Donald Trump: "Just the other day they came out with a statement that 85% of the people that wear masks catch it."

This is obviously totally wrong, and this is not at all what the study found. Let's have a closer look at the study in question.

#TrumpTownHall
The study compared 154 symptomatic patients who tested positive for Covid with 160 symptomatic patients who tested negative (link below). The researchers asked the patients about their behaviors, such as social distancing and wearing a face mask. https://www.cdc.gov/mmwr/volumes/69/wr/pdfs/mm6936a5-H.pdf
The study found that 85% of participants who tested positive had often worn a mask before getting sick.

Trump probably saw this result on Fox News and interpreted it to mean that 85% of people who wear a mask contract the virus. That's clearly a totally incorrect interpretation.
The study looked at the proportion of people who test positive who usually wear a mask.

It *did not* look at the proportion of people who wear a mask who contract the virus, which is the much more interesting question.
Some people noted that the participants in the study who tested negative were no more likely to wear a mask.

But this is not a particularly interesting finding. Why not?

There are a couple of reasons.
First, the two groups of patients who tested positive and negative, respectively, were not comparable.

The people who tested positive were much more likely to (a) have a family member who had tested positive, and (b) have had close contact with a person who had tested positive.
To properly measure the extent to which wearing a mask protects the person who wears it, you would ideally conduct an experiment where some participants are randomly assigned to wear a mask and some are assigned not to wear one. Then the two groups would be comparable.
Second, wearing a mask protects not only the person who wears it, but also people who have close contact with that person.

Indeed, the study above found that people who tested positive were more likely to go to restaurants where not all patrons wore a mask.
In other words, exposure to other people who did not wear a mask was correlated with testing positive for Covid.

So, to measure the full effectiveness of masks, we can't just look at whether people wear a mask and test positive, but also at whether other people wear a mask.
Third, if people wear masks and still contract or spread Covid, the people who get sick might potentially experience a less severe illness.

A recent study hypothesizes that wearing a mask "might help reduce the severity of disease." https://www.nejm.org/doi/full/10.1056/NEJMp2026913
This is a very important hypothesis. If true, it would mean that wearing mask helps ensure that new cases of Covid are asymptomatic. It would help generate immunity without causing symptoms.
While it is by no means conclusive, one interesting piece of evidence is data from cruise ships. This is because cruise ships are closed spaces where a lot of people, unfortunately, contract the virus.
In several Covid outbreaks on cruise ships where people did not have access to masks, only 20% of those infected experienced no symptoms.

By contrast, in an outbreak on an Argentinian cruise ship where passengers and staff wore masks, the rate of asymptomatic infection was 81%.
Put differently, universal masking policies, at least in indoor settings, could potentially reduce the proportion of new Covid cases who experience symptoms by quite a lot.
Why might wearing a mask help reduce the severity of disease?

Because the viral inoculum (the infecting dose of virus) might help determine the severity of an infection.
If the viral inoculum is found to have an impact on severity of Covid, masks could play an important role by filtering out some droplets that contain the virus.

By doing that, masks might reduce the inoculum that exposed people inhale and thereby reduce the severity of illness.
However, this is just a hypothesis. We have a lot less data supporting the notion that masks reduce the severity of Covid than we have evidence supporting the efficacy of masks in reducing the spread of Covid. But it's worth studying. Read more here: https://www.nejm.org/doi/full/10.1056/NEJMp2026913
H/T @Nakhasi_MD for sharing the New England Journal of Medicine article.
To sum up:

(1) Trump's statement is totally wrong.

(2) Wearing a mask protects you from getting infected.

(3) Wearing a mask protects others from getting infected by you.

(4) Wearing a mask might potentially reduce the proportion of new cases who experience symptoms.
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