# Survival analysis - time-dependent covariate with left truncation

I have some data on patients receiving pancreas transplants. Some of these patients have a procedure done post-transplant called enteric conversion, and I am looking at the effect of this conversion as time dependent for several outcomes, including mortality. Normally this would be very straightforward but there is also truncated data.

In our database, we have all the pancreas transplants at our center going back into the late 1970s. However, we only started collecting retrospective data on pancreas transplants in 2003. That means that if a person was transplanted prior to 2003, and either died or was lost to follow-up prior to 2003, we would not know if they had this procedure done after their transplant.

My first step was to limit the cohort to only those who were alive and not lost to follow-up as of 2003. The timing of the enteric conversion could still occur any time after transplant, for example if someone is transplanted in 1995, has a conversion in 1999, and is followed up through 2003 or later we would know the date of the conversion.

However, I realize there is a real issue of left truncation here as someone has to survive to 2003 to be included - thus my survival estimates (especially for mortality) will be overly optimistic.

My question is how to analyze such data. I typically use R, but am using SAS here as you don't to convert the data to a counting process style. It seems like you cannot account for both left truncation and time-dependent covariates in one model, but I'm not sure.

Here is the SAS code for mortality using a TDC (convert_yrs is the time from transplant to conversion only for those with conversion - it is missing otherwise):

proc phreg data=panc;
model death_time*death_censor(0)=convert_tdc;
if convert_yrs>=death_time or convert_yrs=. then convert_tdc=0; else
convert_tdc=1;
run;


And here is what I understand to be the SAS code for left truncation. I believe "t1" should be the age as of 1/1/2003 but I'm not sure:

proc phreg data=panc;
model death_time*death_censor(0)= /entry=t1;
run;


Thanks for any help you can provide.