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The volume under the receiver operating characteristic surface (VUS) isuseful for measuring the overall accuracy of a diagnostic test when thepossible disease status belongs to one of three ordered categories. In medicalstudies, the VUS of a new test is typically estimated through a sample ofmeasurements obtained by some suitable sample of patients. However, in manycases, only a subset of such patients has the true disease status assessed by agold standard test. In this paper, for a continuous-scale diagnostic test, wepropose four estimators of the VUS which accommodate for nonignorablemissingness of the disease status. The estimators are based on a parametricmodel which jointly describes both the disease and the verification process.Identifiability of the model is discussed. Consistency and asymptotic normalityof the proposed estimators are shown, and variance estimation is discussed. Thefinite-sample behavior is investigated by means of simulation experiments. Anillustration is provided.

Estimation of the Volume Under the ROC Surface in Presence of Nonignorable Verification Bias