Wednesday, March 25, 2020

That Oxford study, in full, in brief

This post refers. And this manuscript which has received an unreasonable amount of attention.

Here are a few simulations from the SEIR model I've been using, with different death rates (presented in the pic as death per case), adjusted to give the same cumulative death toll in the early phase of the epidemic. Death is assumed to lag infection by 17 days as in the Oxford study. The model used here is possibly just a bit simpler than theirs in some respects but very similar as to the overall behaviour. I have not tried to calibrate precisely to observed data as I'm just making a simple theoretical point. By shifting the epidemic curve backwards and forwards, I can match the death toll from all of these models up to where it peaks, at which point we are already past the peak of the epidemic. The only thing you can rule out from the initial exponential growth (linear in log space) is that we haven't passed the peak as in the pink curve (perhaps also cyan), or else deaths would already have tailed off.

In reality we have lots of reasons to discount the lowest and highest extreme values, and we have observed a lot more than just death toll. For example, if there really had been a large epidemic by early Feb, the first discovered cases would not all have been clearly linked to foreign travel (and each other). And, contrary to their claim that only 1 in 1000 are seriously ill, there are decent-sized areas in Italy where a higher proportion than this are already dead.  All this research shows is that the death toll doesn't tell us about how big the epidemic is (and therefore how big the mortality rate is) until after we've passed it. Rightly, it is getting a drubbing on Twitter. It's all very well playing mathematical games like this on an idle afternoon but I think it's deeply irresponsible to have pushed this out to the press as it suggests a level of uncertainty and disagreement among experts that simply isn't there.


winston said...

Any chance you could put your various bits of code on this topic up somewhere like Github? I've been meaning to learn R, and now we're in lockdown in NZ I might as well make a start now.

James Annan said...

I can certainly put stuff on dropbox which is simpler for me. Strongly recommend you get Rstudio an an environment.

this is an Rmarkdown doc that generates the figs in this post

and this is the longer post on calibration and death rates.

Code is embedded within in chunks, and rstudio will run it all with a click...

..all a bit shonky and not really written for publication of course!

winston said...

Great, thanks a lot for that. It's always good to have a real example when learning new stuff.