Comment on 'A vine copula mixed effect model for trivariate meta-analysis of diagnostic test accuracy studies accounting for disease prevalence' by Aristidis K Nikoloulopoulos.

Abstract

With interest and excitement we noticed the recently published paper from Nikoloulopoulos. The author proposes an approach for the meta-analysis of diagnostic accuracy studies accounting for disease prevalence with modelling random effects by vine copulas. The use of copulas in metaanalysis opens up a new research area and we expect interesting and practically useful results to emerge in the future. For example, Nikoloulopoulos extends the family of available copulas to asymmetric ones and examines all possible permutations of the vine copulas. In his paper, Nikoloulopoulos repeatedly refers to recent works of ours, henceforth referred as the HK model, and we like to comment on some aspects. Nikoloulopoulos explicitly states twice in his paper that the main parameters of interest in the meta-analysis of diagnostic studies are sensitivity and specificity and we fully agree. However, we were surprised that Nikoloulopoulos calls our model inefficient, because in one of his previous papers, he observed that the HK model had problems with estimating the copula association parameter in the bivariate case. Again, the parameters of interest are sensitivity and specificity, and we show in our paper that these can be estimated also in the trivariate case with essentially no bias and good coverage from the HK model. Moreover, results from the HK model are frequently better than those from the standard trivariate generalized linear mixed model (GLMM) as proposed by Chu et al. As an important advantage of the HK, as compared to the GLMM model, we consider its robustness. Our SAS NLMIXED code for the copula models showed superior convergence as compared to PQL estimation (SAS PROC GLIMMIX) in the bivariate as well as in the trivariate case. We even abandoned estimating parameters by Gauss–Hermite Quadrature estimation for the GLMM model (SAS PROC NLMIXED) in the course of our trivariate simulation study because of