Statistical methods for multivariate meta-analysis of diagnostic tests: An overview and tutorial

In this article, we present an overview and tutorial of statistical methods for meta-analysis of diagnostic tests under two scenarios: (1) when the reference test can be considered a gold standard and (2) when the reference test cannot be considered a gold standard. In the first scenario, we first review the conventional summary receiver operating characteristics approach and a bivariate approach using linear mixed models. Both approaches require direct calculations of study-specific sensitivities and specificities. We next discuss the hierarchical summary receiver operating characteristics curve approach for jointly modeling positivity criteria and accuracy parameters, and the bivariate generalized linear mixed models for jointly modeling sensitivities and specificities. We further discuss the trivariate generalized linear mixed models for jointly modeling prevalence, sensitivities and specificities, which allows us to assess the correlations among the three parameters. These approaches are based on the exact binomial distribution and thus do not require an ad hoc continuity correction. Lastly, we discuss a latent class random effects model for meta-analysis of diagnostic tests when the reference test itself is imperfect for the second scenario. A number of case studies with detailed annotated SAS code in MIXED and NLMIXED procedures are presented to facilitate the implementation of these approaches.