Thanks, Martin, for your thoughts and questions. Yes, chaining the Bayes' rule does make the estimate more accurate. It is about increasing the confidence of having a true-positive case, which is why the PPV increases, not the false positive rate.

It is difficult for me to off-hand answer your question about the incidentaloma issue related to CT colonoscopy. I remember one author coining the term VOMIT "victims of modern imaging technologies" which encapsulates the concept of "risks" associated with incidental findings of benign or indolent lesions that wouldn't cause problems if they remained undetected and untreated. Aside from the mental stress triggered by these findings, unnecessary treatments constitute harm to the patient. Incidentalomas certainly present a dilemma to the medical practitioner, but should also make us question the "better safe than sorry" mentality. Add to that the radiation exposure, though carrying a very small risk, and you have a bit of a headache about what to recommend to your patient (or so I assume). It is a matter of joint decision making, not a matter that can be settled simply by the numbers, I presume.