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Medical Decision Making
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Bivariate Random Effects Meta-Analysis of ROC Curves

L.R. Arends, PhD

Department of Epidemiology & Biostatistics, Erasmus Medical Center, Rotterdam, The Netherlands, Institute of Psychology, Erasmus University Rotterdam, Rotterdam, The Netherlands, l.arends{at}erasmusmc.nl

T.H. Hamza, PhD

Department of Epidemiology & Biostatistics, Erasmus Medical Center, Rotterdam, The Netherlands

J.C. van Houwelingen, PhD

Department of Medical Statistics, Leiden University Medical Center, Leiden, The Netherlands

M.H. Heijenbrok-Kal, PhD

Department of Epidemiology & Biostatistics, Erasmus Medical Center, Rotterdam, The Netherlands, Department of Radiology, Erasmus Medical Center, Rotterdam, Netherlands

M.G.M. Hunink, PhD

Department of Epidemiology & Biostatistics, Erasmus Medical Center, Rotterdam, The Netherlands, Department of Radiology, Erasmus Medical Center, Rotterdam, Netherlands, Department of Health Policy & Management, Harvard School of Public Health, Boston, Massachusetts

T. Stijnen, PhD

Department of Epidemiology & Biostatistics, Erasmus Medical Center, Rotterdam, The Netherlands

Meta-analysis of receiver operating characteristic (ROC)-curve data is often done with fixed-effects models, which suffer many shortcomings. Some random-effects models have been proposed to execute a meta-analysis of ROC-curve data, but these models are not often used in practice. Straightforward modeling techniques for multivariate random-effects meta-analysis of ROC-curve data are needed. The 1st aim of this article is to present a practical method that addresses the drawbacks of the fixedeffects summary ROC (SROC) method of Littenberg and Moses. Sensitivities and specificities are analyzed simultaneously using a bivariate random-effects model. The 2nd aim is to show that other SROC curves can also be derived from the bivariate model through different characterizations of the estimated bivariate normal distribution. Thereby the authors show that the bivariate random-effects approach not only extends the SROC approach but also provides a unifying framework for other approaches. The authors bring the statistical meta-analysis of ROC-curve data back into a framework of relatively standard multivariate meta-analysis with random effects. The analyses were carried out using the software package SAS (Proc NLMIXED).

Key Words: meta-analysis • diagnostic tests • multivariate random effects models • sensitivity • specificity • receiver operating characteristic (ROC) analysis.

This version was published on September 1, 2008

Medical Decision Making, Vol. 28, No. 5, 621-638 (2008)
DOI: 10.1177/0272989X08319957
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