I have a massive data set of about 25000 pancreatic cancer patients; extremely quick and depressing mortality rate. I'm interested in survival differences between three groups--no treatment, chemotherapy, and chemo-radiation. Below is the survival function produced by PROC LIFETEST.
I have some evidence that the proportionality of hazards assumption is violated. Statistically, the estimated group*time interaction (programmed within PROC PHREG) is statistically significant. This makes sense given the large N. However, the graphical approach is a bit more subjective; see the log-negative-log survival function below.
If I choose to retain the group*time interaction, the survival differences estimated by this extended Cox model diverge from what I would expected based on what I see in the Kaplan-Meier analysis. Specifically, both chemotherapy and chemo-radiation show significantly lower risk of death (or better survival) than the no treatment group until about 12-months post-diagnosis, at which point the effect switches, and by 18-months post-diagnosis the no treatment group has significantly lower risk of death than either treatment group.
Knowing who I am working with (err, for...), I'm going to have a hard time explaining this result. I'm guessing it has to do with the interaction. Do you think that I mis-specified time function? Any thoughts on this? Has anyone else seen this?