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An Empirical Assessment of Bivariate Methods for Meta-Analysis of Test Accuracy

Methods Research Reports

Investigators: , MD, MS,* , MD,* , MD, and , PhD*.

Tufts Evidence-based Practice Center, Tufts Medical Center
Rockville (MD): Agency for Healthcare Research and Quality (US); .
Report No.: 12(13)-EHC136-EF

Structured Abstract


Meta-analyses of sensitivity and specificity pairs reported from diagnostic test accuracy studies employ a variety of statistical models for estimating mean performance and performance across different test thresholds. The impact of these alternative models on conclusions in applied settings has not been studied systematically.


We constructed a database of PubMed-indexed meta-analyses (1987–2003) from which 2×2 tables for each included primary study could be readily extracted. We evaluated the following methods for meta-analysis of sensitivity and specificity: fixed and random effects univariate meta-analyses using inverse variance methods; univariate random effects meta-analyses with maximum likelihood (ML; both using a normal approximation and the exact binomial likelihood to describe between-study variability); bivariate random effects meta-analyses (both using a normal approximation and the exact binomial likelihood to describe between-study variability). The bivariate model using the exact binomial likelihood was also fit using a fully Bayesian approach. We constructed summary receiver operating characteristic (SROC) curves using the Moses-Littenberg fixed effects method (weighted and unweighted) and the Rutter-Gatsonis hierarchical SROC (HSROC) method. We also obtained alternative SROC curves corresponding to different underlying regression models [logit-true positive rate (TPR) over logit-false positive rate (FPR); logit-FPR over logit-TPR; difference of the logit-TPR and logit-TPR over their sum; and major axis regression of logit-TPR over logit-FPR].


We reanalyzed 308 meta-analyses of test performance. Fixed effects univariate analyses produced estimates with narrower confidence intervals compared to random effects methods. Methods using the normal approximation (both univariate and bivariate, inverse variance and ML) produced estimates of summary sensitivity and specificity closer to 0.5 and smaller standard errors compared to methods using the exact binomial likelihood. Point estimates from univariate and bivariate random effects meta-analyses were similar when performing pairwise (univariate vs. bivariate) comparisons, regardless of the estimation method (inverse variance, ML with normal approximation, or ML with the exact binomial likelihood for estimation). Fitting the bivariate model using ML and fully Bayesian methods produced almost identical point estimates of summary sensitivity and specificity; however, Bayesian results indicated additional uncertainty around summary estimates. The correlation of sensitivity and specificity across studies was imprecisely estimated by all bivariate methods. The SROC curves produced by the Moses-Littenberg and Rutter-Gatsonis models were similar in most examples. Alternative parameterizations of the HSROC regression resulted in markedly different summary lines in a third of the meta-analyses; this depends to a large extent on the estimated covariance between sensitivity and specificity in the bivariate model. Our results are generally in agreement with published simulation studies and the theoretically expected behavior of meta-analytic estimators.


Bivariate models are more theoretically motivated compared to univariate analyses and allow estimation of the correlation between sensitivity and specificity. Bayesian methods fully quantify uncertainty and their ability to incorporate external evidence may be particularly useful for parameters that are poorly estimated in the bivariate model. Alternative SROC curves provide useful global summaries of test performance.

Prepared for: Agency for Healthcare Research and Quality, U.S. Department of Health and Human Services2, Contract No. 290-2007-10055-I. Prepared by: Tufts Evidence-based Practice Center, Tufts Medical Center, Boston, MA

Suggested citation:

Dahabreh IJ, Trikalinos TA, Lau J, Schmid C. An Empirical Assessment of Bivariate Methods for Meta-Analysis of Test Accuracy. Methods Research Report. (Prepared by Tufts Evidence-based Practice Center under Contract No. 290-2007-10055-I.) AHRQ Publication No 12(13)-EHC136-EF. Rockville, MD: Agency for Healthcare Research and Quality. November 2012.

This report is based on research conducted by the Tufts Evidence-based Practice Center (EPC) under contract to the Agency for Healthcare Research and Quality (AHRQ), Rockville, MD (Contract No. 290-2007-10055-I). The findings and conclusions in this document are those of the authors, who are responsible for its contents; the findings and conclusions do not necessarily represent the views of AHRQ. Therefore, no statement in this report should be construed as an official position of AHRQ or of the U.S. Department of Health and Human Services.

The information in this report is intended to help health care decisionmakers—patients and clinicians, health system leaders, and policymakers, among others—make well-informed decisions and thereby improve the quality of health care services. This report is not intended to be a substitute for the application of clinical judgment. Anyone who makes decisions concerning the provision of clinical care should consider this report in the same way as any medical reference and in conjunction with all other pertinent information, i.e., in the context of available resources and circumstances presented by individual patients.

This report may be used, in whole or in part, as the basis for development of clinical practice guidelines and other quality enhancement tools, or as a basis for reimbursement and coverage policies. AHRQ or U.S. Department of Health and Human Services endorsement of such derivative products may not be stated or implied.

None of the investigators have any affiliations or financial involvement that conflicts with the material presented in this report.


Currently at: Center for Evidence-based Medicine, Program in Public Health, Brown University, Providence, RI


540 Gaither Road, Rockville, MD 20850; www​

Bookshelf ID: NBK115736PMID: 23326899


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