CopulaDTA: Copula Based Bivariate Beta-Binomial Models for Diagnostic Test Accuracy Studies in a Bayesian Framework

Abstract

The current statistical procedures implemented in statistical software packages for pooling of diagnostic test accuracy data include hSROC regression (Rutter and Gatsonis 2001) and the bivariate random-effects meta-analysis model (BRMA) (Reitsma et al. (2005), Arends et al. (2008), Chu and Cole (2006), Riley et al. (2007b)). However, these models do not report the overall mean but rather the mean for a central study with random-effect equal to zero and have difficulties estimating the correlation between sensitivity and specificity when the number of studies in the meta-analysis is small and/or when the between-study variance is relatively large (Riley et al. 2007a). This tutorial on advanced statistical methods for meta-analysis of diagnostic accuracy studies discusses and demonstrates Bayesian modeling using CopulaDTA (Nyaga 2015) to fit different models to obtain the meta-analytic parameter estimates. The focus is on the joint modelling of sensitivity and specificity using copula based bivariate beta distribution. Essentially, we extend the work of Nikoloulopoulos (2015a) by: i) presenting the Bayesian approach which offers flexibility and ability to perform complex statistical modelling even with small data sets and ii) including covariate information, and iii) providing an easy to use code. The statistical methods are illustrated by re-analysing data of two published meta-analyses. Modelling sensitivity and specificity using the bivariate beta distribution provides marginal as well as study-specific parameter estimates as opposed to using bivariate nor- mal distribution (e.g. in BRMA) which only yields study-specific parameter estimates. Moreover, copula based models offer greater flexibility in modelling different correlation structures in contrast to the normal distribution which allows for only one correlation structure.