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: kevin.thorpe at utoronto.ca Tel: 416.946.8081 Fax: 416.946.3297
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
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: kevin.thorpe at utoronto.ca Tel: 416.946.8081 Fax: 416.946.3297