Confidence intervals for the symmetry point: an optimal cutpoint in continuous diagnostic tests

Abstract

Continuous diagnostic tests are often used for discriminating between healthy and diseased populations. For this reason, it is useful to select an appropriate discrimination threshold. There are several optimality criteria: the North-West corner, the Youden index, the concordance probability and the symmetry point, among others. In this paper, we focus on the symmetry point that maximizes simultaneously the two types of correct classifications. We construct confidence intervals for this optimal cutpoint and its associated specificity and sensitivity indexes using two approaches: one based on the generalized pivotal quantity and the other on empirical likelihood. We perform a simulation study to check the practical behaviour of both methods and illustrate their use by means of three real biomedical datasets on melanoma, prostate cancer and coronary artery disease.

GsymPoint: An R Package to Estimate the Generalized Symmetry Point, an Optimal Cut-off Point for Binary Classification in Continuous Diagnostic Tests

“…Generalized confidence intervals refer to a parametric methodology based on the normality assumption, first introduced by Weerahandi (1993Weerahandi ( , 1995 and recently applied in the context of diagnostic studies to the Youden index by Lai et al (2012) and Zhou and Qin (2013), and to the generalized symmetry point by López-Ratón et al (2016).…”

“…Two statistical approaches have been recently introduced in the literature (López-Ratón et al, 2016) to obtain point estimates and confidence intervals for the generalized symmetry point and its associated sensitivity and specificity measures, a parametric method based on the Generalized Pivotal Quantity (GPQ) under the assumption of normality (Weerahandi, 1993(Weerahandi, , 1995Lai et al, 2012), and a nonparametric method based on the Empirical Likelihood (EL) methodology without any parametric assumptions (Thomas and Grunkemeier, 1975;Molanes-López and Letón, 2011).…”

“…In this paper we present GsymPoint, a package written in R for estimating the generalized symmetry point (López-Ratón et al, 2017), which is freely available from the Comprehensive R Archive Network (CRAN) at http://CRAN.R-project.org/package=GsymPoint. Specifically, this package enables end-users to obtain point estimates and 100(1 − α)% confidence intervals (with α the signification level) for the cost-based generalization of the symmetry point, c GS , and its associated sensitivity and specificity measures, Se(c GS ) and Sp(c GS ), by means of the two statistical approaches pointed out above, the GPQ and EL approaches, that turn out to be more efficient than the empirical one.…”

Construction of confidence intervals for the maximum of the Youden index and the corresponding cutoff point of a continuous biomarker

“…In some cases different weights may be appropriate resulting in a generalization of . Lopez-Raton, Cadarso-Suarez, Molanes-Lopez, & Leton, 2016;Zou, Yu, Liu, Carisson, & Carbera, 2013). The weights depend on disease prevalence and the relative cost of missclassification that can be difficult to ascertain in practice (Greiner et al, 2000;Zhou et al, 2011).…”

“…Alternative metrics have been proposed in the literature (e.g. Lopez-Raton, Cadarso-Suarez, Molanes-Lopez, & Leton, 2016;Zou, Yu, Liu, Carisson, & Carbera, 2013). The application of our methods to these is not discussed here.…”