Lehmann Family of ROC Curves
Year: 2010
Type: article
Abstract: Receiver operating characteristic (ROC) curves evaluate the discriminatory power of a continuous marker to predict a binary outcome. The most popular parametric model for an ROC curve is the binormal model, which assumes that the marker, after a monotone transformation, is normally distributed conditional on the outcome. Here, the authors present an alternative to the binormal model based on the Lehmann family, also known as the proportional hazards specification. The resulting ROC curve and its functionals (such as the area under the curve and the sensitivity at a given level of specificity) have simple analytic forms. Closed-form expressions for the functional estimates and their corresponding asymptotic variances are derived. This family accommodates the comparison of multiple markers, covariate adjustments, and clustered data through a regression formulation. Evaluation of the underlying assumptions, model fitting, and model selection can be performed using any off-the-shelf proportional hazards statistical software package.
Source: Medical Decision Making
Authors: Mithat Gönen, Glenn Heller
Institution: Memorial Sloan Kettering Cancer Center
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Cancer Institute
Award: Cancer Center Support Grant
OpenAlex ID: W2016667287