Method: We extend existing bivariate meta-analysis methods to simultaneously synthesize multiple index tests. The proposed methods respect the natural grouping of data by studies, account for the within-study correlation (induced because tests are applied to the same participants) between the tests’ true-positive rates (TPRs) and between their false-positive rates (FPRs), and allow for between-study correlations between TPRs and FPRs (such as those induced by threshold effects). We focus mainly on algorithms in the Bayesian setting, using discrete (binomial and multinomial) likelihoods. We use as an example a meta-analysis of 11 studies on the screening accuracy of detecting Down syndrome in liveborn infants using two tests: shortened humerus (arm bone), and shortened femur (thigh bone). Secondary analyses included an additional 19 studies on shortened femur only.
Result: In the application, separate and joint meta-analyses yielded very similar estimates. For example, in models using the discrete likelihood, the summary TPR for a shortened humerus was 35.3% (95% credible interval [CrI]: 26.9, 41.8%) with the novel method, and 37.9% (27.7 to 50.3%) when shortened humerus was analyzed on its own. The corresponding numbers for the summary FPR were 4.9% (2.8 to 7.5%) and 4.8% (3.0 to 7.4%).
However, when calculating comparative accuracy, joint meta-analyses resulted in shorter credible intervals compared with separate meta-analyses for each test. In analyses using the discrete likelihood, the difference in the summary TPRs was 0.0% (-8.9, 9.5%; TPR higher for shortened humerus) with the novel method versus 2.6% (-14.7, 19.8%) with separate meta-analyses. The standard deviation of the posterior distribution of the difference in TPR with joint meta-analyses is half of that with separate meta-analyses.
Conclusion: The joint meta-analysis of multiple tests is feasible. It may be preferable to separate analyses for estimating measures of comparative accuracy of diagnostic tests, and therefore, of primary interest in parameterizing models that compare diagnostic strategies. Simulation and empirical analyses are needed to better define the role of the proposed methodology.