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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. [ABSTRACT FROM AUTHOR]

This paper introduces an R package for ROC analysis in three-class classification problems, for clustered data in the presence of covariates, named ClusROC. The clustered data that we address have some hierarchical structure, i.e., dependent data deriving, for example, from longitudinal studies or repeated measurements. This package implements point and interval covariate-specific estimation of the true class fractions at a fixed pair of thresholds, the ROC surface, the volume under the ROC surface, and the optimal pairs of thresholds. We illustrate the usage of the implemented functions through two practical examples from different fields of research. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Evaluation of accuracy of diagnostic tests is frequently undertaken under nonignorable (NI) verification bias. Here, we discuss an approach, based on a mean score equation, aimed to estimate the volume under the receiver operating characteristic (ROC) surface of a diagnostic test under NI verification bias. The proposed approach rests on a parametric regression model for the verification process, which accommodates for possible NI missingness in the disease status of sample subjects, and may employ instrumental variables, to help avoid possible identifiability problems. The solution of the mean score equation derived from the verification model requires to preliminarily estimate the parameters of a model for the disease process, whose specification is limited to verified subjects. Verification bias-corrected estimators, an alternative to those recently proposed in the literature and based on a full likelihood approach, are obtained from the estimated verification and disease probabilities. Consistency and asymptotic normality of the new estimators are established. Simulation experiments are conducted to evaluate their finite-sample performances, and an application to a data set from are search on epithelial ovarian cancer is presented. Although the narrative is driven by the three-class case, the extension to high-dimensional ROC analysis is also presented. [ABSTRACT FROM AUTHOR]

The volume under the receiver operating characteristic surface (VUS) is useful for measuring the overall accuracy of a diagnostic test when the possible disease status belongs to one of three ordered categories. In medical studies, the VUS of a new test is typically estimated through a sample of measurements obtained by some suitable sample of patients. However, in many cases, only a subset of such patients has the true disease status assessed by a gold standard test. In this paper, for a continuous-scale diagnostic test, we propose four estimators of the VUS which accommodate for nonignorable missingness of the disease status. The estimators are based on a parametric model which jointly describes both the disease and the verification process. Identifiability of the model is discussed. Consistency and asymptotic normality of the proposed estimators are shown, and variance estimation is discussed. The finite-sample behavior is investigated by means of simulation experiments. An illustration is provided. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Presents a study which assessed the finite sample performance of the inferential procedures based on quasi- and empirical likelihood in the construction of robust confidence region using Monte Carlo method. Details on M-estimators, quasi- and empirical likelihoods; Example comparing the finite-sample behavior of the inferential procedures.

Examines a version of the empirical log-likelihood ratio function for quantiles. Basis on usual empirical distribution function; Confidence intervals yielded; Simulation results.