Semiparametric and parametric transformation models for comparing diagnostic markers with paired design

Abstract

We develop semiparametric and parametric transformation models for estimation and comparison of ROC curves derived from measurements from two diagnostic tests on the same subjects. We assume the existence of transformed measurement scales, one for each test, on which the paired measurements have bivariate normal distributions. The resulting pair of ROC curves are estimated by maximum likelihood algorithms, using joint rank data in the semiparametric model with unspecified transformations and using Box-Cox transformations in the parametric transformation case. Several hypothesis tests for comparing the two ROC curves, or characteristics of them, are developed. Two clinical examples are presented and simulation results are provided.