Binormal association-marginal models for empirically evaluating and comparing diagnostics

Abstract

Anew method for empirically evaluating and comparing two diagnostics is introduced. Specifically, correlated ordinal rating data from a paired-comparison study are modelled using a flexible, new class of binormal association-marginal (BAM) models. Among other things, these models, which are fitted via maximum likelihood (ML), afford efficient estimators of (i) the diagnostics’ receiver operating characteristic curves and (ii) the level of manifest agreement between the diagnostics. BAM models use the latent binormal structure of classic signal detection theory to model each ordinal response marginal distribution. In contrast to bivariate binormal models, BAM models do not impose the added restriction that the ordinal responses have joint distributions that are determined by latent bivariate normal distributions. Instead, the association structure of the ordinal variables is directly specified using standard loglinear models. An ML fitting algorithm, which is related to those algorithms used to fit composite-link generalized linear marginal models, is introduced. The method is illustrated through the analyses of a neonatal radiograph data set and a simulated data set.