I have some difficulties understanding the effect of the truncated data on my estimation of survival function.
I am studying the survival for some "dependent" people (policyholder with Long Term Care contracts). I want to study how long they survive based on their age at entry (because the survival function is different by age at entry into dependency state). I have a database of 15 years where I can observe entries and exit from dependency (for death or other type of event). I also have some people that are already dependent at the start of the study.
I've set this start of study to 01/01/2000 because data before are not reliable and where death event and censorship are melted. However, I want to keep the information provided by already dependent policyholder at 01/01/2000 especially that I have their real entry date into dependency state.
I choose to look at their survival starting from 0. It's easy to understand what happen with all new dependent within our observation period. Starting from 0, we can observe them until they left the study (death or other).
However, I'm wondering how the already dependent people at begining will influence my risk set (or exposure). Do I have to consider these people at the begining (starting time spent of 0) or as entering the risk set with a time spent in the dependency state corresponding to their real time spent (as I know the entry date even before 01/01/2000).
In the first case, I would include them in the exposure at the begining of the study, while in the latter case, the exposure will be the sum of all new dependent people entering within the observation period, and then having the exposure variating when we reach time spent by the policyholder (calculated at the begining of the study).
Let me know if it's not clear and sorry if english is approximate
thank you for your help