In August I wrote a blog post moaning about (some) medics and epidemiologists relying only on poor quality randomised controls when considering whether wearing an FFP2 mask offers more protection than a surgical mask. Little did I know that a group of scientists/mathematicians that included Nassim Nicholas Taleb were also grumpy about this. Taleb is known as the author of the black swan theory – and the book of the same name that I started and found interesting but did not finish.
The first author is Yaneer Bar Yam and the preprint of Bar Yam, Samet, Siegenfeld and Taleb is here. Their approach is that of data analysis, and essentially they point out that it is very hard to interpret data on mask use to reduce infection. There are so many difficulties that they help the reader with a table of them (their figure 2).
One of the difficulties – that they study in detail – is due to the fact that the studies are of healthcare workers who wear masks for their job, but presumably not at home, while shopping, etc. The studies cannot distinguish between infections caught at work (while hopefully wearing a mask) from those at home, etc (while not masked). The maths can get hairy but the idea is simple. For example, in the study of Loeb and coworkers in 2022, the infection rate for the healthcare workers with surgical masks was 1.14 times higher than those wearing FFP2s. With substantial uncertainties, this gives an estimated range of values of 0.77 to 1.69, for the relative risk to surgical mask versus FFP2 wearers.
Now if all infections occurred at work that is fine. But what if, for example, only some of the infections occurred at work, the rest occurred while unmasked. To keep the maths simple, say, for arguments sake that the infection risk while at work wearing a surgical mask is actually 1.5 times that while wearing an FFP2 mask. Then if say of 5000 healthcare workers who wore FFP2s at work, only 150 caught COVID at work while 350 caught COVID outside work, while of 5000 healthcare workers who wore surgical masks, 225 caught COVID-19 at work and the same 350 caught it outside work.
Then the standard analysis that assumes (incorrectly) that all infections are acquired at work has (225+350)/(150+350) = 575/500 = 1.15 as the relative risk of surgical mask wearers relative to FFP2 wearers, while the true answer is 1.5. These are just some simple made-up numbers to illustrate the point, but they do show that if people in the study are getting infected outside work then this will mean that the result will underestimate the advantage of wearing an FFP2.
This is just one of the problems discussed at length by Bar Yam and coworkers, there are many others. Analysing observational studies such as that of Loeb and coworkers is very hard, and randomised controlled trials are not much easier. This makes it all the more frustrating that when the Royal Society published a review of masks, it completely ignored every published paper on masks except observational and randomised controlled studies. Sigh.
Chance & Necessity 