Veterans Administration Data wrong hazard ratio reported

[aeleuteri]

Dear Professor, There seems to be an issue with the reported hazard ratio (and interpretation) of the Veterans data in the timedep vignette:

https://github.com/therneau/survival/blob/37792dbd5f5d28370c2f16526cff514466e362cb/vignettes/timedep.Rnw#L879

The coefficient from the fit is -0.033771, which means that the hazard ratio for the karno quantiles is exp(-0.033771*(75-40))=0.31, i.e. the Karnofsky score is overall protective; and the graph shows a large protective effect at the start, which wanes later. These considerations reflect section 6.3 in the textbook Modeling Survival Data.

Regards Antonio

[therneau]

Someone at the first quartile of Karnofsky score (40) is at much higher risk than someone at the third quartile (75). Remember that a Karnofsky of 100 is good, 0 is dead. The sentence is correct as stated.

[aeleuteri]

Thanks for the reply. I am missing something then, I think. Assuming that -0.05 is meant to approximate the (almost) -0.06 at time 0 in figure 1 from the spline smoothing, then we get that for subjects with Karnofsky 40, the hazard is exp(-0.05 x 40)=0.14, and for subjects with Karnofsky 75, it's exp(-0.05 x 75)=0.024; so higher Karnofsky, lower risk (as intuition suggests). So why the statement that "Early on it has a large negative effect"?

[therneau]

I am saying that "abnormal value of Karnofsky at enrollment is bad" and you that "high Karnofsky is good".
Later in time the enrollment Karnofsky (which is the only one we have in this data) is so out of date that it is no longer predictive. In this advanced cancer cor(Karnofsky at enrollment, Karnofsky at 200 days) is, unfortunately, not very strong. The originally low K have died, and other subjects who once were high are failing.

[aeleuteri]

Thank you! I was "lost in translation"; I am not a native English speaker, so I misinterpreted the meaning of "early on".