dear patrick,
actually the formulas in my poster are not something you need to account for: they are an opportunity for you to work less to obtain the same information 
indeed, if you have PPV already, you don’t need sensitivity AND specificity. you just need one among sensitivity and specificity, and the other is analytically derived. or, if you happen to have some external information on the prevalence of your cohort on the study population (were false negatives live), you don’t need anything else.
le me show it explicitly. call P the observed prevalence (this is something you know, because it is observed), pi the ‘true’ prevalence (which may be unknown), SE the sensitivity and SP the specificity. then from the formulas you can quickly see that, if you have PPV and SE
SP=1-(PxSEx(1-PPV))/(SE-PxPPV)
on the other hand, if you have PPV and pi
SE=P x PPV/pi
SP=1-(Px(1-PPV))/(1-pi)
so: life is easier!
(this was presented at ICPE, and is currently submitted for publication, but actually it is just solving the system in the poster)