A model for adjusting for nonignorable verification bias in estimation of the ROC curve and its area with likelihood-based approach.

In estimation of the ROC curve, when the true disease status is subject to nonignorable missingness, the observed likelihood involves the missing mechanism given by a selection model. In this article, we proposed a likelihood-based approach to estimate the ROC curve and the area under the ROC curve when the verification bias is nonignorable. We specified a parametric disease model in order to make the nonignorable selection model identifiable. With the estimated verification and disease probabilities, we constructed four types of empirical estimates of the ROC curve and its area based on imputation and reweighting methods. In practice, a reasonably large sample size is required to estimate the nonignorable selection model in our settings. Simulation studies showed that all four estimators of ROC area performed well, and imputation estimators were generally more efficient than the other estimators proposed. We applied the proposed method to a data set from research in Alzheimer's disease.