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Semiparametric estimation of the covariate-specific ROC curve in presence of ignorable verification bias. (English) Zbl 1226.62031
Summary: Covariate-specific receiver operating characteristic (ROC) curves are often used to evaluate the classification accuracy of a medical diagnostic test or a biomarker, when the accuracy of the test is associated with certain covariates. In many large-scale screening tests, the gold standard is subject to missingness due to high cost or harmfulness to the patient. We propose a semiparametric estimation of the covariate-specific ROC curves with a partial missing gold standard. A location-scale model is constructed for the test result to model the covariates’ effect, but the residual distributions are left unspecified. Thus the baseline and link functions of the ROC curve both have flexible shapes. With the gold standard missing at random (MAR) assumption, we consider weighted estimating equations for the location-scale parameters, and weighted kernel estimating equations for the residual distributions. Three ROC curve estimators are proposed and compared, namely, imputation-based, inverse probability weighted, and doubly robust estimators. We derive the asymptotic normality of the estimated ROC curve, as well as the analytical form of the standard error estimator. The proposed method is motivated and applied to the data in an Alzheimer’s disease research.

62G05 Nonparametric estimation
62P10 Applications of statistics to biology and medical sciences; meta analysis
92C50 Medical applications (general)
62G20 Asymptotic properties of nonparametric inference
62N02 Estimation in survival analysis and censored data
65C60 Computational problems in statistics (MSC2010)
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