Abstract
Background: When meta-analysing studies examining the diagnostic/predictive accuracy of classifications based on a continuous test, each study may provide results for one or more thresholds, which can vary across studies. Researchers typically meta-analyse each threshold independently. We consider a multivariate meta-analysis to synthesise results for all thresholds simultaneously and account for their correlation. Methods: We assume that the logit sensitivity and logit specificity estimates follow a multivariate-normal distribution within studies. We model the true logit sensitivity (logit specificity) as monotonically decreasing (increasing) functions of the continuous threshold. This produces a summary ROC curve, a summary estimate of sensitivity and specificity for each threshold, and reveals the heterogeneity in test accuracy across studies. Application is made to 13 studies of protein:creatinine ratio (PCR) for detecting significant proteinuria in pregnancy that each report up to nine thresholds, with 23 distinct thresholds across studies. Results: In the example there were large within-study and between-study correlations, which were accounted for by the method. A cubic relationship on the logit scale was a better fit for the summary ROC curve than a linear or quadratic one. Between-study heterogeneity was substantial. Based on the summary ROC curve, a PCR value of 0.30 to 0.35 corresponded to maximal pair of summary sensitivity and specificity. Limitations of the proposed model include the need to posit parametric functions for the relationship of sensitivity and specificity with the threshold, to ensure correct ordering of summary threshold results, and the multivariate-normal approximation to the within-study sampling distribution. Conclusion: The joint analysis of test performance data reported over multiple thresholds is feasible. The proposed approach handles different sets of available thresholds per study, and produces a summary ROC curve and summary results for each threshold to inform decision-making.
Highlights
In the evaluation of diagnostic or predictive tests, meta-analysis methods are needed to synthesise the evidence about test accuracy from multiple studies
In this article we propose a new approach for meta-analysing diagnostic test accuracy studies when there are multiple threshold results per study, when the studies use the same methods of measuring the continuous test
We propose a model that accounts for within-study correlations in the sensitivities and specificities at various thresholds, and allows for relationships between test performance metrics at the between-study level
Summary
In the evaluation of diagnostic or predictive tests, meta-analysis methods are needed to synthesise the evidence about test accuracy from multiple studies. When the test is measured on a continuous scale studies often report test performance at multiple thresholds, each relating to a different choice of threshold above which test results are classed as 'positive' and below which test results are classed as 'negative', either by reporting multiple two by two tables or labelled ROC curves In this situation, researchers may select single thresholds per study, to allow estimation of a summary ROC curve using standard metaanalysis approaches [1,2,3,4,5,6,7,8]; or they may do a separate meta-analysis for each reported threshold [9]. We consider a multivariate meta-analysis to synthesise results for all thresholds simultaneously and account for their correlation
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