Nonparametric Estimation of ROC Surfaces Under Verification Bias

Verification bias is a well known problem when the predictive ability of a diagnostic test has to be evaluated. In this paper, we discuss how to assess the accuracy of continuous-scale diagnostic tests in the presence of verification bias, when a three-class disease status is considered. In particular, we propose a fully nonparametric verification bias-corrected estimator of the ROC surface. 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 estimator are proved and its finite sample behavior is investigated by means of several Monte Carlo simulation studies. Variance estimation is also discussed and an illustrative example is presented.