Statistical Modelling 1 (2001), 4964
Binormal Association-Marginal
Models for Empirically Evaluating and Comparing Diagnostics
Joseph B. Lang
Dept. of Statistics and Actuarial Science,
Univ. of Iowa, IA 52242, USA
eMail: jblang@stat.uiowa.edu
Thor Aspelund
Dept. of Statistics and Actuarial Science,
Univ. of Iowa, IA 52242, USA
eMail: aspelund@stat.uiowa.edu
Abstract:
A new method for empirically evaluating and comparing two diagnostics
is introduced. Specifically, correlated ordinal
rating data from a paired-comparison study are modeled using a
flexible, new class of binormal association-marginal
(BAM) models. Among other things, these models, which are fitted via maximum
likelihood, afford efficient estimators of (i) the diagnostics' receiver
operating characteristic (ROC) 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. A
maximum likelihood 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.
Keywords:
agreement; binormal
model; correlated ordinal data; kappa statistic; loglinear model;
receiver operating characteristic curve; signal detection theory.
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