Non-Parametric Estimation of ROC Curves in the Absence of a Gold Standard

In evaluation of diagnostic accuracy of tests, a gold standard on the disease status is required. However, in many complex diseases, it is impossible or unethical to obtain such the gold standard. If an imperfect standard is used as if it were a gold standard, the estimated accuracy of the tests would be biased. This type of bias is called imperfect gold standard bias. In this paper we develop a maximum likelihood (ML) method for estimating ROC curves and their areas of ordinal-scale tests in the absence of a gold standard. Our simulation study shows the proposed estimates for the ROC curve areas have good finite-sample properties in terms of bias and mean squared error (MSE). Further simulation studies show that our non-parametric approach is comparable to a parametric method without specific model assumptions, and is easier to implement. Finally, we illustrate the application of the proposed method in a real clinical study on assessing the accuracy of seven specific pathologists in detecting carcinoma in situ of the uterine cervix.