Did any of these studies compare people who were vaccinated with people who had COVID19 at the same time relative to sampling? In this paper the two groups are

Did any of these studies compare people who were vaccinated with people who had COVID19 at the same time relative to sampling? In this paper the two groups are separated in time, making it very hard to interpret the results. The effect could simply be due to difference in antibody titer at different times from infection.