Data Suitability Assessment Guidance

I’m working on medical diagnostic data meta-analyses. Some data come from direct presentations of raw data, some from logistic-regression output, others from ROC curves, and I would like to know when it is defensible to “reverse-engineer” true-positive, false-positive, false-negative and true-negative counts from summary measures such as sensitivity, specificity or AUC or regression.

Here’s what I’m looking for you to deliver:
• A short, clearly written memo or a brief call that walks through and states whether the back-calculation is appropriate in a number of example case. I will be happy to provide additional explanation of intended methods (hsROC) and provide som examples of references or excerpts of published data that I am not sure is appropriate for "backwards" calculations of to fo fn tn from sensitivity and specificity.
• If avaisble, citations or links to authoritative methods papers or guidelines explaining in which cases "backwards calculations" are appropriate