Kentucky study of Covid resistance among previous infected is a bad study

Israeli study: Natural immunity better than vaccine.

The dishonest press release for the Kentucky study

Kentucky Study: 

Overall, 246 case-patients met eligibility requirements and were successfully matched by age, sex, and date of initial infection with 492 controls. Among the population included in the analysis, 60.6% were female, and 204 (82.9%) case-patients were initially infected during October–December 2020 (Table 1). Among case-patients, 20.3% were fully vaccinated, compared with 34.3% of controls

This study found that among Kentucky residents who were previously infected with SARS-CoV-2 in 2020, those who were unvaccinated against COVID-19 had significantly higher likelihood of reinfection during May and June 2021. This finding supports the CDC recommendation that all eligible persons be offered COVID-19 vaccination, regardless of previous SARS-CoV-2 infection status.

So, the study does not compare "people who previously had covid" with "people who did not previously have covid, but were vaccinated".  it compares "people who previously had covid and since then were vaccinated" vs "people who previously had covid and did not get the vaccine."

So, on the question of "what provides better protection, being infected, or getting the vaccine", the study says nothing.

On the study design, what I can say is "it's crap".

Here's the meat of the study:

Overall, 246 case-patients met eligibility requirements and were successfully matched by age, sex, and date of initial infection with 492 controls. Among the population included in the analysis, 60.6% were female, and 204 (82.9%) case-patients were initially infected during October–December 2020 (Table 1). Among case-patients, 20.3% were fully vaccinated, compared with 34.3% of controls

1: They only took people who had Covid between March and December of 2020.  So to the extent that there's a time delay fall off issue, they weighted it in favor of the vaccine (they should have taken anyone who had previously had Covid, including those who had it this year).

2: 246 positive cases over May and June.  I pulled up the Worldometer KY Covid totals

By eyeball, KY averaged 400 - 500 cases a day over that time period (61 days)

That means ~1% of the cases in May and June were people who had previously had Covid.

~14% of KY has had Covid

By June 30, 49.46% of KY had at least one vaccine shot, and 43.48% were fully vaccinated

So, what are the numbers that they had access to, but did not report as part of their study:

1: The % of those who had ever had covid, who got it again between May 1 - June 30

2: The % of those who were partially vaccinated, who got covid between May 1 - June 30.  With a breakout for "had covid before" vs "didn't have covid before"

3: The % of those who were fully vaccinated, who got covid between May 1 - June 30.  With a breakout for "had covid before" vs "didn't have covid before"

4 The % of those who had never had covid, and who weren't vaccinated, who got covid for the first time between May 1 - June 30

Because "relative risk" is garbage.  "Oh, by not getting vaccinated you went from a 1 in 10,000 chance of getting Covid again, to a 2.34 in 10,000 chance of getting Covid again!  The horror!"

Whenever someone gives you relative numbers without giving you the absolute numbers, they're BSing you.

So, this study does not even address what its press release claims it proved (Covid infection vs vaccinated), and was poorly designed to prove anything.

I'm going with the Israeli study.  And so is anyone else with any sense