Estimation Of ROC Curve In The Presence Of Missing Biomarker Values

In medical studies,the receiver operating characteristic curve(ROC curve)based on specificity and sensitivity is often used to evaluate the intrinsic accuracy of a diagnostic test.Due to various reasons in the experiment,measurements of the diagnostic test and variable related to the diagnostic test are subject to missing.Under the literature of ROC curve with missing data,most literature considered the issue of missing of the subject's disease status,while few literature considered the issue of missing of the biomarker value.Therefore,the estimation of ROC curve will be studied in the presence of missing biomarker values in the dissertation.To estimate a ROC curve directly only with complete observation data may result in biased and incorrect diagnostic accuracy of the test.In this dissertation,these approaches based on the inverse probability weighting,imputation,augmented inverse probability weighting are developed to estimate ROC curve,the area under the ROC curve(AUC),and the covariate-specific time-dependent ROC curve when missing biomarker values are missing at random and nonignorable missing.The main content of this dissertation is summarized as follows:1.This dissertation considers statistical inference for ROC curve of the high specifity in the presence of missing biomarker values by utilizing estimating equations(EEs)together with smoothed empirical likelihood(SEL).Three approaches are developed to estimate ROC curve and construct its SEL-based confidence intervals based on the kernel-assisted EE imputation,multiple imputation and hybrid imputation combining the inverse probability weighted imputation and multiple imputation.Under some regularity conditions,It is shown that asymptotic properties of the proposed maximum SEL estimators for ROC curve.Simulation studies and a real example are conducted to investigate the performance of the proposed SEL approaches.Empirical results show that the hybrid imputation method behaves better than the kernel-assisted imputation and multiple imputation methods,and the proposed three SEL methods outperform existing nonparametric method.2.The area under the ROC curve is a widely utilized diagnostic accuracy index in diagnostic medicine.Existing approaches to estimate the area under the ROC curve have been developed for the fully observed data or ignorable missing data.However,in diagnostic tests,biomarker values may be subject to nonignorable missing for some subjects.To this end,rather than the widely conducted sensitivity analysis on the area under the ROC curve estimation in the presence of nonignorable missing biomarker values,this dissertation considers an exponential tilting model for the propensity score function,and addresses the identifiability issue of the nonignorable missing by the idea of instrumental variables.Then,two new estimators based on the nonparametric imputation technique and the augment inverse probability weighting method are proposed to estimate the area under the ROC curve.Under some regularity conditions,the asymptotic properties of the two proposed estimators are established,and an attractive feature that the two estimators have the same asymptotic variance is obtained.Several simulation studies and a real example are conducted to investigate the finite sample performance of the proposed estimators,and verify the effectiveness and feasibility of the proposed estimators.3.The main purpose of this dissertation is to consider statistical inference for covariate-specific time-dependent ROC curves with nonignorable missing continuous biomarker values.A Cox proportional hazards model for the failure time conditional on the continuous biomarker and the covariates,and a semiparametric location model for the biomarker conditional on the covariates,are considered to estimate the covariate-specific time-dependent incident ROC curve and covariate-specific time-dependent cumulative ROC curve through the inverse probability weighting and augmented inverse probability weighting under missing not at random,the estimation of confidence intervals is also developed.Finally,two simulation studies and a real example are conducted to assess the performance of our proposed approaches,and verify the effectiveness and feasibility of the proposed estimators.