Also, I assume it would be mostly done on higher risk patients (certain work conditions, certain age, etc..). Only once in couple of years on younger population for example. Or if it's really cheap everyone could get it and then there could be more focused blood screening done next so you don't have to get full body cat scans.

But first of all you need to account for the negative effects of a false positive, and they are much worse than that. They include anything from stress and psychological effects, cost and risks of all the additional screening, to the much worse issue that you also need to account for the fact that for some cancers in some instances it will be hard enough to determine if the growth is malignant in the sense that some proportion of cancerous growth will never pose a threat to the patient, but once diagnosed there tends to be a strong pressure to treat. As a result too frequent screening will save some, but will also result in a large amount of unnecessary chemo, radiation therapy and/or surgeries - all of which come with risks in addition to the pain and discomfort.

Then you need to account for frequency of testing. A 1% false positive rate per test looks distinctly worse if the test is repeated every year for a 10-20 year timespan, for example.

Then you'll also want to account for how much it improves outcomes. If the cancers it detects are ones that would generally be detected in time anyway, and/or have low mortality, and where treatment outcomes are good, the incremental improvement would not necessarily be big enough to justify the negatives.

For breast cancer, for example, there has in recent years been a push to reduce large scale routine mammogram screening because it's not clear if it does more good than harm for many groups of patients (in large part because it leads to overtreatment). This article goes into some of the issues related to that in some detail (and presents both proponents and detractors of large scale screening):

http://www.healthbeatblog.com/2009/04/mammography-screening-...

If I remember correctly, the argument went like this: early screening may detect some forms of prostate cancer which, given the estimated natural lifespan of the patient, would have failed to kill/discomfort him before he died of other causes. But once it's been detected, the recommendation will be to treat the cancer; and treatment has a chance to cause discomfort (such as impotence) right now. So in effect, early detection of some forms of prostate cancer may negatively impact the quality of life of patients who would have otherwise lived a normal life without noticing the cancer.

I might be remembering some details incorrectly.

"Given the considerable time that has passed since PSA screening began, most of this excess incidence must represent overdiagnosis."

true positive rate (TPR, a.k.a. hit rate, recall, specificity)

TPR = TP / P = TP / (TP + FN)

specificity (SPC) or true negative rate

SPC = TN / N = TN / (TN + FP)

"Sensitive" has a clearer intuition: For example when you want to detect a weak signal, then if your antenna is more sensitive, you can better pick up the signal, thus you are better at telling whether the signal is really there (you have a better true positive rate).

I cannot think of a better name for TNR, though, other than simply sticking with TNR and TPR.