gms | German Medical Science

Introduction: The development of new statistical methods for the meta-analysis of diagnostic test accuracy (DTA) studies is a vivid field of research, especially with respect to summarizing full receiver operating characteristic (ROC) curves. Most current approaches utilize random effects to account for between-study heterogeneity and within-study correlation between sensitivity and specificity [1], leading to two main disadvantages: First, random effects are usually assumed to be normally distributed and second, estimation of such models can be numerically challenging.

Methods: In this contribution, we substitute random effects with copulas, leading to the ability to directly model the dependence between sensitivity and specificity and an increased control over the estimation procedure. While the resulting models are still hard to estimate, they lead to much more flexible model structures when compared to random effects. Combined with interpreting the results reported by DTA studies as being interval-censored time-to-event data [2] and clinically plausible parametric assumptions for the marginal distributions of sensitivity and specificity, this leads to a powerful model to estimate summary ROC curves.

Results: In a simulation study, we use Clayton and Joe copulas [3] with Weibull-binomial and Weibull-normal marginal distributions to compare the resulting models to alternatives from the literature [4]. Our copula models are able to create very flexible model fits and perform similarly to competing models. However, they are also numerically unstable, leading to large variations in bias in the simulation. We also show the practical applicability of the models to data from a meta-analysis for the screening of type 2 diabetes, leading to plausible summary ROC curves.

Discussion: The main appeal of using copulas to model the dependence between sensitivity and specificity instead of random effects in the meta-analysis of DTA studies lies in the added flexibility through the choice of the copula and its parameter(s) as well as in avoiding involved optimization methods that are used to estimate random effect models. In this respect, our model can emulate much more complicated dependence structures than established models from the literature. A numerically stable estimation of the copulas, however, remains a challenge to be further investigated.

Conclusion: Modeling the dependencies of bivariate information through copulas increases the flexibility in the meta-analysis of full ROC curves. While first results are promising in this regard, there remains the need for increasing numerical stability in parameter estimation.

The authors declare that they have no competing interests.

The authors declare that an ethics committee vote is not required.