Yes the absolute risk reduction would “only” be 8% but it doesn’t change the fact that ARR is a better measure than RRR. RRR which tells you nothing without knowing how prevalent the disease is in the untreated group – in which case you can recover ARR from the combination of prevalence and RRR. After all, if you have an extremely rare disease, knowing you have a 99%, RRR still doesn’t tell you what you want to know.

(1) True, if you test 1000 people you get 1 true positive and 10 false positives, for 11 total positives. The 10 false positives dwarf the single true positive.

(2) But, if you’re in the pool of people who test positive, you’re now 1/11 = 9.1% chance of having the disease, vs 0.1% in the general population. So the test has enriched the pool of sick people over the general population by about 100-fold, which is really good information in the real world.

This is why when you get a positive test, your doc orders another test of a different kind, to winnow out the false positives. Get a couple positives in a row from different kinds of tests, and your doc can be pretty sure you’ve got the disease.

Our present problem is people look at test like oracles, which Give The Answer immediately.

Even the oracles were confusing (https://en.wikipedia.org/wiki/Ibis_redibis_nunquam_per_bella_peribis).

A test with no false positives has 100% positive predictive value. 
PPV is defined as TP/(TP +FP)If FP = 0, then PPV is 1
(It is very unusual I admit for a test to have no false positives…)
I wanted to add a discussion of PPV and NPV but they said no. It will hopefully be in another article.

The base rate fallacy comes up all the time and it’s never good. Every few years they survey doctors about what would they do if a patient had a positive result on an accurate disease if the disease is rare. The results are always scary.

There’s nothing wrong with stating a fact: that 75% of the infected were vaccinated. But things go south in a hurry when an enforced behavioral intent gets attached to it.

Yes, Americans can’t do stats (or math). But framing the facts to intentional outcomes, such as higher vaccination rates, are deceptive and (often wrongly) prescriptive. So we get framing to encourage vaccinations obscuring the truth of how vaccinations do not prevent infection or spread. BOTH are important details.

Hence we get the CDC lifting mask mandates a month ago among “Freedom Day” declarations in part because they worried about reducing vaccination incentives: manipulative intentions over facts. Yet we knew the UK and India were raging with Delta and it was only a matter of time.

But by discouraging masking, the CDC encouraged the false belief that vaccines were a magic amulet that prevented infection or transmission and the vaccinated could simply pretend like COVID no longer existed … resulting in unnecessary infections and deaths.

I think you are missing the point of using an extreme example, it is to show the base rate fallacy at its starkest i.e that you have to choose the right denominator. Yes, a more realistic scenario might be something like 60% vaccinated and 20% of the cases among the vaccinated and 80% of the cases among the unvaccinated. You could then do the calculation and see the same mistake but the arithmetic would be a bit more painful. The key issue is that any statement that says “X% of the reported cases are among the vaccinated” (or “among the unvaccinated” for that matter) is falling victim to the base rate fallacy, such statements are useless and provide no good information absent knowing how many people are in each group, putting them as the lead in an article is just plain bad, that was the point of the article.