Summary ROC curve based on a weighted Youden index for selecting an optimal cutpoint in meta-analysis of diagnostic accuracy

Abstract

Established approaches for analyzing meta-analyses of diagnostic accuracy model the bivariate distribution of the observed pairs of specificity Sp and sensitivity Se, thus accounting for across-study correlation. However, it is still a matter of debate how to define a summary ROC (SROC) curve. It was recently pointed out that the SROC curve is in principle unidentifiable if only one (Sp, Se) pair per study is known. We evaluate an alternative approach, modeling the study-specific ROC curves based on the assumption of linearity in logit space. A setting is considered in which the pair (Sp, Se) that is selected for publication in a particular study maximizes a weighted Youden index λSe+(1-λ)Sp with a given weight λ.This leads to a fixed slope (1-λ)/λ of the ROC curve in (1-Sp, Se), equivalent to a slope of (1-λ)Sp(1-Sp)/(λSe(1-Se)) for the corresponding straight line in logit space. While the slope depends on the variance ratio of the underlying distributions, the intercept is a function of the mean difference. Our approach leads in a natural way to a new, model-based proposal for a summary ROC curve. It is illustrated using an example from the literature.