Study On The Theory And Application Of Logistic Regression Model In The ROC Curve Based On Stratified Control Data

Logistic regression model is widely used in medical research,especially in the research of investigating the diagnostic performance of a factor,namely ROC(Receiver Operating Characteristic)curve.However,in the common diagnostic test,when the diagnostic performance of a certain factor is studied,it is often affected by the covariates.In this situation,we should make full use of the auxiliary information of the covariates.For example,when studying the diagnostic performance of disease factors in a certain area,due to the limited sample data available and the limited information collected,the statistical inference results obtained from the existing data are often inaccurate.At this time,we can rely on the relevant data of this disease factor in the existing adjacent areas.Or when studying the diagnostic performance of a population's disease factor,we can consider the diagnostic performance of the factor in different age groups.In order to effectively use information,this master dissertation maily studies the statistical modeling theory,method of ROC curve based on logistic regression model of stratified control data and its application.The following results are obtained.In this master dissertation,we learn from the research ideas and methods of the ROC curve in the logistic regression model with non-stratified control data,and study the theory and application of ROC curve based on logistic regression model of stratified control data.We give two logistic regression models of stratified control data using a hierarchical approach to the existing information and experimental information,because the influence of exposure factors between different layers on the disease may not always be consistent.The one model is the independent logistic regression model with inconsistent regression coefficients between each layer,namely the logistic regression model I.Another is that there is only a confounding effect between exposure factors and diseases between different layers,namely the logistic regression model II with consistent regression coefficients between each layer.We give the estimation methods of covariate adjusted ROC curve in two regression models respectively,including parameter estimation,non parametric estimation and semi parametric estimation,and give the asymptotic theory and proof of semi parametric estimation of covariate adjusted ROC curve;It is proved that the asymptotic efficiency of semi parametric estimation of ROC curve adjusted by covariates in model I is better than that of non parametric estimation.Through numerical simulation,the semi parametric bootstrap interval estimation of the area under the covariate adjusted ROC curve in model I and model II and the three kinds of estimation of the area under the covariate adjusted ROC curve are given,and the conclusion that the semi parametric estimation is superior to the general non parametric estimation and general parameter estimation is obtained.Apply the conclusion to practice.