Interval estimation in three-class receiver operating characteristic analysis: A fairly general approach based on the empirical likelihood.

The empirical likelihood is a powerful nonparametric tool, that emulates its parametric counterpart-the parametric likelihood-preserving many of its large-sample properties. This article tackles the problem of assessing the discriminatory power of three-class diagnostic tests from an empirical likelihood perspective. In particular, we concentrate on interval estimation in a three-class receiver operating characteristic analysis, where a variety of inferential tasks could be of interest. We present novel theoretical results and tailored techniques studied to efficiently solve some of such tasks. Extensive simulation experiments are provided in a supporting role, with our novel proposals compared to existing competitors, when possible. It emerges that our new proposals are extremely flexible, being able to compete with contestants and appearing suited to accommodating several distributions, such, for example, mixtures, for target populations. We illustrate the application of the novel proposals with a real data example. The article ends with a discussion and a presentation of some directions for future research.

Receiver operating characteristic estimation and threshold selection criteria in three-class classification problems for clustered data.

Statistical evaluation of diagnostic tests, and, more generally, of biomarkers, is a constantly developing field, in which complexity of the assessment increases with the complexity of the design under which data are collected. One particularly prevalent type of data is clustered data, where individual units are naturally nested into clusters. In these cases, Bias can arise from omission, in the evaluation process, of cluster-level effects and/or individual covariates. Focusing on the three-class case and for continuous-valued diagnostic tests, we investigate how to exploit the clustered structure of data within a linear-mixed model approach, both when the assumption of normality holds and when it does not. We provide a method for the estimation of covariate-specific receiver operating characteristic surfaces and discuss methods for the choice of optimal thresholds, proposing three possible estimators. A proof of consistency and asymptotic normality of the proposed threshold estimators is given. All considered methods are evaluated by extensive simulation experiments. As an application, we study the use of the Lysosomal Associated Membrane Protein Family Member 5 gene expression as a biomarker to distinguish among three types of glutamatergic neurons.

Non-monotone transformation of biomarkers.

We comment here on a recent paper in this journal, on a non-monotone transformation of biomarkers aimed at improving diagnostic accuracy. We highlight that, in a binary classification problem, the proposed transformation finds its motivation in the Neyman-Pearson lemma, so that the underlying approach is very general and it is applicable to many parametric families, other than the normal one.

Nonparametric confidence regions for the symmetry point-based optimal cutpoint and associated sensitivity of a continuous-scale diagnostic test.

In medical research, diagnostic tests with continuous values are widely employed to attempt to distinguish between diseased and non-diseased subjects. The diagnostic accuracy of a test (or a biomarker) can be assessed by using the receiver operating characteristic (ROC) curve of the test. To summarize the ROC curve and primarily to determine an "optimal" threshold for test results to use in practice, several approaches may be considered, such as those based on the Youden index, on the so-called close-to-(0,1) point, on the concordance probability and on the symmetry point. In this paper, we focus on the symmetry point-based approach, that simultaneously controls the probabilities of the two types of correct classifications (healthy as healthy and diseased as diseased), and show how to get joint nonparametric confidence regions for the corresponding optimal cutpoint and the associated sensitivity (= specificity) value. Extensive simulation experiments are conducted to evaluate the finite sample performances of the proposed method. Real datasets are also used to illustrate its application.

Nearest-Neighbor Estimation for ROC Analysis under Verification Bias.

For a continuous-scale diagnostic test, the receiver operating characteristic (ROC) curve is a popular tool for displaying the ability of the test to discriminate between healthy and diseased subjects. In some studies, verification of the true disease status is performed only for a subset of subjects, possibly depending on the test result and other characteristics of the subjects. Estimators of the ROC curve based only on this subset of subjects are typically biased; this is known as verification bias. Methods have been proposed to correct verification bias, in particular under the assumption that the true disease status, if missing, is missing at random (MAR). MAR assumption means that the probability of missingness depends on the true disease status only through the test result and observed covariate information. However, the existing methods require parametric models for the (conditional) probability of disease and/or the (conditional) probability of verification, and hence are subject to model misspecification: a wrong specification of such parametric models can affect the behavior of the estimators, which can be inconsistent. To avoid misspecification problems, in this paper we propose a fully nonparametric method for the estimation of the ROC curve of a continuous test under verification bias. The method is based on nearest-neighbor imputation and adopts generic smooth regression models for both the probability that a subject is diseased and the probability that it is verified. Simulation experiments and an illustrative example show the usefulness of the new method. Variance estimation is also discussed.

Simple nonparametric confidence regions for the evaluation of continuous-scale diagnostic tests.

The evaluation of the ability of a diagnostic test to separate diseased subjects from non-diseased subjects is a crucial issue in modern medicine. The accuracy of a continuous-scale test at a chosen cut-off level can be measured by its sensitivity and specificity, i.e. by the probabilities that the test correctly identifies the diseased and non-diseased subjects, respectively. In practice, sensitivity and specificity of the test are unknown. Moreover, which cut-off level to use is also generally unknown in that no preliminary indications driving its choice could be available. In this paper, we address the problem of making joint inference on pairs of quantities defining accuracy of a diagnostic test, in particular, when one of the two quantities is the cut-off level. We propose a technique based on an empirical likelihood statistic that allows, within a unified framework, to build bivariate confidence regions for the pair (sensitivity, cut-off level) at a fixed value of specificity as well as for the pair (specificity, cut-off level) at a fixed value of sensitivity or the pair (sensitivity, specificity) at a fixed cut-off value. A simulation study is carried out to assess the finite-sample accuracy of the method. Moreover, we apply the method to two real examples.