Enough book bullshit; back to COVID bullshit.

There's an interesting quotation from John Ioannidis at @CNN.

https://www.cnn.com/2020/08/02/health/gupta-coronavirus-t-cell-cross-reactivity-immunity-wellness/index.html

I've commented elsewhere on how epidemiology is the truly dismal science. Whenever you discover something new that would be good news all else equal, it's not as good of news as you think because now not all else is equal.

For example, if you discover that the infectious period is shorter than you thought, that might sound like good news. It would be, ex ante. But ex post, holding the epidemic trajectory constant, it means that the disease is more transmissible per contact event than you expected.

It looks to me as though Ioannidis has stumbled into something along these lines here.

If we *knew* the R0 in a population that was truly 100% susceptible, you could do the math the way that he does.

But if he is right that 50% of the population was already immune, then our original estimates of R0 have to be way off to explain the rate of increase we observed in a population half of which was immune.

Suppose that you originally thought that R0 was 2.5. Then you'd expect (in a well-mixed model, all caveats in place) a herd immunity threshold of 60%.

Then you discover that 50% of the population is immune.

Using Ioannidis's logic, you only have 10% left to go. Great news!

But that's wrong.

Because if 50% was immune from the start, your R0 estimate was off by a factor of 2. R0 was actually 5. Then in a well-mixed model, the herd immunity threshold is 80%. You've got to cover another 30%, not the 10% Ioannidis seems to be claiming.

Update: As usual @StatModeling got there before I did. (h/t @bolkerb)

https://statmodeling.stat.columbia.edu/2020/08/03/math-error-in-herd-immunity-calculation-from-cnn-epidemiology-expert/

I think Gelman is a bit too generous though. Math may be hard but dealing with these kinds of issues is what infectious disease epidemiologists *do* day in and day out.