That's a different study, but one that I really wish more people would look at. They don't seem to WANT to know that critical question.
Natural immunity studies are nearly impossible. A vax injection is precisely known as to exact day of the event. A naturally acquired infection and any immunity derived from it will not be known as to day of the event.
The best that can be done is the date of the PCR test that indicated an actual infection. Quite a few of these “natural immunity” studies are people who never got a specific PCR test but felt ill and “I just knew I got the virus” sort of people.
With all these uncertainties, you will never get a study of decent quality. Further, the general idea is to NOT get the infection and risk death — just to declare you have natural immunity.