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

Victoria Nyawira Nyaga · Marc Arbyn · Marc Aerts

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Meta-analysis and systematic reviews Statistical Methods and Bayesian Inference Statistical Methods in Epidemiology

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 the R package CopulaDTA (Nyaga 2017) to fit different models to obtain the meta-analytic parameter estimates. The focus is on the joint modeling of sensitivity and specificity using a copula based bivariate beta distribution. Essentially, we extend the work of Nikoloulopoulos (2015) by: (i) presenting the Bayesian approach which offers the flexibility and ability to perform complex statistical modeling 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-analyzing data of two published meta-analyses. Modeling sensitivity and specificity using the bivariate beta distribution provides marginal as well as study-specific parameter estimates as opposed to using the bivariate normal distribution (e.g., in BRMA) which only yields study-specific parameter estimates. Moreover, copula based models offer greater flexibility in modeling different correlation structures in contrast to the normal distribution which allows for only one correlation structure.

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2005Bivariate analysis of sensitivity and specificity produces informative summary measures in diagnostic reviews 2006MODELLING ASYMMETRIC EXCHANGE RATE DEPENDENCE*2001A hierarchical regression approach to meta‐analysis of diagnostic test accuracy evaluations 2006An Introduction to Copulas 1993Combining independent studies of a diagnostic test into a summary roc curve: Data‐analytic approaches and some additional considerations 2006Bivariate meta-analysis of sensitivity and specificity with sparse data: a generalized linear mixed model approach 2013Variation of a test’s sensitivity and specificity with disease prevalence 1960The Performance of Some Correlation Coefficients for a General Bivariate Distribution

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