Semiparametric Estimation Method For PAUC And Its Application

ROC curves are often used in the field of medical diagnosis to compare the performance of different diagnostic models.In order to evaluate the accuracy of diagnostic models more directly,researchers proposed area under the curve to describe it.However,in practice,the AUC values of two different models may be equal.In addition,diagnostic models need to maintain high accuracy while having a lower false positive rate.Therefore,some researchers have proposed using partial area under the curve to evaluate the accuracy of diagnostic models.How to effectively estimate pAUC has become a hot topic in medical statistical research.Currently,researchers have estimated pAUC based on different estimation methods and achieved certain results.But there are still shortcomings such as insufficient accuracy or robustness.In order to further improve the accuracy of pAUC estimation and medical diagnostic models,two semi-parametric estimation methods for pAUC based on density ratio model are proposed.Firstly,based on the density ratio model,a semi-parametric maximum likelihood estimator for pAUC is constructed with the semi-parametric maximum likelihood estimation method.The statistical performance of this estimator is analyzed using the large sample theory,and it is found that it has higher asymptotic efficiency than the existing non-parametric estimator for pAUC;Secondly,the semi-parametric estimator for pAUC is improved,which not only has good properties such as consistent asymptotic normality,but also has a simpler mathematical expression.In addition,based on the research on the statistical properties of semi-parametric estimators for pAUC,combined with relevant statistical theories such as empirical likelihood,this thesis proposes various high-performance methods for constructing pAUC semi-parametric confidence intervals.Then,in order to illustrate the reliability and accuracy of the proposed pAUC semi-parametric estimation method,the performance of different pAUC semi-parametric confidence intervals in practical applications is simulated,and compared with the existing higher accuracy pAUC confidence intervals constructed based on non-parametric method.Given the reliability,the accuracy of the pAUC confidence intervals constructed by proposed semi-parametric methods are higher.Finally,in order to make semi-parametric estimation methods for pAUC applicable to the screening of medical diagnostic models,a new method for screening models is provided by combining the pAUC semi-parametric estimation methods with existing methods for selecting models.Some new diagnostic models of breast cancer are obtained by the proposed method,and the test results show that these diagnostic models have higher prediction accuracy in practical applications.Therefore,the new method proposed in this paper can be applied to screening medical diagnostic models with high accuracy.