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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

Actaman

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Your population is 'policy holders in our database from 01/01/2000 or after' but that is not a start date for your study. You are looking at survival after a determination of a dependent condition. This is the known start of duration for each study subject. So since you know this date of determination for subjects prior to 01/01/2000, I would keep them in the study. Since survival analysis permits rolling entry, there is no left censoring.

However, because death data from before 01/01/2000 is excluded, people with policies on 01/01/2000 might be biased to live longer in a dependent condition. For example someone that bought a policy on 01/01/1990 and becomes dependent on 01/01/1998 and dies on 01/01/1999 will be excluded from the study. I would create a dummy variable called ‘pre-2000’ and enter that in the model along with age.

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  • $\begingroup$ Thanks for your answer. It's exactly my problem, as I exclude some of the policies but keep others, I think that it creates an overestimation of survival as I keep only persons who survived after 01/01/2000 (my database start in reality at 01/01/1995). I'm wondering if there is any solution to avoid bias whithout the "easy" solution of excluding all these policyholders $\endgroup$ – Actaman Apr 18 '18 at 6:43
  • $\begingroup$ If I understand well, you propose to add the variable pre-2000 to identify such policies. To do that, I have to use a Cox regression for example to estimate the survival function ? What if, I want to use a non parametric estimation as of Kaplan-Meier, how these policies influences my risk set and at what moment ? $\endgroup$ – Actaman Apr 18 '18 at 6:59
  • $\begingroup$ Is it what we call delayed entries ? If so, and if we consider time spent as our variable of interest (studying the duration between time already spent at entry and exit time, using age at entry and age at leaving), can it be done by including these policyholder wihtin the risk set at time T only when their time already spent at entry is greater than the time T while other complete observation enter at time spent = 0. $\endgroup$ – Actaman Apr 18 '18 at 7:35
  • $\begingroup$ Since you have one continuous covariate, you need to use proportional hazards or some other type of regression. I would be more concerned about external changes over the 15 years such as new medications and definition changes in dependency status than biases from the earlier subjects. I don't understand your definition of delayed entry. $\endgroup$ – Georgette Apr 18 '18 at 15:53

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