Three-group ROC analysis: A nonparametric predictive approach

Abstract

. (2014) Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractMeasuring the accuracy of diagnostic tests is crucial in many application areas, in particular medicine and health care. The receiver operating characteristic (ROC) surface is a useful tool to assess the ability of a diagnostic test to discriminate among three ordered classes or groups. In this paper, nonparametric predictive inference (NPI) for three-group ROC analysis is presented. NPI is a frequentist statistical method that is explicitly aimed at using few modelling assumptions in addition to data, enabled through the use of lower and upper probabilities to quantify uncertainty. It focuses exclusively on a future observation, which may be particularly relevant if one considers decisions about a diagnostic test to be applied to a future patient. This paper presents the NPI approach to three-group ROC analysis, including results on the volumes under the ROC surfaces and choice of decision thresholds for the diagnosis.

Three-group ROC predictive analysis for ordinal outcomes

“…where (x) + = max(x, 0), and the case s = t gives the event that the next observation belongs to one specific Coolen-Maturi et al (2014).…”

“…This will lead to a set of such NPI-based ROC surfaces, which we denote by S roc . The lower and upper envelopes of this set are of interest, they consist of the pointwise infima and suprema for this set, see Coolen-Maturi et al (2014) for more details. These envelopes are presented below.…”

“…NPI has been introduced for assessing the accuracy of a classifier's ability to discriminate between two outcomes (or two groups) for binary data (Coolen-Maturi et al, 2012a) and for diagnostic tests with ordinal observations (Elkhafifi and Coolen, 2012) and with real-valued observations (Coolen-Maturi et al, 2012b). Recently, Coolen-Maturi et al (2014) generalized the results in (CoolenMaturi et al, 2012b) by introducing NPI for three-group ROC surface, with real-valued observations, to assess the ability of a diagnostic test to discriminate among three ordered classes or groups.…”

Predictive inference for best linear combination of biomarkers subject to limits of detection

“…Some initial results of using NPI for combining two biomarkers via copula have been presented by Muhammad [36]. Generalizing the proposed NPI method to three-group ROC surface and the volume under the surface [24,37] is an interesting topic for future research. NPI lower and upper bounds for the well-known Youden index [38,39] have been introduced for both two-group ROC and three-group ROC analysis [23,24].…”

“…Recently, [24] generalized the results in [23] by introducing NPI for three-group ROC analysis, with real-valued observations, to assess the ability of a diagnostic test to discriminate among three ordered classes or groups. Coolen-Maturi [25] generalized the results in [22] by proposing NPI for three-group ROC analysis with ordinal outcomes.…”