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Title: Nonparametric estimation of ROC surfaces under verification bias Authors:  Duc Khanh To - University of Padova (Italy) [presenting]
Monica Chiogna - University of Padua (Italy)
Gianfranco Adimari - University of Padua (Italy)
Abstract: In three-class diagnostic problems, ROC surfaces are commonly used for the evaluation of diagnostic markers. When all subjects are verified, the ROC surface could be constructed by nonparametric estimates of true class fractions. However, sometimes it is not feasible to obtain disease status verification for all study subjects, due to the expensiveness or invasiveness of the gold standard test. In such situations, the estimates based only on the verified subjects are typically biased. This bias is known as verification bias. In the last fifteen years, various methods have been developed to deal with the verification bias problem, most of which assume that the true disease status, if missing, is missing at random. However, the majority of previous work treated the issue of correcting for the verification bias in ROC curves, whereas ROC surface analysis is very scarcely considered in the statistical literature. We discuss how to construct the ROC surfaces of continuous-scale diagnostic tests in the presence of verification bias. Our approach is based on nearest-neighbor imputation and adopts generic smooth regression models for both the disease and the verification processes. Consistency and asymptotic normality of the proposed estimators are proved. An illustrative example is also presented.