gms | German Medical Science

Introduction: Meta-analysis of diagnostic studies is still a rapidly developing area of biostatistical research. Especially, there is an increasing interest in methods to compare different tests to a common gold standard [1]. Restricting to the case of two diagnostic tests, in these meta-analyses the parameters of interest are the differences of sensitivities and specificities (with their corresponding confidence intervals) between the two diagnostic tests while accounting for the various associations within single studies, between the two tests and within patients.

Methods: We propose a statistical model with a quadrivariate response (where sensitivity of test 1, specificity of test 1, sensitivity of test 2, and specificity of test 2 are the four responses) as a sensible approach to this task. Using a quadrivariate generalized linear mixed model (GLMM) naturally generalizes the common standard bivariate model of meta-analysis for a single diagnostic test [2]. Another possibility is to generalize our bivariate copula models [3] to four dimensions, where we use the quadrivariate Gaussian copula and a quadrivariate vine copula which is built out of bivariate Plackett copulas. We illustrate our model by the example of Kodama et al. [4], where two screening methods (HbA1c and fasting plasma glucose) for the diagnosis of type 2 diabetes are compared. Due to the lack of statistical methods, no quantitative results for the difference of the two screening methods have been given so far.

Results: Both copula models give sensible results. For example, from the Gaussian copula we find 3.3% [95%-CI: -4.1%–10.7%] for the difference in sensitivities, favoring HbA1c and -3.5% [95%-CI: -10.2%–3.3%] for the difference in specificities, favoring fasting plasma glucose.

Discussion: Copula models are an appropriate and flexible alternative to the classical generalized linear mixed model to compare two diagnostic tests in meta-analysis.