Wednesday, November 10, 2021

Infection Rates and Vaccination

Unvaccinated people are about 29 times more likely to be hospitalized with Covid-19 than those who are fully vaccinated, according to a study released Tuesday by the Centers for Disease Control and Prevention.

The new study, published in the CDC’s Morbidity and Mortality Weekly Report, also found that unvaccinated people were nearly five times more likely to be infected with Covid than people who got the shots. (CNBC)

The question is not is it true but how could we know. Hospitalization and death are observable, countable events, but infection is only observed when someone is tested. The U.K. has a program of randomly testing people in order to learn, among other things, how many of them were infected with Covid (REACT-1). But the CDC appears to be just counting people known to be infected.

Vaccination is much stronger protection against a serious case of Covid than a mild case, as shown by the difference between the first paragraph quoted above and the second. One would therefor expect a much larger fraction of vaccinated infections to be asymptomatic. If an infection is sufficiently asymptomatic the victim does not notice and so has no reason to get tested. Unless the CDC is somehow compensating for that problem, its count of the infection rate for vaccinated people is not only too low, it is too low by more than its count of the rate for unvaccinated, hence it is overestimating the protection that vaccination provides against infection.

The effect of vaccination on hospitalization and death rates are what you need to persuade someone that it is in his private interest to be vaccinated — and, on those grounds, I am. The effect on the infection rate is what you need to show that vaccinating one person protects others in order to defend forcing people to get vaccinated. The CDC supports vaccination requirements, which is why I doubt that they have gone out of their way to correct the overestimate of the strength of vaccination against infection that comes out of simply counting known infections. 

What the real protection against infection is I do not know. The estimate from the UK study (ignore the headline) is 50 to 60%, much lower than the CDC claim, but that is a different population and a different mix of vaccines.

A second argument is the claim that someone vaccinated and infected is less contagious than someone unvaccinated and infected. I have seen various claims as to whether that is or is not true, based on measured viral levels in the infected, but we now have something better, a study based on observed infections of people who were close contacts of infected individuals:

Unfortunately, the vaccine’s beneficial effect on Delta transmission waned to almost negligible levels over time. In people infected 2 weeks after receiving the vaccine developed by the University of Oxford and AstraZeneca, both in the UK, the chance that an unvaccinated close contact would test positive was 57%, but 3 months later, that chance rose to 67%. The latter figure is on par with the likelihood that an unvaccinated person will spread the virus. (Nature)
All of which explains why the effect of vaccination on Covid rates has been much less than many of us expected. Death rates have fallen sharply but infection rates have gone up and down, even in well vaccinated populations such as the U.K. and Israel, much as they did before. The most one can say, at least from a casual look at the data, is that the reduced infection rate from vaccination has roughly balanced the increased infection rate from the Delta variant.

 

3 Comments:

At 9:42 PM, November 10, 2021, Blogger Tom Hudson said...

Population-wide infection rates are driven by a lot more than vaccination; although UK vaccination rates are high, compliance with the rest of the current protocols is not. I spent a couple of hours on the tube last weekend and masking was around 25% despite the frequent reminders that it is still mandatory on public transport.

One attempt to get a better idea of accrual nonsymptomatic infections is the widespread testing program in the UK; we have free low quality home tests widely available, many work/school contexts encourage you to self-test at least twice a week, and you're expected to report all results, positive or negative. There again compliance doesn't seem to be high, which would among other effects seem to lead to over estimating fraction of tests that are positive.

 
At 10:03 PM, November 11, 2021, Blogger David Friedman said...

One possibility, more generally, is that the protection provided by vaccination is to some degree balanced by people being less careful once they are vaccinated. It's certainly true of me. My probability of getting infected is probably higher now than before I and the rest of my family were vaccinated, since back then we were self-quarantining very tightly.

I don't know how big that effect would be for the U.K. I think the importance of masking, at least as interpreted here, is exaggerated. A well fitting N95 mask probably provides significant protection, but a bandanna over the mouth doesn't, and that gets counted as masking as well. But whether people spend most of their time at home with their family our out interacting with strangers could have a big effect.

 
At 9:04 AM, November 12, 2021, Anonymous Mark P said...

Professor Friedman - You may be interested in this study out of Sweden on the efficacy of vaccines (each of Moderna, Pfizer, AstraZeneca) in reducing both infection and severe outcomes: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3949410. Looks like they have the luxury of a robust national registry, and the Swedish Ethical Review Authority willingness to waive the consent requirement. The cohort study includes almost 1.7 million people paired by age, sex, and location out of a pool of almost 6 million (over half the population of the entire country).
Naturally it is difficult to control for behavioral changes based on personal risk tolerance, which you touch on. But it is pretty damning that the CDC cannot do any better than their numerous, shoddy, largely anecdotal studies - from vaccine efficacy to masks - after almost two years of this experience.

 

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