A multinomial truncated D-vine copula mixed model for the joint meta-analysis of multiple diagnostic tests

There is an extensive literature on methods for meta-analysis of diagnostic studies, but it mainly focuses on a single test. However, the better understanding of a particular disease has led to the development of multiple tests. A multinomial generalized linear mixed model (GLMM) is recently proposed for the joint meta-analysis of studies comparing multiple tests. We propose a novel model for the joint meta-analysis of multiple tests, which assumes independent multinomial distributions for the counts of each combination of test results in diseased and non-diseased patients, conditional on the latent vector of probabilities of each combination of test results in diseased and non-diseased patients. For the random effects distribution of the latent proportions, we employ a truncated drawable vine copula that can cover flexible dependence structures. The proposed model includes the multinomial GLMM as a special case, but can also operate on the original scale of the latent proportions. Our methodology is demonstrated with a simulation study and using a meta-analysis of screening for Down syndrome with two tests: shortened humerus and shortened femur. The comparison of our method with the multinomial GLMM yields findings in the real data meta-analysis that change the current conclusions.