this study, using of these survey data from Zhangwu county in Liaoning Province,set up a back propagation ANNs (BPANNs) prediction EH model, and compared with the Logistic regression model, and evaluated the ANNs for the prediction effects and characteristics. In the process of building neural network model, there was no uniform standard to set the function and parameter, so we need to analyze specific issues. In this study, the model was the BP neural network, known as a "feed-forward back-propagation network", which was the most widely used in the medical field and embodies the essence of neural networks. Because any continuous function in closed interval could be closed by single hidden layer BP ANNs, so this study used three layers (containing a hidden layer) BP neural network. Taking into account that excessive number of neurons requires a higher sample size, so only selected factors closely related to high blood pressure as input variables, that was, p<0.05 in univariate analysis. For the multi-categorical variables in the input variables (such as national) we set the dummy variable to facilitate better use of data. Number of neurons in the hidden layer and training function was determined according to the test. Test showed that compared to other values, when the number of neurons was 22 and training functions are trainlm, the mean square error was small and stable, the initial weights of the network was set to (01) interval of random numbers.Since if the initial value of different then ANNs model was different,so after numerous experiments, the best model selected. In order to avoid over-fitting, we used chedk set to supervise training at intervals in the training process.
In this study, the consistency rate,, sensitivity and specificity of the neural network model were higher than Logistic regression model. The consistency rate of Logistic regression model and neural network model was respectively 77.48% and 78.83%, that could see the predictive ability of neural network model was better than Logistic regression model.Using ROC curve to evaluate the effectiveness of two models, AUC area under the curve of Logistic regression model and ANNs AUC were respectively 0.782,0.800. it also suggested that neural network model fitted slightly better than LR for these diseases such as hypertension of which risk factors were many and complex relationship exists between the various factors.
Neural networks were still some issues to be resolve. First of all,the establishment of neural networks changes with setting parameters, functions, initial value, etc. The correctness of these settings is still a lack of theoretical basis,so that only rely on experience and testing to determine. Second, there is no recognized principle of access and remove as a Logistic regression model about the input variables of neural network. Again, the medical explanation of the role of various factors on the dependent variable was not clear,and hypothesis testing method,confidence intervals and other issues need further study.
Conclusion
Experiments showed that such a complex disease for high blood pressure, neural network prediction model performs was better than the Logistic regression model. Therefore, ANNs could be used as a necessary complement for Logistic regression model, neural network prediction in complex diseases had broad application prospects.
引文
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19马海英.基于神经网络及Logistic回归的混合信用卡评分模型.华东理工大学学报(社会科学版).2008,02：49-52.
20全国血压抽样调查协作组.中国人群高血压患病率及其变化趋势[J].高血压杂志.1995,s1：7-13.
21 曲强,伊琳,杨蓉佳.ACE基因多态性与甘肃人群不同性别原发性高血压的关系[J].中国老年学杂志.2008,28：1498-1499.
22刘忠仁.我国各地高血压流行病学调查近况.医学综述.2004,10(2)：88-89.
23严冬,王招娣,肖党生.721例高血压相关危险因素分析[J]．浙江预防医学.2006,18(9)：41.
24刘涛,张晓石,张风霞.贵阳市社区高血压流行现状及其危险因素分析[J].现代预防医学.2008,35(15)：2839-2841.
25宋春花,张慧珍,段广才.河南省商丘地区农村居民高血压危险因索分析[J].中国公共卫生.2005,21(7)：823-825.
26熊友珍,王旋.高血压的危险因素及研究进展[J].湖南环境生物职业技术学院学报.2008,14(1)：7-9.
27杨艳军,曾俊涛.海口地区高校教师高血压患病率与相关因素调查[J].中国热带医学.2008,9(8)：1607-1610.
28陈冰,刘继艳，孔亮.河南农村社区居民原发性高血压的患病率及其危险因素[J].现代预防医学.2008,35(15)：2823-2838.
29 Cox KL. Exercise and blood:applying findings from the laboratory to the community setting[J]. Clinical and Experimental Pharmacology and Physiology,2006,33(9):868-71.
30 Zhang XL, Yin KS. Wang H, Association between Obstructive Sleep Apnea Hypopnea Syndrome and Cardiovascular Disorders in Adult Snorers[J].Respiration.2006,73(1):73-7.
31 王菡侨,何权瀛.阻塞性睡眠呼吸暂停综合征与高血压[J].中国呼吸与危重监护杂志.2008,4(7)：313-317.
32许雷,费新军,曹源.连云港市城区居民高血压患病现状及危险因索分析[J].疾病控制杂志,2006,6(10)：626-627.
33 Tian JY, Cheng Q, Song XM et al. Birthweight and risk of type-2diabetes, abdominalobesity and hypertension among Chinese adults[J]. Eur J Endocrinol.2006,155(4):601-7
34邸茹杰,华琦.青少年原发性高血压临床特点分析与运动干预[J].中国临床康复.2003,7(15)：2180-2181.
35 罗琪芬.高血压病的危险因素与社区预防[J].医学理论与实践.2000年,8：515-518.
36庞蓓蕾,刘力松.高血压病患者饮食结构的调查分析[J].护理学杂志.2006,21：63-64.
37薛海峰.闰宏.王骋.膳食营养素摄入量与高血压关系研究[J].齐齐哈尔医学院学报,2007,28(6)：695-696.
38李玉青,刘秀荣,刘枫.高血压限盐干预效果评价[J].中国健康教育.2008,24(7)：501-503.
39邓永安.高血压防治策略近况及发展态势[J].医学创新研究.2007,4(29)：32-35.
40 Dengel DR, Brown MD, Reynolds TH, et al. Effect of aerobic exercise training on blood p ressure sensitivity to dietary sodium in older hypertension [J]. J Hum Hypertens,2006,20 (5): 372-8.
41 Majane OH, Woodiwiss AJ, Maseko MJ, Impact of age on the independent association of adiposity with pulse-wave velocity in a population sample of African ancestry[J]. Am J Hypertens.2008 Aug,21(8):936-42.
42 Salinas JJ, Peek MK. Work experience and gender differences in chronic disease risk in older Mexicans[J].Ann Epidemiol.2008,18(8):628-30
43 Chobanian AV, Bakris GL, Black HR, et al. The seventh report ofthe joint national committee on prevention, detection, evaluation and treatment of high blood pressure:The JNC 7 report [J]. JAMA,2003,289 (19):2560-72.
44吴兆苏,姚崇华,赵冬.11省市队列人群心血管疾病发病前瞻性研究[J].中华心血管病杂志.1999,27(1)：5-8.
45 Jousilahti P,Puska P,Vartiainen E, et al. Parental history of premature coronary heart disease:An independent risk factor of myocardial infarction[J]. J Clin Epide,1996,49 (5):497-503.
46 Talmud PJ, Stephens JW. Lipoprotein lipase gene variants and the effect of environmental factors on cardiovascular disease risk[J]. Diabetes Obes Metab,2004,6 (1):1-7.
47 Rosner SA, Stampfer MJ The heart-breaking news about tobacco:It's all bad[J]. Lancet, 2006,368(9536):621-2.
48 宋文宣,曲彦,王晏平.冠心病的诊断与治疗[M].人民卫生出版社,2006：62-71.
49 Hokanson J E, Austin MA. Plasma triglyceride level is a risk factor for cardiovascular disease independent of high-density lipoprotein cholesterol level:A meta-analysis of population-based prospective studies[J] J Cardiovasc Risk,1996,3 (2):213-219.
50 Kjeldsen SE,Julius S,Hedner T, et al. Stroke is more common than myocardial infarction in hypertension:analysis based on 11 major randomized intervention trials[J].Blood Press,2001,10 (4):190-192.
51 Beckman JA,Creager MA,Libby P. Diabetes and atherosclerosis:epidemiology pathophysiology and management [J]. JAMA,2002,287 (19):2570-2581.
52 Mukamal KJ,Ascherio A,Mittleman MA, et al. Alcohol and risk for ischemic stroke in men:the role of drinking patterns and usual beverage [J]. Ann Intern Med,2005,142 (1):11-9.
53 Baldassarre D,Grossi E,Buscema M, et al.Recognition of patients with cardiovascular disease by artificial neural networks.[J] Ann Med 2004;36(8):630-40.
54 Ning G. Su J, Li Y et al. Artificial neural network based model for cardiovascular risk stratification in hypertension[J]. Med Biol Eng Comput.2006,44(3) 202-208.
55 Falk CT, Risk factors for coronary artery disease and the use of neural networks to predict the presence or absence of high blood pressure. BMC Genet 2003; 4 Suppl 1:S67
56贾崇奇,赵仲堂,王立华.高血压危险因素分类树分析[J].中国公共卫生.2003,19(6)：486-586.
57周利锋,高尔生,金丕焕.BP神经网络与logistic回归对比初探[J].中国卫生统计1998,15(1)：1-4.
58丽娜,曹丽,张敬一.河北省成年居民高血压患病状况及相关危险因素分析[J].中国慢性病预防与控制.2008,16(2)：125-132.
59施侣元,李立明,叶冬青.流行病学[M].2005.
60张霞,王建.南京市部分居民肥胖、高血压患病情况及其危险因素分析[J].预防医学论坛.2008,14(5)：390-395.
61 Parker ED, Schmitz KH, Jacobs DR Jr, et al. Physical activity in young adults and incident hypertension over 15 year of follow-up:the CARDIA study[J].Am J Public Health,2007,97 (4):703-709.
62葛哲学,孙志强井．神经网络理论与MATLAB R2007实现[M].电子工业出版社.2007.
63 Wang WH, Zhao D, Zeng ZC et al A cross-sectional study on knowledge and the ability of hypertension treatment among physicians in district and community hospitals (in Chinese) [J].Chin J Epidemiol 2003,24(12):1086-1089
64 Linder R, Konig IR, Weimar C.Two models for outcome prediction-a comparison of logistic regression and neural networks [J]. Methods Inf Med.2006,45(5):536-40.
65 Yologlu S, Sezgin AT, Sezgin N Comparison of different regression analyses for identifying risk factors in obese and nonobese patients with coronary artery disease[J]. Angiology. 2007;58(5):543-9.
66高蔚,王声涌,王自能.在糖尿病危险因素分析中人工神经网络的应用[J]．中华流行病学杂志.2004,25(8)：715-718.
67 Sacks FM; Expert Group on HDL Cholesterol.The role of high-density lipoprotein(HDL) cholesterol in the Prevention and treatment of eoronary heart disease:expert group commendations[J).Am J Cardiol,2002,90(2):139-143.
68 Tiire M, Kurt I, Yavuz E, Kurum T Comparison of multiple prediction models for hypertension (Neural networks, logistic regression and flexible discriminant analyses). Anadolu Kardiyol Derg 2005; 5(1):24-8
2 Trujillano J, March J, Sorribas A.Methodological approach to the use of artificial neural networks for predicting results in medicine[J]. Med Clin (Barc),2004;122 Suppl 1:59-67.
3 孙振球.医学统计学[M].人民卫生出版社,2007：333-341.
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5 时景璞,王海龙,李辉,董卫,付凌雨,齐国先,贾志梅,杨慧英,宫伟,康辉,王文利,曹成,姜玉山,李继光.辽宁省彰武县农村人群高血压患病率调查.中华流行病学杂志,2003,24(7)：547-550.
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8 Zhang XL, Yin KS, Wang H.Association between Obstructive Sleep Apnea Hypopnea Syndrome and Cardiovascular Disorders in Adult Snorers[J].Respiration,2006,73(1):73-7.
9 Baldassarre D,Grossi E,Buscema M, et al.Recognition of patients with cardiovascular disease by artificial neural networks.[J] Ann Med,2004,36(8):630-40.
10葛哲学,孙志强．神经网络理论与MATLAB R2007实现[M].电子工业出版社.2007.
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13 Baxt W, Shofer F, Sites F, Hollander J. A neural network aid for the early diagnosis of cardiac ischemia in patients resenting to the emergency department with chest pain[J],Ann Emerg Med,2002,40(6)575-83.
14 Harrison R, Kennedy R. Artificial neural network models for prediction of acute coronary syndromes using clinical data from the time of presentation[J],Ann Emerg Med,2005,46(5) 431-9.
15陈金宏,何耀,屈波,王发强,秦银河.人工神经网络在缺血性心血管疾病中的研究及应用.中国心血管病研究[J],2009,7(8)：612-615.
1 中华人民共和国卫生部.中国居民营养与健康状况2002[R].人民卫生出版社,2005：15-16.
2 孙振球.医学统计学[M].人民卫生出版社,2007：333-341.
3 赵一鸣.分类与回归树——一种适用于临床研究的统计分析方法[J].北京大学学报(医学版).2001,33(6)：265-565.
4 莫春梅,倪宗瓒,高凤琼.回归树的建模与应用[J].中华预防医学杂志.2002,36(5)：346-347.
5 张青贵.人工神经网络导论[M].中国水利水电出版社.2004：25-38.
6 张良均,曹晶,蒋世忠．神经网络实用教程[M].机械工业出版社,2008：31-36.
7 蒋宗礼.人工神经网络导论[M].中国水利水电出版社,2004：11.
8 Trujillano J, March J, Sorribas A Methodological approach to the use of artificial neural networks for predicting results in medicine[J]. Med Clin (Barc).2004,122 Suppl 1:59-67
9 Faraggi D,LeBlanc M.Crowley J.Understanding neural networks using regression trees:an application to multiplemyeloma survival data[J].Stat Med.2001,20:2965-76.
10 Green M, Bjork J, Forberg J, et al Comparison between neural networks and multiple logistic regression to predict acute coronary syndrome in the emergency room[J].Artif Intell Med. 2006,38(3):305-18.
11 Baxt W, Shofer F, Sites F, Hollander J. A neural network aid for the early diagnosis of cardiac ischemia in patients resenting to the emergency department with chest pain[J].Ann Emerg Med 2002,40(6):575-83.
12 Harrison R, Kennedy R. Artificial neural network models for prediction of acute coronary syndromes using clinical data from the time of presentation [J].Ann Emerg Med 2005,46(5):431-9.
13 Kennedy R, Harrison R. Identification of patients with evolving coronary syndromes by using statistical models with data from the time of presentation [J]. Heart 2006,92(2):183-9.
14陈建新,西广成,王伟.数据挖掘分类算法在冠心病临床应用的比较.北京生物医学工程.2008,27(3)：249-252.
15 Trujillano J, Sarria-Santamera A, Esquerda A, Approach to the methodology of classification and regression trees[J].Gac Sanit.2008,22(1):65-72.
16傅传喜,马文军,梁建华.高血压危险因素logistic回归与分类树分析.Chin J Dis Control Prev.2006,10(3):652-952.
17 Muller R, Mockel M. Logistic regression and CART in the analysis of multimarker studies[J]. Clin Chim Acta.2008,394(1-2):1-6.
18 Green M, Bjork J, Forberg J Comparison between neural networks and multiple logistic regression to predict acute coronary syndrome in the emergency room[J].Artif Intell Med. 2006,38(3):305-18.
19马海英.基于神经网络及Logistic回归的混合信用卡评分模型.华东理工大学学报(社会科学版).2008,02：49-52.
20全国血压抽样调查协作组.中国人群高血压患病率及其变化趋势[J].高血压杂志.1995,s1：7-13.
21 曲强,伊琳,杨蓉佳.ACE基因多态性与甘肃人群不同性别原发性高血压的关系[J].中国老年学杂志.2008,28：1498-1499.
22刘忠仁.我国各地高血压流行病学调查近况.医学综述.2004,10(2)：88-89.
23严冬,王招娣,肖党生.721例高血压相关危险因素分析[J]．浙江预防医学.2006,18(9)：41.
24刘涛,张晓石,张风霞.贵阳市社区高血压流行现状及其危险因素分析[J].现代预防医学.2008,35(15)：2839-2841.
25宋春花,张慧珍,段广才.河南省商丘地区农村居民高血压危险因索分析[J].中国公共卫生.2005,21(7)：823-825.
26熊友珍,王旋.高血压的危险因素及研究进展[J].湖南环境生物职业技术学院学报.2008,14(1)：7-9.
27杨艳军,曾俊涛.海口地区高校教师高血压患病率与相关因素调查[J].中国热带医学.2008,9(8)：1607-1610.
28陈冰,刘继艳，孔亮.河南农村社区居民原发性高血压的患病率及其危险因素[J].现代预防医学.2008,35(15)：2823-2838.
29 Cox KL. Exercise and blood:applying findings from the laboratory to the community setting[J]. Clinical and Experimental Pharmacology and Physiology,2006,33(9):868-71.
30 Zhang XL, Yin KS. Wang H, Association between Obstructive Sleep Apnea Hypopnea Syndrome and Cardiovascular Disorders in Adult Snorers[J].Respiration.2006,73(1):73-7.
31 王菡侨,何权瀛.阻塞性睡眠呼吸暂停综合征与高血压[J].中国呼吸与危重监护杂志.2008,4(7)：313-317.
32许雷,费新军,曹源.连云港市城区居民高血压患病现状及危险因索分析[J].疾病控制杂志,2006,6(10)：626-627.
33 Tian JY, Cheng Q, Song XM et al. Birthweight and risk of type-2diabetes, abdominalobesity and hypertension among Chinese adults[J]. Eur J Endocrinol.2006,155(4):601-7
34邸茹杰,华琦.青少年原发性高血压临床特点分析与运动干预[J].中国临床康复.2003,7(15)：2180-2181.
35 罗琪芬.高血压病的危险因素与社区预防[J].医学理论与实践.2000年,8：515-518.
36庞蓓蕾,刘力松.高血压病患者饮食结构的调查分析[J].护理学杂志.2006,21：63-64.
37薛海峰.闰宏.王骋.膳食营养素摄入量与高血压关系研究[J].齐齐哈尔医学院学报,2007,28(6)：695-696.
38李玉青,刘秀荣,刘枫.高血压限盐干预效果评价[J].中国健康教育.2008,24(7)：501-503.
39邓永安.高血压防治策略近况及发展态势[J].医学创新研究.2007,4(29)：32-35.
40 Dengel DR, Brown MD, Reynolds TH, et al. Effect of aerobic exercise training on blood p ressure sensitivity to dietary sodium in older hypertension [J]. J Hum Hypertens,2006,20 (5): 372-8.
41 Majane OH, Woodiwiss AJ, Maseko MJ, Impact of age on the independent association of adiposity with pulse-wave velocity in a population sample of African ancestry[J]. Am J Hypertens.2008 Aug,21(8):936-42.
42 Salinas JJ, Peek MK. Work experience and gender differences in chronic disease risk in older Mexicans[J].Ann Epidemiol.2008,18(8):628-30
43 Chobanian AV, Bakris GL, Black HR, et al. The seventh report ofthe joint national committee on prevention, detection, evaluation and treatment of high blood pressure:The JNC 7 report [J]. JAMA,2003,289 (19):2560-72.
44吴兆苏,姚崇华,赵冬.11省市队列人群心血管疾病发病前瞻性研究[J].中华心血管病杂志.1999,27(1)：5-8.
45 Jousilahti P,Puska P,Vartiainen E, et al. Parental history of premature coronary heart disease:An independent risk factor of myocardial infarction[J]. J Clin Epide,1996,49 (5):497-503.
46 Talmud PJ, Stephens JW. Lipoprotein lipase gene variants and the effect of environmental factors on cardiovascular disease risk[J]. Diabetes Obes Metab,2004,6 (1):1-7.
47 Rosner SA, Stampfer MJ The heart-breaking news about tobacco:It's all bad[J]. Lancet, 2006,368(9536):621-2.
48 宋文宣,曲彦,王晏平.冠心病的诊断与治疗[M].人民卫生出版社,2006：62-71.
49 Hokanson J E, Austin MA. Plasma triglyceride level is a risk factor for cardiovascular disease independent of high-density lipoprotein cholesterol level:A meta-analysis of population-based prospective studies[J] J Cardiovasc Risk,1996,3 (2):213-219.
50 Kjeldsen SE,Julius S,Hedner T, et al. Stroke is more common than myocardial infarction in hypertension:analysis based on 11 major randomized intervention trials[J].Blood Press,2001,10 (4):190-192.
51 Beckman JA,Creager MA,Libby P. Diabetes and atherosclerosis:epidemiology pathophysiology and management [J]. JAMA,2002,287 (19):2570-2581.
52 Mukamal KJ,Ascherio A,Mittleman MA, et al. Alcohol and risk for ischemic stroke in men:the role of drinking patterns and usual beverage [J]. Ann Intern Med,2005,142 (1):11-9.
53 Baldassarre D,Grossi E,Buscema M, et al.Recognition of patients with cardiovascular disease by artificial neural networks.[J] Ann Med 2004;36(8):630-40.
54 Ning G. Su J, Li Y et al. Artificial neural network based model for cardiovascular risk stratification in hypertension[J]. Med Biol Eng Comput.2006,44(3) 202-208.
55 Falk CT, Risk factors for coronary artery disease and the use of neural networks to predict the presence or absence of high blood pressure. BMC Genet 2003; 4 Suppl 1:S67
56贾崇奇,赵仲堂,王立华.高血压危险因素分类树分析[J].中国公共卫生.2003,19(6)：486-586.
57周利锋,高尔生,金丕焕.BP神经网络与logistic回归对比初探[J].中国卫生统计1998,15(1)：1-4.
58丽娜,曹丽,张敬一.河北省成年居民高血压患病状况及相关危险因素分析[J].中国慢性病预防与控制.2008,16(2)：125-132.
59施侣元,李立明,叶冬青.流行病学[M].2005.
60张霞,王建.南京市部分居民肥胖、高血压患病情况及其危险因素分析[J].预防医学论坛.2008,14(5)：390-395.
61 Parker ED, Schmitz KH, Jacobs DR Jr, et al. Physical activity in young adults and incident hypertension over 15 year of follow-up:the CARDIA study[J].Am J Public Health,2007,97 (4):703-709.
62葛哲学,孙志强井．神经网络理论与MATLAB R2007实现[M].电子工业出版社.2007.
63 Wang WH, Zhao D, Zeng ZC et al A cross-sectional study on knowledge and the ability of hypertension treatment among physicians in district and community hospitals (in Chinese) [J].Chin J Epidemiol 2003,24(12):1086-1089
64 Linder R, Konig IR, Weimar C.Two models for outcome prediction-a comparison of logistic regression and neural networks [J]. Methods Inf Med.2006,45(5):536-40.
65 Yologlu S, Sezgin AT, Sezgin N Comparison of different regression analyses for identifying risk factors in obese and nonobese patients with coronary artery disease[J]. Angiology. 2007;58(5):543-9.
66高蔚,王声涌,王自能.在糖尿病危险因素分析中人工神经网络的应用[J]．中华流行病学杂志.2004,25(8)：715-718.
67 Sacks FM; Expert Group on HDL Cholesterol.The role of high-density lipoprotein(HDL) cholesterol in the Prevention and treatment of eoronary heart disease:expert group commendations[J).Am J Cardiol,2002,90(2):139-143.
68 Tiire M, Kurt I, Yavuz E, Kurum T Comparison of multiple prediction models for hypertension (Neural networks, logistic regression and flexible discriminant analyses). Anadolu Kardiyol Derg 2005; 5(1):24-8