惩罚三项Logit模型区分丙型肝炎患者的临床分期  

Penalized Trinomial Logit Models Distinguish Clinical Stages in Patients with Hepatitis

作　　者：胡雪梅[1,2] 杨俊文 HU XUEMEI;YANG JUNWEN(School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing Key Laboratory of Social Economy and Applied Statistics;Research Institute for Digital Economy and Interdisciplinary Sciences,School of Business Administration,Southwestern University of Finance and Economics;School of Mathematics and Statistics,Chongqing Technology and Business University)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]经济社会应用统计重庆市重点实验室,重庆400067 [3]西南财经大学数字经济与交叉科学研究院,西南财经大学工商管理学院,成都611130

出　　处：《应用数学学报》2024年第1期154-173,共20页Acta Mathematicae Applicatae Sinica

基　　金：重庆市教委科学技术研究计划重大项目(KJZD-M202100801);重庆市社科规划项目(2019WT59);重庆市科委基础研究与前沿探索一般项目(cstc.2018jcyjA2073);重庆市第五批高等学校优秀人才支持计划(68021900601);重庆市“统计学”研究生导师团队(yds183002);社会经济应用统计重庆市重点实验室平台开放项目(KFJJ2022056);重庆工商大学数理统计团队资助项目(ZDPTTD201906)。

摘　　要：丙型病毒性肝炎(简称丙型肝炎或丙肝)是一种由丙型肝炎病毒(HCV)感染引起的病毒性肝炎,可导致肝脏慢性炎症坏死和纤维化,部分患者可发展为肝硬化甚至肝细胞癌(HCC).本文利用丙型肝炎数据建立惩罚三项logit模型诊断患者的疾病分期:首先选取患者的12项生理指标作为预测向量,丙型肝炎的三种疾病分期作为响应变量;接着利用70%的数据作为训练集学习LASSO/Ridge/ENet惩罚三项logit模型,得到模型的参数估计和概率估计;再利用30%的数据作为测试集,结合三类混淆矩阵,ROC(receiver operating characteristic)曲面,HUM(hypervolume under the ROC manifold),PDI(polytomous discrimination index)和Kappa(Cohen’s kappa coefficient)等评估疾病分期的预测精度;最后引入人工神经网络(ANN),支持向量机(SVM)和随机森林(RF)等机器学习方法和惩罚三项logit模型进行比较,发现惩罚三项logit模型的三类分类预测表现最好,不仅能够进一步提高疾病分期的诊断精度,而且可以降低丙型肝炎的检测成本.Viral hepatitis C(simply referred to as hepatitis C)is a form of viral hepatitis caused by infection with the hepatitis C Virus(HCV).HCV will cause chronic inflammation,necrosis,and fibrosis of the liver,some patients may develop cirrhosis and hepatocellular carcinoma(HCC).In this paper we take advantage of the hepatitis data set to construct penalized trinomial logit models to diagnose the disease stages of patients.Firstly,we select 12 physiological indicators of patients as a predictor vector,and choose 3 disease stages of hepatitis C as the response variable.Secondly,we apply the 70%data as the training set to learn LASSO/Ridge/ENet penalized trinomial logit model,and take advantage of the coordinate descent algorithm to complete variable selection and obtain parameter estimations.Thirdly,we apply the remaining 30%data as the testing set,and combine three-class confusion matrix,the ROC(receiver operating characteristic)surface,HUM(hypervolume under the ROC manifold),PDI(polytomous discrimination index)to assess the prediction accuracy to disease stages.Finally,we introduce some machine learning methods such as artificial neural network(ANN),support vector machine(SVM)and random forest(RF)to compare with the proposed penalized trinomial logit models,and found that penalized trinomial logit models possess the best three-class prediction performance.They can not only improve the diagnostic accuracy to disease stages,but also reduce the cost of hepatitis C detection.

关 键 词：丙型肝炎 疾病分期 惩罚三项logit模型 贝叶斯分类器 机器学习方法 

分 类 号：O212.4[理学—概率论与数理统计] R512.63[理学—数学]