A pseudo-likelihood approach for multivariate meta-analysis of test accuracy studies with multiple thresholds
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Multivariate meta-analysis of test accuracy studies when tests are evaluated in terms of sensitivity and specificity at more than one threshold represents an effective way to synthesize results by fully exploiting the data if compared to univariate meta-analyses performed at each threshold independently. The approximation of logit transformations of sensitivities and specificities at different thresholds through a normal multivariate random-effects model is a recent proposal which straightforwardly extends the bivariate models well recommended for the one threshold case. Drawbacks of the approach, such as poor estimation of the within-study correlations between sensitivities and specificities and severe computational issues, can make it unappealing. We propose a pseudo-likelihood approach constructed under an independence working assumption between sensitivity and specificity at different thresholds in the same study. The method does not require within-study correlations and it is not prone to convergence issues. The effortless implementation with standard software is an interesting additional feature. Simulation studies highlight a good performance of the pseudo-likelihood approach, substantially improving the corresponding results from the multivariate normal counterpart. The performance is maintained under different scenarios including increasing number of studies and number of thresholds per study and possibly missing completely at random thresholds across studies. The applicability of the pseudo-likelihood approach is illustrated on two real meta-analyses of accuracy of diagnostic tests to detect significant proteinuria from pre-eclampsia of pregnancies and to identify type 2 diabetes mellitus.
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