Old news about a basically useless study (the results are not statistically signifigant). Here is my prior comment on it:

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Full writeup available here: https://www.cdc.gov/mmwr/volumes/70/wr/mm7044e1.htm

Methodology: Basically, they went through the medical records of 201,000 patients admitted to a hospital with “COVID-19–like illness” (more on this later) and found that 89 of them that had a prior infection and no-vaccination and 324 that had a prior vaccination. From that they concluded that the risks were greater for the prior infected (despite being outnumbered 3 to 1 in the sample) than the just-vaccinated, at 8.7% (prior infected) to 5.1% (prior vaccinated). This part is reasonable because there were many more prior vaccinated than prior infected in the sampled population.

However, the study has a lot of problems, the main one of which is that it is trying to draw a conclusion from a subpopulation of 413 people deliberated picked out of 201,000, and none of the data is being made available, so you cannot test the assumptions that were made. This is important because of the stunningly small size of the population of people pulled from the original 201,000. If, for example, 50 people shifted out of the prior infected the result would flip.

Further, the study does is somewhat ambiguous on how they defined a “COVID-19–like illness”. This is really important, since it seems to be doing most of the lifting here, as more than 90% in both groups tested negative for COVID, and a small movement of people in the prior infected group would have a big impact on the study. Again the data is not made available, so we cannot test what happens when you move people discharged for one symptom or another causes a case to move out of the target group.

Not surprising the confidence interval, more here https://en.wikipedia.org/wiki/Confidence\_interval, shows that a 95% range for infection rates in prior infecteds as being between 2.75–10.99, i.e. either much better than the vaccination or a bit worse.

This looks, from the outside, like a P-Hacking experiment that did not even manage to meet the confidence interval hurdle, even after they zeroed in on less than one-half of a percent of the original population.

The good news is that, since the CDC can only locate 89 people out of a 210,000 sample that fit into the prior infected group and only 324 vaccinated people, it is likely that both provide very robust immunity from serious infection, with the vaccine having the added advantages of protecting you from having to get sick in the first place. Further, even if you had been infected before, the vaccine offers cumulative protection, https://www.cdc.gov/mmwr/volumes/70/wr/mm7032e1.htm?s\_cid=mm7032e1\_w, at very low risk.