Article
Statistical Methods for Meta-Analysis of Diagnostic Tests accounting for Prevalence – A new Model using trivariate Copulas
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Published: | August 27, 2013 |
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Outline
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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.
Literatur
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- Glas AS, et al. Tumor markers in the diagnosis of primary bladder cancer. A systematic review. Journal of Urology. 2003;169(6):1975-1982.