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Statistical evaluation of diagnostic tests, and, more generally, of biomarkers, is a constantly developing field, in which complexity of the assessment increases with 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. Focussing 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 estimation of covariate-specific ROC 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 (Lamp5) gene expression as biomarker to distinguish among three types of glutamatergic neurons.

Supplemental material, sj-pdf-1-smm-10.1177_09622802221089029 for Receiver operating characteristic estimation and threshold selection criteria in three-class classification problems for clustered data by Duc-Khanh To, Gianfranco Adimari, Monica Chiogna and Davide Risso in Statistical Methods in Medical Research

Verification bias is a well known problem when the predictive ability of a diagnostic test has to be evaluated. In this paper, we discuss how to assess the accuracy of continuous-scale diagnostic tests in the presence of verification bias, when a three-class disease status is considered. In particular, we propose a fully nonparametric verification bias-corrected estimator of the ROC surface. Our approach is based on nearest-neighbor imputation and adopts generic smooth regression models for both the disease and the verification processes. Consistency and asymptotic normality of the proposed estimator are proved and its finite sample behavior is investigated by means of several Monte Carlo simulation studies. Variance estimation is also discussed and an illustrative example is presented., Comment: arXiv admin note: text overlap with arXiv:1510.03225

Recently, a technique based on pseudo-observations has been proposed to tackle the so called convex hull problem for the empirical likelihood statistic. The resulting adjusted empirical likelihood also achieves the highorder precision of the Bartlett correction. Nevertheless, the technique induces an upper bound on the resulting statistic that may lead, in certain circumstances, to worthless confidence regions equal to the whole parameter space. In this paper we show that suitable pseudo-observations can be deployed to make each element of the generalised power divergence family Bartlett-correctable and released from the convex hull problem. Our approach is conceived to achieve this goal by means of two distinct sets of pseudo-observations with dfferent tasks. An important effect of our formulation is to provide a solution that permits to overcome the problem of the upper bound. The proposal, whose effectiveness is confirmed by simulation results, gives back attractiveness to a broad class of statistics that potentially contains good alternatives to the empirical likelihood.

In several applications, the model of interest is such that its likelihood function is difficult, or even impractical, to compute. For these situations, it is common to substitute the likelihood with a surrogate, which resembles the full likelihood but is easier to calculate. Among these surrogates are composite likelihoods and in particular pairwise likelihoods. Their properties in classical inference have been widely discussed in the literature; their use within a Bayesian approach has been seldom considered. The substitution of the likelihood with a surrogate is not straightforward in Bayesian inference: the posterior distribution which is obtained must be validated on a case by case basis, as general results are not available. We propose a Bayesian procedure in which the surrogate is the empirical likelihood derived from the pairwise score equation. This pseudo-likelihood has standard asymptotic properties, so the validation of the posterior distribution is based on its asymptotic behavior.

The evaluation of the ability of a diagnostic test to separate diseaded from non-diseaded 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 diseaded and non-diseaded subjects, respectively. In practice, sensitivity and specificity of the test are unknown. Moreover, the cut-o level to use is also generally unknown, in that no preliminary indications driving its choice could be available. In this paper, we try to 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 make inference about the pair (sensitivity, cut-off level), at a fixed value of specificity, as well as about the pair (specificity, cut-off level), at a fixed value of sensitivity, or about 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.

Let X and Y be two independent continuous random variables. We discuss three techniques to obtain confidence intervals for ρ_Pr[Y > X] in a semiparametric framework. One method relies on the asymptotic normality of an estimator for ρ; the remaining methods involve empirical likelihood and combine it with maximum likelihood estimation and with full parametric likelihood, respectively. Finite-sample accuracy of the confidence intervals is assessed through a simulation study. An illustration is given using a dataset on the detection of carriers of Duchenne Muscular Dystrophy.

This paper presents a new quasi-profile loglikelihood with the standard kind of distributional limit behaviour, for inference about an arbitrary one-dimensional parameter of interest, based on unbiased estimating functions. The new function is obtained by requiring to the corresponding quasi-profile score function to have bias and information bias of order 0(1). We illustrate the use of the proposed pseudo-likelihood with an application for robust inference in linear models.