Bivariate random effects meta-analysis of diagnostic studies using generalized linear mixed models

Bivariate random effect models are currently one of the main methods recommended to synthesize diagnostic test accuracy studies. However, only the logit transformation on sensitivity and specificity has been previously considered in the literature. In this article, the authors consider a bivariate generalized linear mixed model to jointly model the sensitivities and specificities, and they discuss the estimation of the summary receiver operating characteristic curve (ROC) and the area under the ROC curve (AUC). As the special cases of this model, the authors discuss the commonly used logit, probit, and complementary log-log transformations. To evaluate the impact of misspecification of the link functions on the estimation, they present 2 case studies and a set of simulation studies. Their study suggests that point estimation of the median sensitivity and specificity and AUC is relatively robust to the misspecification of the link functions. However, the misspecification of link functions has a noticeable impact on the standard error estimation and the 95% confidence interval coverage, which emphasizes the importance of choosing an appropriate link function to make statistical inference.