Likelihood-based clustering of meta-analytic SROC curves

Holling, Heinz, Böhning, Walailuck and Böhning, Dankmar (2012) Likelihood-based clustering of meta-analytic SROC curves. Psychometrika, 77 (1), 106-126. (doi:10.1007/S11336-011-9236-2).

Abstract

Meta-analysis of diagnostic studies experience the common problem that different studies might
not be comparable since they have been using a different cut-off value for the continuous or ordered
categorical diagnostic test value defining different regions for which the diagnostic test is defined to be
positive. Hence specificities and sensitivities arising from different studies might vary just because the
underlying cut-off value had been different. To cope with the cut-off value problem interest is usually
directed towards the receiver operating characteristic (ROC) curve which consists of pairs of sensitivities
and false-positive rates (1-specificity). In the context of meta-analysis one pair represents one study and
the associated diagram is called an SROC curve where the S stands for “summary”. In meta-analysis of
diagnostic studies emphasis has traditionally been placed on modelling this SROC curve with the intention
of providing a summary measure of the diagnostic accuracy by means of an estimate of the summary ROC
curve. Here, we focus instead on finding sub-groups or components in the data representing different
diagnostic accuracies. The paper will consider modelling SROC curves with the Lehmann family which
is characterised by one parameter only. Each single study can be represented by a specific value of that
parameter. Hence we focus on the distribution of these parameter estimates and suggest modelling a
potential heterogeneous or cluster structure by a mixture of specifically parameterised normal densities.
We point out that this mixture is completely nonparametric and the associated mixture likelihood is welldefined
and globally bounded. We use the theory and algorithms of nonparametric mixture likelihood
estimation to identify a potential cluster structure in the diagnostic accuracies of the collection of studies
to be analysed. Several meta-analytic applications on diagnostic studies, including AUDIT and AUDIT-C
for detection of unhealthy alcohol use, the mini-mental state examination for cognitive disorders, as well
as diagnostic accuracy inspection data on metal fatigue of aircraft spare parts, are discussed to illustrate
the methodology.

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Contributors

Author: Dankmar Böhning

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