Thanks a lot to Terry Therneau for his very complete answer.
Sylvie DALLOT
USDA/ARS/USHRL
2001 South Rock Road
FORT PIERCE, FL 34945
USA
phone: 1 772 462 58 60
FAX: 1 772 462 59 86
>>> Terry Therneau <therneau@mayo.edu> 08/21/03 05:22PM >>>
Yes, cox.zph is still valid for time dependent covariates.
However, there is one caveat, sometimes important. As a purely computational
shortcut, cox.zph assumes that the variance matrix of X, V(t), does not
actually vary substantially over time. And in most data sets, this is
true. With time-dependent covariates one can obviously construct a counter
example: X is spread out at the beginning, but after day 30 everyone has X=15.
In this case cox.zph is just wrong, in the simple arithmetic sense that it
was using a shortcut approximation that didn't work. Fixing the computation
has been on my list for a long while, constantly put off by other more pressing
concerns.
There is a growing sense in the literature that for long term studies the
V(t) assumption is not "almost certainly" correct, as I once thought
(usually ok, but not certain). One can use coxph.detail to get V(t) directly
and look at it.
Terry Therneau
>>> "Sylvie Dallot" <sdallot@ushrl.ars.usda.gov> 08/21/03 04:43PM >>>
Hello all,
I want to use an extended Cox model to allow for the incorporation of a
time-varying covariate (each individual is subjected to several measurements
over time).
I modified my data set adequatly to get as many time intervals as necessary
and use the coxph(Surv(start, stop, event) ~ X1 + X2.+ X3.) function, where X1
and X2 are fixed-time covariates and X3 the time-varying covariate.
I wonder if the cox.zph function can still be used to assess the independence
of the beta coefficients with time?
Thanks
sylvie
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