Meta-analysis of diagnostic test accuracy assessment studies with varying number of thresholds

Abstract

Current meta-analytic methods for diagnostic test accuracy are generally applicable to a selection of studies reporting only estimates of sensitivity and specificity, or at most, to studies whose results are reported using an equal number of ordered categories. In this article, we propose a new meta-analytic method to evaluate test accuracy and arrive at a summary receiver operating characteristic (ROC) curve for a collection of studies evaluating diagnostic tests, even when test results are reported in an unequal number of nonnested ordered categories. We discuss both non-Bayesian and Bayesian formulations of the approach. In the Bayesian setting, we propose several ways to construct summary ROC curves and their credible bands. We illustrate our approach with data from a recently published meta-analysis evaluating a single serum progesterone test for diagnosing pregnancy failure.

Figure 1.

Pregnancy failure meta-analysis (FE model without covariate): summary ROC curve and its 95% confidence pointwise bands (obtained via delta method). The dashed lines are the individual-study empirical ROC curves.

Figure 2.

Pregnancy failure meta-analysis (FE model with covariate): Summary ROC curves for 13 prospective and 7 retrospective studies reporting on distinction between pregnancy failure and viable intra-uterine pregnancy. The line with dots and filled circles correspond to retrospective studies and the lines with clear circles correspond to prospective studies.

Figure 3.

Pregnancy failure meta-analysis (HM with covariate): Mean summary ROC curves for 13 prospective and 7 retrospective studies reporting on distinction between pregnancy failure and viable intra-uterine pregnancy, with envelope $95\%$ bands over $\left(\mathrm{0.1,0.9}\right)$ FPR region.