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 \u201coptimal\u201d 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\ua0application

Bayesian inference with a pairwise likelihood: an approach based on empirical likelihood

In several applications, the model of interest is such that its likelihood function is dif\ufb01cult, 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

Quasi-Profile Log Likelihoods for Unbiased Estimating Functions

Estimating equation, M-estimator, profile likelihood, quasi-likelihood, second Bartlett identity,

Partially parametric interval estimation of Pr(Y>X)

Let X andY be two independent continuous random variables. Three techniques to obtain confidence intervals for \rho=PrY >X are discussed in a partially parametric framework. One method relies on the asymptotic normality of an estimator for \rho; 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 data set on the detection of carriers of Duchenne Muscular Dystrophy

Semiparametric interval estimation of Pr(Y>X)

Let X and Y be two independent continuous random variables. We discuss three techniques to obtain confidence intervals for \u3c1 = Pr{Y > X} in a semiparametric framework. One method relies on the asymptotic normal- ity of an estimator for \u3c1; 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

Likelihood-type confidence regions for optimal sensitivity and specificity of a diagnostic test

New methods are proposed that provide approximate joint confidence regions for the optimal sensitivity and specificity of a diagnostic test, i.e., sensitivity and specificity corresponding to the optimal cutpoint as defined by the Youden index criterion. Such methods are semi-parametric or non-parametric and attempt to overcome the limitations of alternative approaches. The proposed methods are based on empirical likelihood pivots, giving rise to likelihood-type regions with no predetermined constraints on the shape and automatically range-respecting. The proposal covers three situations: the binormal model, the binormal model after the use of Box-Cox transformations and the fully non-parametric model. In the second case, it is also shown how to use two different transformations, for the healthy and the diseased subjects. The finite sample behaviour of our methods is investigated using simulation experiments. The simulation results also show the advantages offered by our methods when compared with existing competitors. Illustrative examples, involving three real datasets, are also provided

Robust inference for the stress–strength reliability

Delta method, Influence function, M-estimator, Stress–strength model, Studentized test statistic, 62F35,