title: Univariate and bivariate likelihood-based meta-analysis methods performed comparably when marginal sensitivity and specificity were the targets of inference.
abstract: OBJECTIVE
  To compare statistical methods for meta-analysis of sensitivity and specificity of medical tests (e.g., diagnostic or screening tests).
  
  
  METHODS
  We constructed a database of PubMed-indexed meta-analyses of test performance from which 2 × 2 tables for each included study could be extracted. We reanalyzed the data using univariate and bivariate random effects models fit with inverse variance and maximum likelihood methods. Analyses were performed using both normal and binomial likelihoods to describe within-study variability. The bivariate model using the binomial likelihood was also fit using a fully Bayesian approach.
  
  
  RESULTS
  We use two worked examples-thoracic computerized tomography to detect aortic injury and rapid prescreening of Papanicolaou smears to detect cytological abnormalities-to highlight that different meta-analysis approaches can produce different results. We also present results from reanalysis of 308 meta-analyses of sensitivity and specificity. Models using the normal approximation produced sensitivity and specificity estimates closer to 50% and smaller standard errors compared to models using the binomial likelihood; absolute differences of 5% or greater were observed in 12% and 5% of meta-analyses for sensitivity and specificity, respectively. Results from univariate and bivariate random effects models were similar, regardless of estimation method. Maximum likelihood and Bayesian methods produced almost identical summary estimates under the bivariate model; however, Bayesian analyses indicated greater uncertainty around those estimates. Bivariate models produced imprecise estimates of the between-study correlation of sensitivity and specificity. Differences between methods were larger with increasing proportion of studies that were small or required a continuity correction.
  
  
  CONCLUSIONS
  The binomial likelihood should be used to model within-study variability. Univariate and bivariate models give similar estimates of the marginal distributions for sensitivity and specificity. Bayesian methods fully quantify uncertainty and their ability to incorporate external evidence may be useful for imprecisely estimated parameters.
authors.affiliation: Center for Evidence Synthesis in Health, School of Public Health, Brown University, 121 South Main St, Box G-S121-8, Providence, RI 02912, USA; Department of Health Services Policy & Practice, School of Public Health, Brown University, 121 South Main St, Box G-S121-8, Providence, RI 02912, USA.
authors.forename: Issa J
authors.initials: IJ
authors.lastname: Dahabreh
authors.affiliation: Center for Evidence Synthesis in Health, School of Public Health, Brown University, 121 South Main St, Box G-S121-8, Providence, RI 02912, USA; Department of Health Services Policy & Practice, School of Public Health, Brown University, 121 South Main St, Box G-S121-8, Providence, RI 02912, USA.
authors.forename: Thomas A
authors.initials: TA
authors.lastname: Trikalinos
authors.affiliation: Center for Evidence Synthesis in Health, School of Public Health, Brown University, 121 South Main St, Box G-S121-8, Providence, RI 02912, USA; Department of Health Services Policy & Practice, School of Public Health, Brown University, 121 South Main St, Box G-S121-8, Providence, RI 02912, USA.
authors.forename: Joseph
authors.initials: J
authors.lastname: Lau
authors.affiliation: Center for Evidence Synthesis in Health, School of Public Health, Brown University, 121 South Main St, Box G-S121-8, Providence, RI 02912, USA; Department of Biostatistics, School of Public Health, Brown University, Providence, 121 South Main St, Box G-S121-8, Providence, RI 02912, USA. Electronic address: christopher_schmid@brown.edu.
authors.forename: Christopher H
authors.initials: CH
authors.lastname: Schmid
mesh_terms: D001011:Aorta / Q000000981:diagnostic imaging / Q000293:injuries; D001499:Bayes Theorem; D003627:Data Interpretation, Statistical; D006801:Humans; D016013:Likelihood Functions; D015201:Meta-Analysis as Topic; D065006:Papanicolaou Test; D013902:Radiography, Thoracic / Q000379:methods; D012680:Sensitivity and Specificity; D014057:Tomography, X-Ray Computed
keywords: Diagnostic tests; False-positive rate; Multivariate meta-analysis; Screening tests; Test performance; True-positive rate