I have a question on diagnostic test accuracy (DTA) meta-analysis.
I understand that the current practice is to use either bivariate or HSROC method.
Wondering, why can't we just pool the area under ROC (AUROC) for each study? Then, the meta-analysis could have easily been done in the usual way (ie pooling of one estimate). Is there any problem if I do it this way?
If you want to pool a single statistic then you could always calculate the diagnostic odds ratio and use that in the usual formula.
If you want a method which corresponds to ROC curves then the Lehmann model may suit you. Define $p_i$ and $u_i$ as the sensitivity and false positive rate respectively. Then assume they are related as $p_i = u_i^{\theta_i}$. Small values of $\theta_i$ correspond to large areas under the curve as the AUC is just $\frac{1}{\theta + 1}$.
If you want to go ahead and you use R I would recommend the mada https://CRAN.R-project.org/package=mada package and its very helpful vignette from which I have taken the section above.
