Introduction/Objective: In studies of diagnostic tests with a quantitative result, the relation of sensitivity and specificity for possible cut-off points is often presented as a ROC curve: a graph of sensitivity against one minus specificity. A meta-analysis of several such studies should comprise the construction of a summary ROC curve, with an indication of the accuracy of the curve. This could possibly be done by separate meta-analyses per cut-off point. However, these analyses would not be independent, and the accuracy of the combining summary curve would not be easy to obtain. Moreover, equating cut-off points between studies might be inappropriate, and finally, all data (sensitivity, specificity per cut-off point) for each of the studies would have to be available.

Methods: We propose a parametric approach based on the ROC curve and the numbers of patients and non-patients in each study only. The parametrization is borrowed from Moses, Shapiro and Littenberg (Statistics in Medicine 12 1293-1316 (1993)): we assume a linear relation of V=logit (sensitivity) and U=logit (1-specificity). For tests with a continuous scale outcome, this relation is estimated for each ROC curve by weighted linear regression from a plot of V-U against V+U. Since the data-points in such a plot are not independent, we use a bootstrap method to estimate the standard errors of intercept and slope for each study. Intercepts and slopes can then be combined using known bivariate meta-analysis methods. While in principle, the weighted regression plus bootstrap technique could be used for curves of Likert scale tests, practical problems make it then more convenient to estimate by maximum likelihood.

Results: The techniques are demonstrated using simulated continuous test data and real Likert scale test data.

Discussion: The proposed methods comprised a feasible if computer-intensive technique for meta-analysis of ROC curves.