A mixed effect model for bivariate meta-analysis of diagnostic test accuracy studies using a copula representation of the random effects distribution

TL;DR

This paper introduces a copula-based mixed model for bivariate meta-analysis of diagnostic test accuracy, offering a flexible alternative to traditional models by capturing the dependence structure of sensitivity and specificity.

Contribution

It develops a general copula mixed model that extends GLMM, operates on original scales, and improves data fit in diagnostic accuracy meta-analyses.

Findings

Copula mixed model outperforms GLMM in data fit.

Model can be applied on original sensitivity and specificity scales.

Implementation available in R package CopulaREMADA.

Abstract

Diagnostic test accuracy studies typically report the number of true positives, false positives, true negatives and false negatives. There usually exists a negative association between the number of true positives and true negatives, because studies that adopt less stringent criterion for declaring a test positive invoke higher sensitivities and lower specificities. A generalized linear mixed model (GLMM) is currently recommended to synthesize diagnostic test accuracy studies. We propose a copula mixed model for bivariate meta-analysis of diagnostic test accuracy studies. Our general model includes the GLMM as a special case and can also operate on the original scale of sensitivity and specificity. Summary receiver operating characteristic curves are deduced for the proposed model through quantile regression techniques and different characterizations of the bivariate random effects distribution. Our general methodology is demonstrated with an extensive simulation study and illustrated by re-analysing the data of two published meta-analyses. Our study suggests that there can be an improvement on GLMM in fit to data and makes the argument for moving to copula random effects models. Our modelling framework is implemented in the package CopulaREMADA within the open source statistical environment R.