Nonparametric estimation of ROC surfaces under verification bias

Verification bias is a well known problem that can affect the statistical evaluation of the predictive ability of a diagnostic test when the true disease status is unknown for some of the patients under study. In this paper, we deal with the assessment of continuous diagnostic tests when an (ordinal) three-class disease status is considered and propose a fully nonparametric verification bias-corrected estimator of the ROC surface based on nearest-neighbor imputation. Consistency and asymptotic normality of the proposed estimator are proved under the missing at random assumption, and its nite sample behavior is investigated by means of Monte Carlo experiments. Variance estimation is also discussed and an illustrative example is presented.