  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, that straightforwardly extends the bivariate models well
recommended for the one threshold case. However, drawbacks of the approach,
such as poor estimation of the within-study correlations between sensitivities
and between specificities and severe computational issues, can make it
unappealing. We propose an alternative method for inference on common
diagnostic measures using a pseudo-likelihood constructed under a working
independence assumption between sensitivities and between specificities at
different thresholds in the same study. The method does not require
within-study correlations, overcomes the convergence issues and can be
effortlessly implemented. Simulation studies highlight a satisfactory
performance of the method, remarkably improving the results from the
multivariate normal counterpart under different scenarios. The
pseudo-likelihood approach is illustrated in the evaluation of a test used for
diagnosis of pre-eclampsia as a cause of maternal and perinatal morbidity and
mortality.
