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Meta‐analysis of diagnostic tests accounting for disease prevalence: a new model using trivariate copulas
Author(s) -
Hoyer A.,
Kuss O.
Publication year - 2015
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.6463
Subject(s) - copula (linguistics) , bivariate analysis , vine copula , econometrics , statistics , mathematics , logistic regression , marginal distribution , random variable
In real life and somewhat contrary to biostatistical textbook knowledge, sensitivity and specificity (and not only predictive values) of diagnostic tests can vary with the underlying prevalence of disease. In meta‐analysis of diagnostic studies, accounting for this fact naturally leads to a trivariate expansion of the traditional bivariate logistic regression model with random study effects. In this paper, a new model is proposed using trivariate copulas and beta‐binomial marginal distributions for sensitivity, specificity, and prevalence as an expansion of the bivariate model. Two different copulas are used, the trivariate Gaussian copula and a trivariate vine copula based on the bivariate Plackett copula. This model has a closed‐form likelihood, so standard software (e.g., SAS PROC NLMIXED ) can be used. The results of a simulation study have shown that the copula models perform at least as good but frequently better than the standard model. The methods are illustrated by two examples. Copyright © 2015 John Wiley & Sons, Ltd.