[R] Why is transform="km" the default for cox.zph?

[Thomas Lumley]

On Fri, 7 Apr 2006, Kevin E. Thorpe wrote:

> To enhance my understanding, and that of my students, I have a question
> about cox.zph in the survival package.
>
> If I have correctly gleaned the high-level point from the 1994
> Biometrika paper of Grambsch and Therneau, it looks to me like
> cox.zph provides a mechanism to test for a simple trend in plots
> of a function of time, g(t) versus the scaled schoenfeld
> residuals and it also provides some built-in ones and the capability
> to provide your own.  It also appears to me that different forms look
> at different departures from proportionality.

Yes. The tests are approximately score tests against beta(t)=beta0+beta1*g(t)

> So, my question is what are the advantages and disadvantages of the
> default transform="km" compared to say, identity or log?

The person most likely to be able to answer this question is the author of 
the code, Terry Therneau, who doesn't (AFAIK) read any of the R mailing 
lists. I think he still reads s-news, though.

One advantage of transform="km" is that there are always observed events 
when the KM estimator is changing, so it doesn't try to pick up changes in 
hazard ratio where there is no information.  This is good behaviour for a 
default, especially if you assume that anyone with an actual hypothesis as 
to g(t) will specify transform= explicitly.

An obvious disadvantage is the lack of ready interpretation of beta*g(t).

 	-thomas

Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle