Mean score equation and instrumental variables: Another look at estimating the volume under the receiver operating characteristic surface when data are missing not at random

Evaluation of accuracy of diagnostic tests is frequently undertaken under nonignorable (NI) verification bias. Here, we discuss an approach, based on a mean score equation, aimed to estimate the volume under the receiver operating characteristic (ROC) surface of a diagnostic test under NI verification bias. The proposed approach rests on a parametric regression model for the verification process, which accommodates for possible NI missingness in the disease status of sample subjects, and may employ instrumental variables, to help avoid possible identifiability problems. The solution of the mean score equation derived from the verification model requires to preliminarily estimate the parameters of a model for the disease process, whose specification is limited to verified subjects. Verification bias-corrected estimators, an alternative to those recently proposed in the literature and based on a full likelihood approach, are obtained from the estimated verification and disease probabilities. Consistency and asymptotic normality of the new estimators are established. Simulation experiments are conducted to evaluate their finite-sample performances, and an application to a dataset from a research on epithelial ovarian cancer is presented. Although the narrative is driven by the three-class case, the extension to high-dimensional ROC analysis is also presented.