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

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

Kevin E. Thorpe
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.

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

Thank you.

Kevin

--
Kevin E. Thorpe
Biostatistician/Trialist, Knowledge Translation Program
Assistant Professor, Department of Public Health Sciences
Faculty of Medicine, University of Toronto
email: [hidden email]  Tel: 416.946.8081  Fax: 416.946.3297

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Re: 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
[hidden email] University of Washington, Seattle

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Re: Why is transform="km" the default for cox.zph?

Kevin E. Thorpe
In reply to this post by Kevin E. Thorpe
At the suggestion of Thomas Lumley, I posted this to s-news.
Dr. Therneau replied and I have posted (with permission) his
answer below the original question.

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

=== Begin Dr. Therneau's Reply ===

There are 2 reasons for making the KM the default:

  1. Safety:  The test for PH is essentially a least-squares fit of
     line to a plot of f(time) vs residual.  If the plot contains an
     extreme oulier in x, then the test is basically worthless.  This
     sometimes happens with transform= identity or transform =log.
     It doesn't with transform='KM'.

     As a default value for naive users, I chose the safe course.

  2. A secondary reason is efficiency.  In DY Lin, JASA 1991
     Dan-Yu argues that this is a "good" test statistic under various
     assumptions about censoring. (His measure has the same score
     statistics as the KM option).

But #1 is the big one.

     Terry T.

=== End Dr. Therneau's Reply ===


--
Kevin E. Thorpe
Biostatistician/Trialist, Knowledge Translation Program
Assistant Professor, Department of Public Health Sciences
Faculty of Medicine, University of Toronto
email: [hidden email]  Tel: 416.946.8081  Fax: 416.946.3297

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https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html