体外冲击波治疗上尿路结石的疗效预测：人工神经网络和Logistic回归模型的建立与比较
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摘要
研究背景和目的
泌尿系结石是泌尿外科的常见病与多发病,尤其在我国南方的部分省份,发病率较高。随着人们生活水平的提高,近年来上尿路结石的发病率明显增高。自上个世纪80年代问世以来,体外冲击波碎石(Extracorporeal Shockwave Lithotripsy,ESWL)经过三十年的技术改进和临床经验积累,使得很大一部分的上尿路结石患者免除开刀之苦,其治疗上尿路结石具有安全、有效、痛苦小、恢复快和费用不高的特点。然而,对于较大上尿路结石的治疗,可能需要多次碎石,一方面,可能增加肾脏不可逆损伤的风险；另一方面,排石过程中经常会伴随肾绞痛、发热、血尿、石街等并发症,从而不得不转为其它外科方法治疗,影响ESWL的疗效。临床实践证明,并不是所有的上尿路结石都适合ESWL治疗,有些结石ESWL无法击碎,有些结石ESWL击碎后病人无法自行排出。伴随ESWL不成功而带来的问题是,病人可能会为失败的ESWL承担经济、时间及痛苦就医经历的后果,从而使得ESWL的优势不能最大化。如果在体外冲击波碎石前,能对其治疗效果准确预测,一方面可以制定相对正确的治疗方案,避免减少病人不必要的痛苦和经济损失、降低医疗服务成本；另一方面也有利于在治疗前向病人充分告知,有利于医患的沟通和理解。
尽管对于ESWL治疗上尿路结石疗效预测的研究不少,然而,因受限于研究条件,存在以下不足：1)个别病例数较少,仅局限在方法学上的探索,并未广泛应用在临床实践中；2)受研究条件等限制,纳入的疗效影响因素不全面,因此预测的准确性还有待提高；3)部分研究对病例没有分层,将肾结石与输尿管结石合并在一起研究,临床应用意义不大。本研究分别运用logistic回归分析和人工神经网络建立ESWL治疗肾结石和输尿管结石的疗效预测模型,确定ESWL治疗上尿路结石疗效的重要影响因素和预测变量重要性评价,并对人工神经网络和Logistic回归分析方法、预测效果和优缺点进行比较,最后,确定预测效果较好的模型的工作概率分界值,使研究成果直接转化为临床应用。
方法
对325例肾结石患者和1,065例输尿管结石ESWL治疗前的临床资料如性别、尿路刺激症、治疗前血尿、肾绞痛、结石位置、结石患侧、年龄、身高、体重、病程时间、结石长径、结石宽径等影响因素和ESWL治疗结局进行回顾性分析。
首先,将ESWL治疗的肾结石和输尿管结石的病例资料分别进行无偏随机化分组,对于Logistic回归分析和建模,约70%的病例分配至训练样本,约30%病例分配至坚持样本；而对于人工神经网络,则是约56%的病例分配至训练样本,约14%的病例分配至检验样本,约30%的病例分配至坚持样本。
采用χ2检验对分类变量如性别、尿路刺激症、治疗前血尿、肾绞痛、结石位置、结石患侧等进行每个预测变量与应变量(ESWL治疗结局)关系的显著性检验。通过拟合单变量logistic回归取得连续预测变量(年龄、体重指数、病程时间、结石长径与短径的乘积)的显著性检验,初步找出对应变量(ESWL治疗结局)有影响的因素,再将上述预测变量显著性检验分析中P<0.25者,与其它重要预测变量一起,纳入多元模型的候选预测变量。然后采用logistic逐步回归分析(前向法：LR法)多因素分析,建立logistic回归预测模型,并将训练样本组和坚持样本组回代至此模型,得到ESWL治疗结局预测概率,绘制ROC曲线,计算曲线下面积(AUC),并计算敏感度,特异度和总准确度,评价预测模型的准确性。
建立3层前向型神经网络模型,隐含层设置为1层,输入层的参数为所有10项可能有临床意义的预测指标,预测因子设置依次为性别、尿路刺激症、治疗前血尿、肾绞痛、结石位置、结石患侧,预测协变量依次为年龄、体重指数、病程时间、结石长径与结石宽径的乘积(文中简称“结石大小”),标准化协变量。其中,性别编码为“男”=1、“女”=2；尿路刺激症、治疗前血尿、肾绞痛编码为‘有”=1、“无”=2；结石位置编码为“肾上盏”=1、“中盏”=2、“下盏”=3、“肾盂”=4、“混合”=5或“输尿管上段”=1、“中段”=2,“下段”=3。输出层为ESWL治疗结局,“成功”编码为1,“失败”编码为0。以前述“分区变量”分配病例样本,选择“自动体系结构选择”,隐含层中最小单位数为1,最大单位数为50,训练类型为“批处理”(肾结石组)或“袖珍批处理”(输尿管结石组),优化算法选用“调整的共轭梯度”(肾结石组)或“梯度下降”(输尿管结石组),间隔中心点为0,间隔偏移量为±0.5。运行神经网络后,获得ESWL治疗结局预测的拟概率,以0.50为预测分界值,计算预测的总准确率、灵敏度和特异度,绘制ROC(Receiver Operating Characteristic curve, ROC)曲线,计算曲线下面积(Area Under Curve,AUC),评价人工神经网络预测的准确性。
最后,从建模原理与方法、预测效果、优缺点三方面比较logistic回归预测模型和人工神经网络。
统计学软件包
应用IBM(?)公司出品的统计软件包SPSS20.0进行χ2检验,单变量Logistic回归和多元logistic分析和建立模型,并以其附带的神经网络模块中的多层感知器建立人工神经网络。采用Hosmer-Lemeshow进行logistic回归拟合优度检验,并以χ2检验进行模型的显著性检验。P值精确到小数点后3位,以P<0.05为有统计学差异。
用统计软件包Medcal(?)进行ROC曲线的绘制和ROC曲线下面积的比较,进行约登指数的计算和预测概率分界值的筛选。
结果
1) ESWL治疗肾结石组
共325例肾结石,最长随访3个月,碎石成功250例,转为其它方法治疗75例,总成功率76.9%。对全部肾结石患者性别、结石患侧、结石位置、尿路刺激症状、血尿或肾绞痛进行单因素分析,我们发现结石患侧、结石位置、尿路刺激症状、血尿对ESWL治疗结局有显著性影响。对本组患者年龄、体重指数、病程时间、结石大小进行单因素logistic回归拟合,结果排除体重指数,其余预测因素均纳入候选变量。
进一步用logistic逐步回归进行多因素分析,发现病程时间、血尿和结石大小,是ESWL治疗肾结石疗效的独立影响因素(P<0.05),其AOR(Adjusted OddsRatio)值(95%可信区间)依次是0.977(0.964-0.989)、12.388(3.44-44.565)、0.192(0.113-0.323)。
建立以训练样本为基础的logistsic预测模型。对预测模型进行χ2检验验证其显著性,χ2值为108.938,P<0.001,预测变量对应变量(ESWL碎石结局)有显著的解释能力。通过分类交互表计算Hosmer-Lemeshow拟合优度检验统计量,得到χ2=6.927,df=8,P=0.545,无统计学显著性差异,因此认为模型拟合观测数据良好。通过预测-观察分类表,对于模型预测的准确性进行评价。将训练样本和坚持样本的观察数据分别回代到模型,得到模型对训练样本和坚持样本的预测概率值,以0.5作为预测结果的分界值,结果显示模型对训练样本的灵敏度为94.4%,特异度63.3%,总体准确率为86.0%,而对坚持样本的灵敏度100%,特异度20.0%,总体准确率为88.4%。
人工神经网络自动剔除建模过程中典型的“冗余”单元后,输入层共建立19个单元。自动体系结构选择了建立一个隐含层,隐含层内共有6个单元,激活函数为hyperbolic tangent,输出层共有2个单元,激活函数为softmax。将预测变量重要性指标除以最大指标值,得到标准化的预测变量重要性排序,发现列于前五位的是：结石大小、病程时间、血尿、结石位置、体重指数。以0.5作为预测拟概率分界值,运用人工神经网络对全部样本进行预测,结果显示训练样本的敏感度、特异度和总体准确率为98.4%、72.5%和90.8%；检验样本的敏感度、特异度和总体准确率为97.4%、55.6%和89.6%；坚持样本的敏感度、特异度和总体准确率为93.3%、46.7%和86.5%。
Logistic回归模型的AUC为0.625,95%可信区间为0.525-0.718；人工神经网络AUC为0.856,95%可信区间为0.774-0.917,与AUC为0.5进行显著性检验,前者P值为0.122,后者为P<0.001。两者AUC差异的非参数显著性检验,z值为3.988,P=0.0001,两者AUC存在统计学上显著性差异,意味着logistic回归模型的预测效果差,ANN的预测效果优于logistic回归模型。
计算约登指数并权衡敏感度与特异度后,发现概率分界值为0.595时,肾结石ESWL疗效预测的ANN模型的敏感度和特异度达到较为理想状态,分别为92%和60%。
2) ESWL治疗输尿管结石组
共纳入1065例输尿管结石,最长随访3个月,碎石成功874例,转为其它方法治疗191例,总成功率82.1%。用χ2检验对本组患者性别、结石患侧、结石位置、尿路刺激症状、血尿或肾绞痛进行单因素分析,按着P<0.25的预测变量筛选标准,我们发现除治疗前是否出现血尿外,其余预测因素对ESWL治疗结局有显著性影响。对本组患者年龄、体重指数、病程时间、结石大小进行单因素logistic回归逐一拟合,均纳入候选预测变量。
用logistic回归对进行多因素分析,结果显示治疗前肾绞痛、结石位置(输尿管上段、输尿管中段)结石大小为ESWL治疗输尿管结石疗效的独立影响因素,其AOR值(95%可信区间)分别是1.508(0.999-2.277)、0.651(0.391-1.086)、0.374(0.191-0.731)、0.246(0.152-0.396)。Logistic回归预测模型的χ2值为54.460,P值<0.001,提示纳入模型的预测变量对治疗结局有显著的解释能力。预测模型的拟合优度通过Hosmer-Lemeshow检验,显示模型拟合程度尚好(χ2=8.406,df=8,P=0.395)。将训练样本和坚持样本分别回代至预测模型,得到对训练样本和坚持样本进行预测概率值,以0.5作为预测概率分界值,结果显示训练样本灵敏度98.1%,特异度4.2%,总体准确率为82.9%。坚持样本灵敏度99.3%,特异度11.3%,总体准确率为84.7%。
人工神经网络自动剔除建模过程中典型的“冗余”单元后,输入层共建立17个单元。自动体系结构选择了建立一个隐含层,隐含层内共有5个单元,激活函数为hyperbolic tangent,输出层共有2个单元,激活函数为softmax。将预测变量重要性指标除以最大指标值,得到标准化的预测变量重要性排序,结石大小、结石位置、病程时间、年龄和体重指数列于前五位。
应用人工神经网络对全部样本进行预测,以0.5作为预测拟概率分界值,结果显示训练样本的敏感度、特异度和总体准确率分别为98.8%,12.7%和84.0%；检验样本的敏感度、特异度和总体准确率分别为99.2%,16.7%和89.3%；坚持样本的敏感度、特异度和总体准确率分别为97.8%,9.4%和83.2%。
Logistic回归模型的AUC为0.729,人工神经网络的AUC为0.751,与AUC为0.5进行显著性检验,前者P值<0.001,95%可信区间为0.676-0.777,后者为P值<0.001,95%可信区间为0.700-0.797,借助统计软件包MedCalc(?)对AUC进行非参数显著性检验,计算z统计量为0.750,对应的P值为0.4534,即两种预测模型的AUC面积在统计学上无显著性差异,换言之,输尿管结石ESWL疗效的logistic回归模型和ANN模型的预测效果相差不大。权衡敏感度与特异度后,确定概率分界值为0.769时,ESWL治疗肾结石疗效预测的ANN模型的敏感度和特异度达到较为理想状态,分别为81%和60%。
结论
本研究发现,患者病程时间、结石大小、治疗前血尿是影响肾结石ESWL疗效的独立影响因素,而影响输尿管结石的ESWL疗效的重要因素为性别、肾绞痛、结石位置和结石大小。和Logistic逐步回归法建立的预测模型相比较,人工神经网络具有自学习、并行计算的功能,虽对预测变量的解释性不如logistic回归模型,但预测效果较好,仍可做为预测ESWL成功率的有利工具,有助于筛选更加适用ESWL治疗的患者,有利于患者充分知情,与患者共同制定治疗方案,减轻患者医疗风险和经济负担。
Background and Objection:
Urinary stone is a common disorder of urology, and the prevalence of urolithiasis is higher in some provinces of southern China. Following the improvement of nutritional condition, the incidence of upper urinary tract stone became significantly higher in the recent decade. Since the advent in the early80s of the last century, extracorporeal shock wave lithotripsy (ESWL)cured numerous patients with upper urinary tract stones, who had to undergo surgery before. ESWL has been proved to be safe, effective, less painful, rapid to recovery and inexpensivedue to its minimally invasive character, and low morbidity. However, for larger upper urinary tract stones, ESWL may need to repeat several times or combine others methods of treatment. But repetition of ESWL may lead to irreversible damage to kidney. Furthermore, the process of stone fragments removing is often accompanied by some complications such as renal colic, fever, hematuria, steinstrasse, which may also result in conversion to surgery. These morbidities may compromise the clinical outcome of ESWL-treated calculi, thus not all upper urinary tract calculi are suitable for ESWL.The patient would pay for the consequences of unsuccessful ESWL with a cost of money, time, and an experience of distressful medical treatment.
If the outcome of ESWL can be predicted, on one hand, the clinicians could develop relatively correct strategy to avoid the patient's unnecessary cost, to reduce the cost of medical services; On the other hand, the prediction could help patients be well informed and help doctors share the decision-making with patients.
In this study, logistic regression (LR) analysis and artificial neural network (ANN) were used to establish the predictive model of ESWL for renal and ureteral calculi, respectively.Under logistic regression models, the important impact factors influencing outcome of ESWL for upper urinary tract stones were determined. By ANN, the importance of predictor variables was evaluated. A comparative study afterwards was done between LR model and ANN to compare the accuracy of prediction and pros&cons between these two models of prediction. Eventually the cut-off values of optimal probabilities were identified to facilitate the clinical application.
Methods and materials
Pre-ESWL clinical data of325cases of kidney stones treated with ESWL and those of1065cases of ureteral calculi were included retrospectively. The information of gender, urinary irritation symptom, hematuria, renal colic, stone location, stone side, age, height, weight, history of stone, stone length, stone width was collected.
All cases of kidney stones and ureteral stones were grouped separately with a randomized method. For LR analysis and modeling, about70%of cases were assigned to training-sample group, and approximate30percent of cases were assigned to holdout-sample group. For ANN, about56%of the cases were assigned to training-sample group, and about14%of the cases assigned to test-sample group, about30%of cases were assigned to the holdout-sample group.
χ2test was performed for the significance test of relationship between the ESWL outcome and every categorical variable (gender, urinary irritation symptom, hematuria, renal colic, stone location, stone side).The significant test of continuous predictive variables (age, body mass index, history of stone, the product of stone length&width) were done by univariate logistic regression to initially identify the corresponding influential factors of ESWL outcome.
Then all the predictive variables which have P<0.25, together with other important predictive variables were included as candidate predictive variables for multivariate analysis. Thereafter logistic stepwise regression analysis (forward:LR) was performed. The training sample and the holdout sample were respectively substituted to the LR model, and the respective predictive probabilities for ESWL outcome were obtained. Then the area under curve (AUC), sensitivity, specificity and were calculated to evaluate the accuracy of prediction after drawing receiver operating characteristic curve (ROC).
Three-layer forward neural network model was constructed. Hidden layer was set to1layer; the parameters of the input layer comprise all10predictive variables. Predictive factors were set to be gender, urinary irritation symptom, hematuria, renal colic, stone location, and stone side. Predictive covariates were age, BMI, history of stone, stone size. Value of gender was coded by male=1, female=2. And the value of urinary irritation symptom, hematuria, renal colic were set to yes=1, no=2. In the cases of kidney stone, location of stone in the kidney was set to the upper calyces=1, the middle calyces=2, the lower calyces=3, the pelvis=4, combined location=5. In the cases of ureter stone, it was set to upper ureter=1, middle ureter=2, lower ureter=3.
The output layer is ESWL-treated calculi outcome. Successful and failed outcome is set to1and0, respectively. All cases were assigned randomly basing on partitioning variable aforementioned."Automatic architecture selection" was chosen, implying that the minimum number of units in hidden layer is1, and the maximum number is50. The type of training was chosen as "batch"(for renal calculi sample) or "mini-batch"(for ureteral calculi sample),"optimization algorithm selection"(for renal calculi sample) and "scaled conjugate gradient"(for ureteral calculi sample). Initial Lambda value is0.0000005, and the initial Sigma value of is0.00005, the interval center is0, the interval offset is±0.5.
The predictive pseudo probabilities of ESWL outcome were obtained.0.50was set as the cut-off value of predictive pseudo probabilities, and the area under curve (AUC), sensitivity, and specificity were calculated to evaluate the accuracy of prediction after drawing receiver operating characteristic curve (ROC). The efficacy together with advantages&disadvantages of LR predictive model and ANN were then evaluated and compared.
The statistical package of SPSS20.0published by IBM(?) were used statistically, by which χ2test, univariate logistic regression, multivariate logistic analysis and modeling were performed. Hosmer-Lemeshow goodness of fit test for LR model and the χ2test are used for significance test of LR model. P value is accurate to three decimal. P<0.05is for significant difference. The statistical package of Medcalc(?) was used for drawing of ROC curve and the comparison of AUC and for calculation of Youden index, then the cut-offs value of optimal predictive probabilities were identified.
Results:
A. Prediction of ESWL outcome for kidney stones cases
Among a total of325cases of kidney stones,250cases (76.9%) were free of stones at3months.Post-ESWL auxiliary treatment was required in75cases who failed to respond to the ESWL treatment. The longest follow-up attained three months.
The success rate of ESWL was significantly affected by stones side, stone location, urinary irritation symptom, and hematuria.Additionally, after further LR multivariate analysis to the training-sample, history of stone, hematuria and the product of stone length&width were found to be3independent impact factors of the outcome of ESWL treatment of kidney stones (P<0.05) with AOR (Adjusted Odds Ratio)(95%confidence interval) being0.977(0.964-0.989),12.388(3.443-44.565),0.192(0.113-0.323), respectively.
χ2value of LR prediction model is108.938(P<0.001), which means the predictive variables have significant explanatory power for the dependent variable (ESWL outcome). The result of Hosmer-Lemeshow goodness of fit test indicated that the prediction model could represent the data well (χ2=6.927, df=8, P=0.545).
To evaluate the accuracy of prediction of LR model, the prediction-observation cross classification table was employed. The cut-off value of probabilitywas set at0.5. The results showed that the training sample's sensitivity, specificity, overall accuracy rate were94.4%63.3%86.0%, respectively. The sensitivity, specificity, overall accuracy rate of holdout samples were100%,20.0%,88.4%, respectively.
The ANN automatically removed the typical modeling process "redundant" unit, and established an input layer with of19units, a hidden layer of6units and an output layer of2units. The activation function of input was set as "hyperbolic tangent", The activation function of output was set as "softmax". The order of importance of predictive variables showed that stone size, history of stone, hematuria, stone location were listed on the top five. At0.5of cutoff value of probability, the prediction of ANN showed that the sensitivity, specificity, overall accuracy rate of the training sample were98.4%,72.5%and90.8%,respectively; Those of the testing sample were97.4%,55.6%and89.6%. Those of holdout sample were93.3%,46.7%and86.5%.
The AUC of the LR model is0.625(95%confidence interval:0.525-0.718), whereas ANN model is0.856(95%confidence interval:0.774-0.917). Comparing with AUC=0.5, the former's P value is0.122, and the latter's P value0.001. The medical statistics Packages Medcalc was employed for testing the difference of two AUCs, the z value is3.988, P=0.0001, which means there exist statistically significant differences between the AUCs of two models. That is to say, the prediction of ANN model has higher ability than that of the LR model.
The optimal cutoff value of probability of ANN was identified to0.595, with consideration of balancing the sensitivity and specificity. At this cutoff value, the sensitivity and specificity of ANN model were thought to be92%and60%, respectively.
Prediction of ESWL outcome for ureter stones cases
Among a total of1,065cases of ureter stones,874cases (82.1%) were free of stones at3months,191cases failed of ESWL. All failed cased were converted to other auxiliarytreatments. The longest follow-up duration reached3months. Gender, stone side, stone location, urinary irritation symptom, renal colic were found to have significant impacts on the outcome of ESWL. Univariate logistic regressions indicated age, BMI, history of stone, stone size were among the significant contributors to the success rate of ESWL.
Further using LR multivariate analysis to training samples, renal colic, stone location (upper part of ureter and middle part of ureter), stone size were found to be4independent impact factors of outcome of ESWL treatment for ureter stones, with AOR (95%confidence interval) were1.508(0.999-2.277),0.651(0.391-1.086), 0.374(0.191-0.731),0.246(0.151-0.396), respectively.
χ2test was applied to verify the significance of LR prediction model, χ2value was54.460(P<０.001), which means these predictive variables have significant explanatory power for the dependent variable (ESWL outcome). Hosmer-Lemeshow goodness of fit indicated that there was no statistically significant difference (χ2=8.406,df=8,P=0.395).
To evaluate the accuracy of prediction of LR model, the prediction-observation cross classification table was employed. The cut-off value is set at0.5. The results showed that the training sample's sensitivity, specificity, overall accuracy rate were98.1%,4.2%,82.9%, respectively, meanwhile the sensitivity, specificity, overall accuracy rate of the holdout samples were99.3%,11.3%,84.7%, respectively.
The ANN automatically removed the typical modeling process "redundant" unit, and established an input layer with of17units, a hidden layer of5units and an output layer of2units."Hyperbolic tangent" was selected as the activation function of input. The activation function of output was "softmax". The order of importance of predictive variables showed that stone size, stone location, history of stone time, age and BMI were listed on the top five. Atthe cutoff value of0.5, the prediction of ANN showed that the sensitivity, specificity, overall accuracy rate of the training sample were98.8%,12.7%,84.0%.respectively; Those of the testing sample were99.2%,16.7%,89.3%. Those of the holdout sample were97.8%,9.4%,83.2%.
The AUC of the logistic regression model was0.729(95% confidence interval:0.676-0.777), whereas ANN model was0.751(95% confidence interval:0.700-0.797). Comparing with AUC=0.5, theirs P values were less than0.001. With the medical statistics Packages Medcalc(?) for non-parametric tests, the z value is0.750, P=0.4534, which means there is no statistically significant differences between the two AUC. That is to say, the prediction of ANN model may have the same predictive efficacy as that of the LR model.
The cutoff value of probabilities of ANN was identified to0.7694, in consideration of balancing the sensitivity and specificity. The optimal sensitivity and specificity were thought to be81%and60%, respectively.
Conclusion:
This study found that history of stone.the product of stone length&width, hematuria are important impact factors for outcome of ESWL for kidney stones, whereas renal colic, stone location in ureter, and stone size have independent impacts on outcome of ESWL for ureter stones. Logistic stepwise regression prediction model and ANN were also constructed. In comparison with LR model, ANN with self-learning, parallel computing functions has a predictive ability. Although the meaning of predictive variables of ANN is hard to explain, it could still be used to predict ESWL efficacy as a powerful tool. ANN should contribute to the screening of patients more suitable for ESWL treatment. It may help fully share decision-making with patients, and reduce patients' care costs and economic burden.
泌尿系结石是泌尿外科的常见病与多发病,尤其在我国南方的部分省份,发病率较高。随着人们生活水平的提高,近年来上尿路结石的发病率明显增高。自上个世纪80年代问世以来,体外冲击波碎石(Extracorporeal Shockwave Lithotripsy,ESWL)经过三十年的技术改进和临床经验积累,使得很大一部分的上尿路结石患者免除开刀之苦,其治疗上尿路结石具有安全、有效、痛苦小、恢复快和费用不高的特点。然而,对于较大上尿路结石的治疗,可能需要多次碎石,一方面,可能增加肾脏不可逆损伤的风险；另一方面,排石过程中经常会伴随肾绞痛、发热、血尿、石街等并发症,从而不得不转为其它外科方法治疗,影响ESWL的疗效。临床实践证明,并不是所有的上尿路结石都适合ESWL治疗,有些结石ESWL无法击碎,有些结石ESWL击碎后病人无法自行排出。伴随ESWL不成功而带来的问题是,病人可能会为失败的ESWL承担经济、时间及痛苦就医经历的后果,从而使得ESWL的优势不能最大化。如果在体外冲击波碎石前,能对其治疗效果准确预测,一方面可以制定相对正确的治疗方案,避免减少病人不必要的痛苦和经济损失、降低医疗服务成本；另一方面也有利于在治疗前向病人充分告知,有利于医患的沟通和理解。
尽管对于ESWL治疗上尿路结石疗效预测的研究不少,然而,因受限于研究条件,存在以下不足：1)个别病例数较少,仅局限在方法学上的探索,并未广泛应用在临床实践中；2)受研究条件等限制,纳入的疗效影响因素不全面,因此预测的准确性还有待提高；3)部分研究对病例没有分层,将肾结石与输尿管结石合并在一起研究,临床应用意义不大。本研究分别运用logistic回归分析和人工神经网络建立ESWL治疗肾结石和输尿管结石的疗效预测模型,确定ESWL治疗上尿路结石疗效的重要影响因素和预测变量重要性评价,并对人工神经网络和Logistic回归分析方法、预测效果和优缺点进行比较,最后,确定预测效果较好的模型的工作概率分界值,使研究成果直接转化为临床应用。
方法
对325例肾结石患者和1,065例输尿管结石ESWL治疗前的临床资料如性别、尿路刺激症、治疗前血尿、肾绞痛、结石位置、结石患侧、年龄、身高、体重、病程时间、结石长径、结石宽径等影响因素和ESWL治疗结局进行回顾性分析。
首先,将ESWL治疗的肾结石和输尿管结石的病例资料分别进行无偏随机化分组,对于Logistic回归分析和建模,约70%的病例分配至训练样本,约30%病例分配至坚持样本；而对于人工神经网络,则是约56%的病例分配至训练样本,约14%的病例分配至检验样本,约30%的病例分配至坚持样本。
采用χ2检验对分类变量如性别、尿路刺激症、治疗前血尿、肾绞痛、结石位置、结石患侧等进行每个预测变量与应变量(ESWL治疗结局)关系的显著性检验。通过拟合单变量logistic回归取得连续预测变量(年龄、体重指数、病程时间、结石长径与短径的乘积)的显著性检验,初步找出对应变量(ESWL治疗结局)有影响的因素,再将上述预测变量显著性检验分析中P<0.25者,与其它重要预测变量一起,纳入多元模型的候选预测变量。然后采用logistic逐步回归分析(前向法：LR法)多因素分析,建立logistic回归预测模型,并将训练样本组和坚持样本组回代至此模型,得到ESWL治疗结局预测概率,绘制ROC曲线,计算曲线下面积(AUC),并计算敏感度,特异度和总准确度,评价预测模型的准确性。
建立3层前向型神经网络模型,隐含层设置为1层,输入层的参数为所有10项可能有临床意义的预测指标,预测因子设置依次为性别、尿路刺激症、治疗前血尿、肾绞痛、结石位置、结石患侧,预测协变量依次为年龄、体重指数、病程时间、结石长径与结石宽径的乘积(文中简称“结石大小”),标准化协变量。其中,性别编码为“男”=1、“女”=2；尿路刺激症、治疗前血尿、肾绞痛编码为‘有”=1、“无”=2；结石位置编码为“肾上盏”=1、“中盏”=2、“下盏”=3、“肾盂”=4、“混合”=5或“输尿管上段”=1、“中段”=2,“下段”=3。输出层为ESWL治疗结局,“成功”编码为1,“失败”编码为0。以前述“分区变量”分配病例样本,选择“自动体系结构选择”,隐含层中最小单位数为1,最大单位数为50,训练类型为“批处理”(肾结石组)或“袖珍批处理”(输尿管结石组),优化算法选用“调整的共轭梯度”(肾结石组)或“梯度下降”(输尿管结石组),间隔中心点为0,间隔偏移量为±0.5。运行神经网络后,获得ESWL治疗结局预测的拟概率,以0.50为预测分界值,计算预测的总准确率、灵敏度和特异度,绘制ROC(Receiver Operating Characteristic curve, ROC)曲线,计算曲线下面积(Area Under Curve,AUC),评价人工神经网络预测的准确性。
最后,从建模原理与方法、预测效果、优缺点三方面比较logistic回归预测模型和人工神经网络。
统计学软件包
应用IBM(?)公司出品的统计软件包SPSS20.0进行χ2检验,单变量Logistic回归和多元logistic分析和建立模型,并以其附带的神经网络模块中的多层感知器建立人工神经网络。采用Hosmer-Lemeshow进行logistic回归拟合优度检验,并以χ2检验进行模型的显著性检验。P值精确到小数点后3位,以P<0.05为有统计学差异。
用统计软件包Medcal(?)进行ROC曲线的绘制和ROC曲线下面积的比较,进行约登指数的计算和预测概率分界值的筛选。
结果
1) ESWL治疗肾结石组
共325例肾结石,最长随访3个月,碎石成功250例,转为其它方法治疗75例,总成功率76.9%。对全部肾结石患者性别、结石患侧、结石位置、尿路刺激症状、血尿或肾绞痛进行单因素分析,我们发现结石患侧、结石位置、尿路刺激症状、血尿对ESWL治疗结局有显著性影响。对本组患者年龄、体重指数、病程时间、结石大小进行单因素logistic回归拟合,结果排除体重指数,其余预测因素均纳入候选变量。
进一步用logistic逐步回归进行多因素分析,发现病程时间、血尿和结石大小,是ESWL治疗肾结石疗效的独立影响因素(P<0.05),其AOR(Adjusted OddsRatio)值(95%可信区间)依次是0.977(0.964-0.989)、12.388(3.44-44.565)、0.192(0.113-0.323)。
建立以训练样本为基础的logistsic预测模型。对预测模型进行χ2检验验证其显著性,χ2值为108.938,P<0.001,预测变量对应变量(ESWL碎石结局)有显著的解释能力。通过分类交互表计算Hosmer-Lemeshow拟合优度检验统计量,得到χ2=6.927,df=8,P=0.545,无统计学显著性差异,因此认为模型拟合观测数据良好。通过预测-观察分类表,对于模型预测的准确性进行评价。将训练样本和坚持样本的观察数据分别回代到模型,得到模型对训练样本和坚持样本的预测概率值,以0.5作为预测结果的分界值,结果显示模型对训练样本的灵敏度为94.4%,特异度63.3%,总体准确率为86.0%,而对坚持样本的灵敏度100%,特异度20.0%,总体准确率为88.4%。
人工神经网络自动剔除建模过程中典型的“冗余”单元后,输入层共建立19个单元。自动体系结构选择了建立一个隐含层,隐含层内共有6个单元,激活函数为hyperbolic tangent,输出层共有2个单元,激活函数为softmax。将预测变量重要性指标除以最大指标值,得到标准化的预测变量重要性排序,发现列于前五位的是：结石大小、病程时间、血尿、结石位置、体重指数。以0.5作为预测拟概率分界值,运用人工神经网络对全部样本进行预测,结果显示训练样本的敏感度、特异度和总体准确率为98.4%、72.5%和90.8%；检验样本的敏感度、特异度和总体准确率为97.4%、55.6%和89.6%；坚持样本的敏感度、特异度和总体准确率为93.3%、46.7%和86.5%。
Logistic回归模型的AUC为0.625,95%可信区间为0.525-0.718；人工神经网络AUC为0.856,95%可信区间为0.774-0.917,与AUC为0.5进行显著性检验,前者P值为0.122,后者为P<0.001。两者AUC差异的非参数显著性检验,z值为3.988,P=0.0001,两者AUC存在统计学上显著性差异,意味着logistic回归模型的预测效果差,ANN的预测效果优于logistic回归模型。
计算约登指数并权衡敏感度与特异度后,发现概率分界值为0.595时,肾结石ESWL疗效预测的ANN模型的敏感度和特异度达到较为理想状态,分别为92%和60%。
2) ESWL治疗输尿管结石组
共纳入1065例输尿管结石,最长随访3个月,碎石成功874例,转为其它方法治疗191例,总成功率82.1%。用χ2检验对本组患者性别、结石患侧、结石位置、尿路刺激症状、血尿或肾绞痛进行单因素分析,按着P<0.25的预测变量筛选标准,我们发现除治疗前是否出现血尿外,其余预测因素对ESWL治疗结局有显著性影响。对本组患者年龄、体重指数、病程时间、结石大小进行单因素logistic回归逐一拟合,均纳入候选预测变量。
用logistic回归对进行多因素分析,结果显示治疗前肾绞痛、结石位置(输尿管上段、输尿管中段)结石大小为ESWL治疗输尿管结石疗效的独立影响因素,其AOR值(95%可信区间)分别是1.508(0.999-2.277)、0.651(0.391-1.086)、0.374(0.191-0.731)、0.246(0.152-0.396)。Logistic回归预测模型的χ2值为54.460,P值<0.001,提示纳入模型的预测变量对治疗结局有显著的解释能力。预测模型的拟合优度通过Hosmer-Lemeshow检验,显示模型拟合程度尚好(χ2=8.406,df=8,P=0.395)。将训练样本和坚持样本分别回代至预测模型,得到对训练样本和坚持样本进行预测概率值,以0.5作为预测概率分界值,结果显示训练样本灵敏度98.1%,特异度4.2%,总体准确率为82.9%。坚持样本灵敏度99.3%,特异度11.3%,总体准确率为84.7%。
人工神经网络自动剔除建模过程中典型的“冗余”单元后,输入层共建立17个单元。自动体系结构选择了建立一个隐含层,隐含层内共有5个单元,激活函数为hyperbolic tangent,输出层共有2个单元,激活函数为softmax。将预测变量重要性指标除以最大指标值,得到标准化的预测变量重要性排序,结石大小、结石位置、病程时间、年龄和体重指数列于前五位。
应用人工神经网络对全部样本进行预测,以0.5作为预测拟概率分界值,结果显示训练样本的敏感度、特异度和总体准确率分别为98.8%,12.7%和84.0%；检验样本的敏感度、特异度和总体准确率分别为99.2%,16.7%和89.3%；坚持样本的敏感度、特异度和总体准确率分别为97.8%,9.4%和83.2%。
Logistic回归模型的AUC为0.729,人工神经网络的AUC为0.751,与AUC为0.5进行显著性检验,前者P值<0.001,95%可信区间为0.676-0.777,后者为P值<0.001,95%可信区间为0.700-0.797,借助统计软件包MedCalc(?)对AUC进行非参数显著性检验,计算z统计量为0.750,对应的P值为0.4534,即两种预测模型的AUC面积在统计学上无显著性差异,换言之,输尿管结石ESWL疗效的logistic回归模型和ANN模型的预测效果相差不大。权衡敏感度与特异度后,确定概率分界值为0.769时,ESWL治疗肾结石疗效预测的ANN模型的敏感度和特异度达到较为理想状态,分别为81%和60%。
结论
本研究发现,患者病程时间、结石大小、治疗前血尿是影响肾结石ESWL疗效的独立影响因素,而影响输尿管结石的ESWL疗效的重要因素为性别、肾绞痛、结石位置和结石大小。和Logistic逐步回归法建立的预测模型相比较,人工神经网络具有自学习、并行计算的功能,虽对预测变量的解释性不如logistic回归模型,但预测效果较好,仍可做为预测ESWL成功率的有利工具,有助于筛选更加适用ESWL治疗的患者,有利于患者充分知情,与患者共同制定治疗方案,减轻患者医疗风险和经济负担。
Background and Objection:
Urinary stone is a common disorder of urology, and the prevalence of urolithiasis is higher in some provinces of southern China. Following the improvement of nutritional condition, the incidence of upper urinary tract stone became significantly higher in the recent decade. Since the advent in the early80s of the last century, extracorporeal shock wave lithotripsy (ESWL)cured numerous patients with upper urinary tract stones, who had to undergo surgery before. ESWL has been proved to be safe, effective, less painful, rapid to recovery and inexpensivedue to its minimally invasive character, and low morbidity. However, for larger upper urinary tract stones, ESWL may need to repeat several times or combine others methods of treatment. But repetition of ESWL may lead to irreversible damage to kidney. Furthermore, the process of stone fragments removing is often accompanied by some complications such as renal colic, fever, hematuria, steinstrasse, which may also result in conversion to surgery. These morbidities may compromise the clinical outcome of ESWL-treated calculi, thus not all upper urinary tract calculi are suitable for ESWL.The patient would pay for the consequences of unsuccessful ESWL with a cost of money, time, and an experience of distressful medical treatment.
If the outcome of ESWL can be predicted, on one hand, the clinicians could develop relatively correct strategy to avoid the patient's unnecessary cost, to reduce the cost of medical services; On the other hand, the prediction could help patients be well informed and help doctors share the decision-making with patients.
In this study, logistic regression (LR) analysis and artificial neural network (ANN) were used to establish the predictive model of ESWL for renal and ureteral calculi, respectively.Under logistic regression models, the important impact factors influencing outcome of ESWL for upper urinary tract stones were determined. By ANN, the importance of predictor variables was evaluated. A comparative study afterwards was done between LR model and ANN to compare the accuracy of prediction and pros&cons between these two models of prediction. Eventually the cut-off values of optimal probabilities were identified to facilitate the clinical application.
Methods and materials
Pre-ESWL clinical data of325cases of kidney stones treated with ESWL and those of1065cases of ureteral calculi were included retrospectively. The information of gender, urinary irritation symptom, hematuria, renal colic, stone location, stone side, age, height, weight, history of stone, stone length, stone width was collected.
All cases of kidney stones and ureteral stones were grouped separately with a randomized method. For LR analysis and modeling, about70%of cases were assigned to training-sample group, and approximate30percent of cases were assigned to holdout-sample group. For ANN, about56%of the cases were assigned to training-sample group, and about14%of the cases assigned to test-sample group, about30%of cases were assigned to the holdout-sample group.
χ2test was performed for the significance test of relationship between the ESWL outcome and every categorical variable (gender, urinary irritation symptom, hematuria, renal colic, stone location, stone side).The significant test of continuous predictive variables (age, body mass index, history of stone, the product of stone length&width) were done by univariate logistic regression to initially identify the corresponding influential factors of ESWL outcome.
Then all the predictive variables which have P<0.25, together with other important predictive variables were included as candidate predictive variables for multivariate analysis. Thereafter logistic stepwise regression analysis (forward:LR) was performed. The training sample and the holdout sample were respectively substituted to the LR model, and the respective predictive probabilities for ESWL outcome were obtained. Then the area under curve (AUC), sensitivity, specificity and were calculated to evaluate the accuracy of prediction after drawing receiver operating characteristic curve (ROC).
Three-layer forward neural network model was constructed. Hidden layer was set to1layer; the parameters of the input layer comprise all10predictive variables. Predictive factors were set to be gender, urinary irritation symptom, hematuria, renal colic, stone location, and stone side. Predictive covariates were age, BMI, history of stone, stone size. Value of gender was coded by male=1, female=2. And the value of urinary irritation symptom, hematuria, renal colic were set to yes=1, no=2. In the cases of kidney stone, location of stone in the kidney was set to the upper calyces=1, the middle calyces=2, the lower calyces=3, the pelvis=4, combined location=5. In the cases of ureter stone, it was set to upper ureter=1, middle ureter=2, lower ureter=3.
The output layer is ESWL-treated calculi outcome. Successful and failed outcome is set to1and0, respectively. All cases were assigned randomly basing on partitioning variable aforementioned."Automatic architecture selection" was chosen, implying that the minimum number of units in hidden layer is1, and the maximum number is50. The type of training was chosen as "batch"(for renal calculi sample) or "mini-batch"(for ureteral calculi sample),"optimization algorithm selection"(for renal calculi sample) and "scaled conjugate gradient"(for ureteral calculi sample). Initial Lambda value is0.0000005, and the initial Sigma value of is0.00005, the interval center is0, the interval offset is±0.5.
The predictive pseudo probabilities of ESWL outcome were obtained.0.50was set as the cut-off value of predictive pseudo probabilities, and the area under curve (AUC), sensitivity, and specificity were calculated to evaluate the accuracy of prediction after drawing receiver operating characteristic curve (ROC). The efficacy together with advantages&disadvantages of LR predictive model and ANN were then evaluated and compared.
The statistical package of SPSS20.0published by IBM(?) were used statistically, by which χ2test, univariate logistic regression, multivariate logistic analysis and modeling were performed. Hosmer-Lemeshow goodness of fit test for LR model and the χ2test are used for significance test of LR model. P value is accurate to three decimal. P<0.05is for significant difference. The statistical package of Medcalc(?) was used for drawing of ROC curve and the comparison of AUC and for calculation of Youden index, then the cut-offs value of optimal predictive probabilities were identified.
Results:
A. Prediction of ESWL outcome for kidney stones cases
Among a total of325cases of kidney stones,250cases (76.9%) were free of stones at3months.Post-ESWL auxiliary treatment was required in75cases who failed to respond to the ESWL treatment. The longest follow-up attained three months.
The success rate of ESWL was significantly affected by stones side, stone location, urinary irritation symptom, and hematuria.Additionally, after further LR multivariate analysis to the training-sample, history of stone, hematuria and the product of stone length&width were found to be3independent impact factors of the outcome of ESWL treatment of kidney stones (P<0.05) with AOR (Adjusted Odds Ratio)(95%confidence interval) being0.977(0.964-0.989),12.388(3.443-44.565),0.192(0.113-0.323), respectively.
χ2value of LR prediction model is108.938(P<0.001), which means the predictive variables have significant explanatory power for the dependent variable (ESWL outcome). The result of Hosmer-Lemeshow goodness of fit test indicated that the prediction model could represent the data well (χ2=6.927, df=8, P=0.545).
To evaluate the accuracy of prediction of LR model, the prediction-observation cross classification table was employed. The cut-off value of probabilitywas set at0.5. The results showed that the training sample's sensitivity, specificity, overall accuracy rate were94.4%63.3%86.0%, respectively. The sensitivity, specificity, overall accuracy rate of holdout samples were100%,20.0%,88.4%, respectively.
The ANN automatically removed the typical modeling process "redundant" unit, and established an input layer with of19units, a hidden layer of6units and an output layer of2units. The activation function of input was set as "hyperbolic tangent", The activation function of output was set as "softmax". The order of importance of predictive variables showed that stone size, history of stone, hematuria, stone location were listed on the top five. At0.5of cutoff value of probability, the prediction of ANN showed that the sensitivity, specificity, overall accuracy rate of the training sample were98.4%,72.5%and90.8%,respectively; Those of the testing sample were97.4%,55.6%and89.6%. Those of holdout sample were93.3%,46.7%and86.5%.
The AUC of the LR model is0.625(95%confidence interval:0.525-0.718), whereas ANN model is0.856(95%confidence interval:0.774-0.917). Comparing with AUC=0.5, the former's P value is0.122, and the latter's P value0.001. The medical statistics Packages Medcalc was employed for testing the difference of two AUCs, the z value is3.988, P=0.0001, which means there exist statistically significant differences between the AUCs of two models. That is to say, the prediction of ANN model has higher ability than that of the LR model.
The optimal cutoff value of probability of ANN was identified to0.595, with consideration of balancing the sensitivity and specificity. At this cutoff value, the sensitivity and specificity of ANN model were thought to be92%and60%, respectively.
Prediction of ESWL outcome for ureter stones cases
Among a total of1,065cases of ureter stones,874cases (82.1%) were free of stones at3months,191cases failed of ESWL. All failed cased were converted to other auxiliarytreatments. The longest follow-up duration reached3months. Gender, stone side, stone location, urinary irritation symptom, renal colic were found to have significant impacts on the outcome of ESWL. Univariate logistic regressions indicated age, BMI, history of stone, stone size were among the significant contributors to the success rate of ESWL.
Further using LR multivariate analysis to training samples, renal colic, stone location (upper part of ureter and middle part of ureter), stone size were found to be4independent impact factors of outcome of ESWL treatment for ureter stones, with AOR (95%confidence interval) were1.508(0.999-2.277),0.651(0.391-1.086), 0.374(0.191-0.731),0.246(0.151-0.396), respectively.
χ2test was applied to verify the significance of LR prediction model, χ2value was54.460(P<０.001), which means these predictive variables have significant explanatory power for the dependent variable (ESWL outcome). Hosmer-Lemeshow goodness of fit indicated that there was no statistically significant difference (χ2=8.406,df=8,P=0.395).
To evaluate the accuracy of prediction of LR model, the prediction-observation cross classification table was employed. The cut-off value is set at0.5. The results showed that the training sample's sensitivity, specificity, overall accuracy rate were98.1%,4.2%,82.9%, respectively, meanwhile the sensitivity, specificity, overall accuracy rate of the holdout samples were99.3%,11.3%,84.7%, respectively.
The ANN automatically removed the typical modeling process "redundant" unit, and established an input layer with of17units, a hidden layer of5units and an output layer of2units."Hyperbolic tangent" was selected as the activation function of input. The activation function of output was "softmax". The order of importance of predictive variables showed that stone size, stone location, history of stone time, age and BMI were listed on the top five. Atthe cutoff value of0.5, the prediction of ANN showed that the sensitivity, specificity, overall accuracy rate of the training sample were98.8%,12.7%,84.0%.respectively; Those of the testing sample were99.2%,16.7%,89.3%. Those of the holdout sample were97.8%,9.4%,83.2%.
The AUC of the logistic regression model was0.729(95% confidence interval:0.676-0.777), whereas ANN model was0.751(95% confidence interval:0.700-0.797). Comparing with AUC=0.5, theirs P values were less than0.001. With the medical statistics Packages Medcalc(?) for non-parametric tests, the z value is0.750, P=0.4534, which means there is no statistically significant differences between the two AUC. That is to say, the prediction of ANN model may have the same predictive efficacy as that of the LR model.
The cutoff value of probabilities of ANN was identified to0.7694, in consideration of balancing the sensitivity and specificity. The optimal sensitivity and specificity were thought to be81%and60%, respectively.
Conclusion:
This study found that history of stone.the product of stone length&width, hematuria are important impact factors for outcome of ESWL for kidney stones, whereas renal colic, stone location in ureter, and stone size have independent impacts on outcome of ESWL for ureter stones. Logistic stepwise regression prediction model and ANN were also constructed. In comparison with LR model, ANN with self-learning, parallel computing functions has a predictive ability. Although the meaning of predictive variables of ANN is hard to explain, it could still be used to predict ESWL efficacy as a powerful tool. ANN should contribute to the screening of patients more suitable for ESWL treatment. It may help fully share decision-making with patients, and reduce patients' care costs and economic burden.
引文
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