WHO Philippines on Coronavirus: Masks are Effective, and… Not Needed?

Should have stopped at three bullet points

Risky tweet

Twitter has essentially limitless potential as a platform for public health agencies to broadcast their consensus recommendations to the people. Unfortunately, a lot of agencies’ recommendations aren’t good.

Consider this one:

Bullet point (1) implies masks are effective at preventing transmission to other people.

(2) and (3) imply masks are effective at preventing infection from other people.

(4) is a broad recommendation to the general public that masks aren’t needed, which seems strange, given (1)-(3).

Probability perspective

To illustrate the contradictions in WHO’s recommendations, consider the event “you get infected with the coronavirus.” The only way that happens is if you come into close contact with someone who has it and you become infected as a result. As a Venn diagram:

In other words, the probability of becoming infected is the probability of coming into contact with an infected person times the probability of becoming infected should such a contact occur. Mathematically: P(I) = P(I|C) P(C).

Medical professionals vs. general population

P(I) is always going to be higher for medical professionals, because:

1. P(C) is larger; they’re far more likely to come into contact with an infected person
2. P(I|C) is likely larger; their interactions with an infected person would tend to be closer and more prolonged

Knowing this, here’s what the Venn diagram might look like for medical professionals vs. the general public, relative to each other:

I’m probably underestimating the differences here, but I made the events {C} and {I given C} twice as probable for medical professionals.

As it relates to masks

The WHO tweet implies that wearing a face mask shrinks the size of the smaller circle in the Venn diagram on the left. If wearing a mask reduces P(I|C) for medical professionals, surely it would also reduce P(I|C) for the general public.

I presume WHO’s logic is that because the overall P(C) is really small for the general public, reducing P(I|C) isn’t all that important.

But recommendations can only target two quantities: P(C) or P(I|C). “Stay in as much as possible” targets P(C). “Wash your hands” targets P(I|C). Do they really mean to abandon P(I|C)?

Of course not — they don’t realize that’s what they’re doing. If they gave up on reducing P(I|C), there wouldn’t be much left for them to do, in terms of messaging.

The notion that reducing P(I|C) isn’t worthwhile for the general public because P(C) is small leads to some contradictions:

1. Why is it necessary to further reduce P(C) by recommending people stay home?
2. Why recommend hand-washing, if not to reduce P(I|C)?

It also betrays an apparent oversight, which is that the general population is much larger than the population of medical professionals. If medical professionals have a 5x larger P(C) than the general population, but the general population comprises 10x more people, widespread adoption of masks in the general population might actually be more effective at minimizing new transmissions.

Bamboozled!