Nonparametric receiver operating characteristic curve analysis with an imperfect gold standard

This article addresses the challenge of estimating receiver operating characteristic (ROC) curves and the areas under these curves (AUC) in the context of an imperfect gold standard, a common issue in diagnostic accuracy studies. We delve into the nonparametric identification and estimation of ROC curves and AUCs when the reference standard for disease status is prone to error. Our approach hinges on the known or estimable accuracy of this imperfect reference standard and the conditional independent assumption, under which we demonstrate the identifiability of ROC curves and propose a nonparametric estimation method. In cases where the accuracy of the imperfect reference standard remains unknown, we establish that while ROC curves are unidentifiable, the sign of the difference between two AUCs is identifiable. This insight leads us to develop a hypothesis-testing method for assessing the relative superiority of AUCs. Compared to the existing methods, the proposed methods are nonparametric so that they do not rely on the parametric model assumptions. In addition, they are applicable to both the ROC/AUC analysis of continuous biomarkers and the AUC analysis of ordinal biomarkers. Our theoretical results and simulation studies validate the proposed methods, which we further illustrate through application in two real-world diagnostic studies.

Kernel density estimation in mixture models with known mixture proportions

In this article, we consider the density estimation for data with a mixture structure, where the component densities are assumed unknown, but for each observation, the probabilities of its membership to the subpopulations are known or estimable from other resources. Data of this kind arise from practice and have wide applications. Motivated from the classical kernel density estimation method for a single population, we propose a weighted kernel density estimation method to estimate the component density functions nonparametrically. Within the framework of the EM algorithm, we derive an algorithm that computes our proposed estimates effectively. Via extensive simulation studies, we demonstrate that our methods outperform the existing methods in most occasions. We further compare our methods with existing methods by real data examples.