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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.

enter image description here

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.

enter image description here

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?

Thanks! Ryan

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  • $\begingroup$ As you suggest, this may be primarily due to N. I wouldn't be surprised if the effect is trivial. That said, for some armchair theoretical speculation, it could be that just chemo &/or radiation are really hard on the body, & those few people who would have survived anyway are worse off for it. $\endgroup$ – gung Jul 27 '16 at 20:55
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    $\begingroup$ I believe this is actually the classic example used to describe non-proportional hazards. Is there any reason not to just use the KM curves? $\endgroup$ – Cliff AB Jul 27 '16 at 23:43
  • $\begingroup$ @gung Also, I (maybe) just had an epiphany that the HR estimated by the Cox model is an instantaneous rate. So, as seen in the KM curves, the tangent line at 18 months for the no treatment group is less negative than the tangent line at 18 months for either treatment group. Thus, the more negative slope at 18 months for both treatment groups relative to no treatment indicates that the hazard is larger in both treatment groups. Had the proportionality of hazards assumption been satisfied, the tangent lines would be identical across all time points for all groups... $\endgroup$ – Ryan W. Jul 28 '16 at 14:47
  • $\begingroup$ @CliffAB I'll be adding patient demographic and clinical characteristics to the Cox model to get adjusted HRs. On a side note, I'm still having problems explaining this model to the oncologist. The no adjuvant therapy (NAT) group has more early deaths compared to the chemo (C) or chemo-radiation (CR) groups. So, C and CR are good at extending life relative to NAT. At 18 months, only 10% of NAT patients are alive to contribute to the risk estimate, so is the lower risk of death after 18 months for NAT not that it is "better" than C or CR, but simply due to the hazard hitting the ceiling? $\endgroup$ – Ryan W. Sep 12 '16 at 19:46

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