Approximate likelihood and pseudo-likelihood inference in meta-analysis of diagnostic accuracy studies accounting for disease prevalence and study design

Bivariate random-effects models represent a recommended approach for meta-analysis of diagnostic test accuracy, jointly modeling study-specific sensitivity and specificity. As the severity of the disease status can vary across studies, a proper analysis should account for the dependence of the accuracy measures on the disease prevalence. To this aim, trivariate generalized linear mixed-effects models have been proposed in the literature, although computational difficulties strongly limit their applicability. In addition, the attention has been mainly paid to cohort studies, where the study-specific disease prevalence can be estimated from, while information from case-control studies is often neglected. To overcome such limits, this article introduces a trivariate approximate normal model, which accounts for disease prevalence along with accuracy measures in cohort studies and sensitivity and specificity in case-control studies. The model represents an extension of the bivariate normal mixed-effects model originally developed for meta-analysis not accounting for disease prevalence, under an approximate normal within-study distribution for the logit of estimated sensitivity and specificity. The components of the approximate within-study covariance matrix are derived and the likelihood function is obtained in closed-form. The approximate likelihood approach is compared to that based on the exact within-study distribution and to its modifications following a pseudo-likelihood strategy aimed at reducing the computational effort. The comparison is based on simulation studies in a variety of scenarios, and illustrated in a meta-analysis about the accuracy of a test to diagnose fungal infection and a meta-analysis of a noninvasive test to detect colorectal cancer.