I'm not too familiar with survival analysis, so this may be a somewhat basic question.
I am interested in the time between two events [$A$ – medication] and [$B$ – time of first treatment], the latter which can be equal to $A$. Specifically, I want to know if this varies across years.
The subjects in question have at least 5 years of data, and I have data from 2001-2011. Because of this, tests on summary statistics won't do (subjects in 2011 have the capacity to have up to 11 years while subjects in 2006 only have the capacity to have 6).
So instead, I'm considering the value $A-B$ to be censored if $B$ falls within one year of the subject entering the dataset, and then constructing a KM curve. However, the time length covered by each group will still end up different, like so:
By visual inspection, the survival curves are different, though only the 2011 vs any other group comparisons are significant by the logrank test.
Alternatively, I can truncate time differences greater than 5 years (considering them censored):
This results in the exact same curve for years <= 5 as expected, however, the logrank test returns more significant differences (2010 vs any other group).
I'm not sure which of these setups is more appropriate.
Best Answer
The censoring process needs to be independent of the survival process. I would advocate the second method of censoring at 5 years, as this ensures that the censoring time is independent of the survival process and any relevant covariates.
Also note that time A and time B may be influenced by the same covariates (e.g. disease severity, but also year due to treatment protocol changes), so using B-A as the time of interest may be problematic. A classic example of this problem is the change in breast cancer mortality due to earlier detection.