Nonparametric analysis for the ROC areas of two diagnostic tests in the presence of nonignorable verification bias

Abstract A paired design is often used to evaluate the accuracies of competing diagnostic tests. One common problem in a paired design is verification bias which occurs when some patients do not receive disease verification and when the reason for verification depends on the test results and other factors. Most of the existing methods for verification bias correction assume the verification process is ignorable, which means that the probability of verifying a patient depends only on the observed covariates, but not on the unobserved disease status of the patient. In this paper, we develop a bias correction procedure without assuming ignorability of the verification mechanism. As far as we know, this proposed method is the first attempt to combine nonignorable verification with estimation of the ROC areas. At issue is the possible existence of multiple local maxima and boundary solutions for the maximum likelihood (ML) equations, which can complicate the computation of the ML estimates. To deal with this computational difficulty, we propose a profile method combined with the EM algorithm to find the global ML estimators for the parameters of interest under a proposed nonignorable verification model. Furthermore, we also find a simple solution to the boundary point problem. After obtaining the ML estimates, we propose likelihood-based inferences on the relative accuracy of two diagnostic tests. Another issue in the analysis is the goodness-of-fit of the proposed nonignorable model for the verification mechanism. We propose to use a bootstrap-based goodness-of-fit test for the proposed nonignorable model. Finally, we apply our method to data from a real study that has motivated this research. In this example, the aim of our analysis is to compare the relative accuracy of MRI and CT imaging in detecting advanced stage pancreatic cancer.