I have data across 8 different time-points that is both left, right, and interval censored (also randomly censored) that I am trying to use to conduct a survival analysis. The left-censoring should not be a problem because I can adjust respondents and set T1 as each respondents' first response (meaning that there will be a lot of right-censoring but I think this is okay).
My issue is that a lot of respondents come and go throughout the dataset (i.e., they may respond at time 1 and 2, not respond at time 3 and 4, and reappear for time 5 and 6, etc.) and I wasn't sure what the best way is to deal with this data... should I use data imputation to propagate those with missing values between valid responses? For context, my data is trying to identify whether smokers 'survive' as smokers or quit smoking (i.e., failure).
Additionally, if anyone has experience with this type of issue particularly when using R, I would greatly appreciate suggestions on what packages/functions I should be using.
I hope this makes sense and I have provided sufficient information. Thanks very much in advance.