Meta-analysis of ROC Curves

Abstract

The authors present a method to combine several independent studies of the same (continuous or semiquantitative) diagnostic test, where each study reports a complete ROC curve; a plot of the true-positive rate or sensitivity against the false-positive rate or one minus the specificity. The result of the analysis is a pooled ROC curve, with a confidence band, as opposed to earlier proposals that result in a pooled area under the ROC curve. The analysis is based on a two-parameter model for the ROC curve that can be estimated for each individual curve. The parameters are then pooled with a bivariate random-effects meta-analytic method, and a curve can be drawn from the pooled parameters. The authors propose to use a model that specifies a linear relation between the logistic transformations of sensitivity and one minus specificity. Specifically, they define V = In(sensitivity/(1 - sensitivity)) and U = In((1 - specificity)/specificity), and then D = V - U, S = V + U. The model is defined as D = α + βS. The parameters α and β are estimated using weighted linear regression with bootstrapping to get the standard errors, or using maximum likelihood. The authors show how the procedure works with continuous test data and with categorical test data. Key words: diagnostic test; ROC curve; bivariate meta-analysis; bootstrap; maximum likelihood estimate. (Med Decis Making 2000;20:430-439)