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GMDS 2013: 58. Jahrestagung der Deutschen Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie e. V. (GMDS)

Deutsche Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie

01. - 05.09.2013, Lübeck

Statistical Methods for Meta-Analysis of Diagnostic Tests accounting for Prevalence – A new Model using trivariate Copulas

Meeting Abstract

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  • Annika Hoyer - Martin-Luther-Universität Halle-Wittenberg, Halle (Saale), DE
  • Göran Kauermann - Ludwig-Maximilians-Universität München, München, DE
  • Oliver Kuß - Martin-Luther-Universität Halle-Wittenberg, Halle (Saale), DE

GMDS 2013. 58. Jahrestagung der Deutschen Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie e.V. (GMDS). Lübeck, 01.-05.09.2013. Düsseldorf: German Medical Science GMS Publishing House; 2013. DocAbstr.73

doi: 10.3205/13gmds169, urn:nbn:de:0183-13gmds1698

Published: August 27, 2013

© 2013 Hoyer et al.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( You are free: to Share – to copy, distribute and transmit the work, provided the original author and source are credited.



Introduction: 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 and Leeflang et al. [1] give empirical examples and plausible mechanisms causing this phenomenon. In meta-analysis of diagnostic studies, accounting for this fact naturally leads to a trivariate expansion of the standard bivariate GLMM [2].

Methods: We propose a new model to this task using trivariate copulas and beta-binomial marginal distributions for sensitivity, specificity and prevalence as an expansion of the bivariate model [3]. We use two different copulas, the trivariate Gaussian copula and a trivariate vine copula based on the bivariate Plackett copula [4]. This model has a closed-form likelihood, so standard software (e.g., SAS PROC NLMIXED) can be used.

Results: We illustrate the methods by the example of Glas et al. [5] on the diagnostic accuracy of telomerase (an urinary tumor marker) for the diagnosis of primary bladder cancer and show the results of a simulation study that compares the three methods.

Discussion: Copula models seem to be a valuable and flexible new tool for the meta-analysis of diagnostic tests.


Leeflang MMG, Bossuyt PMM, Irwig L. Diagnostic test accuracy may vary with prevalence: implications for evidence-based diagnosis. Journal of Clinical Epidemiology. 2009;62(1):5-12.
Chu H, Nie L, Cole SR, Poole C. Meta-analysis of diagnostic accuracy studies accounting for disease prevalence: Alternative parameterizations and model selection. Statistics in Medicine. 2009;28(18):2384-2399.
Kuss O, Hoyer A, Solms A. Meta-analysis for diagnostic accuracy studies. Anew statistical model using beta-binomial distributions and bivariatecopulas. Statistics in Medicine. (in revision)
Aas K, Czado C, Frigessi A, Bakken H. Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics. 2009;44(2):182-198.
Glas AS, et al. Tumor markers in the diagnosis of primary bladder cancer. A systematic review. Journal of Urology. 2003;169(6):1975-1982.