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.
Keywords: beta-binomial distribution; copula; meta-analysis; prevalence; sensitivity; specificity.
Copyright © 2015 John Wiley & Sons, Ltd.