An observational cohort study involves measuring procalcitonin PCT on a daily basis in a cohort of patients with infection who are on antibiotics. When PCT concentration reaches a level of
I suggest you calculate for each patient the difference in days between the day of treatment stopped and the day PCT was less than 0.25. This could be positive or negative but most likely the day of treatment stopping would be greater than the day of PCT < 0.25.
Then find the mean of these differences across patients and test its significance (compared to zero) using the t distribution, and calculate corresponding confidence limits. This is not a paired t test.
You would be interested in comparing the mean number of days to PCT < 0.25 to the mean number of days of antibiotic use, trying to prove that there is a statistically significant difference between the two.
While this is the same sample, you have two different measures an it seems ideal to make an independent sample comparison, assuming normality.