On 03/20/2014 06:00 AM, r-help-requ...@r-project.org wrote:
My question is related to a cox model with time-dependent variable.
When I think about it more, I get a little confused about
non-increasing assumption for survival probability for an individual.
For example, for a time-dependent ,say x, assuming increasing x
increases the risk of event. Assume,time t1 < t2. If at x at t1<< x
at t2, obviously, hazard at t1 will less than hazard at t2, assuming
no other covariaates. But is it possible that s(t2|x at t2) > s(t1|x
at t1), since at t2, an individual is at greater risk. This is kind
of confusing to me.
Thanks for any helpful insights!
Time dependent covariates and survival curves are confusing to a lot of people.
The Cox model is a hazard model
h(t, x) = h_0(t) exp(x beta)
which means it is a model of the moment-by-moment risk. A time dependent model
replaces x with x(t) which is the moment-by-moment value of x.
After the model is fit, one can compute the
time dependent cumulative hazard as
H(t,x) = \integral_0^t h_0(s) exp(x(s) beta) ds
and the survival is S = exp(-H).
Since everthing inside the integral is positive H(t) has to be an increasing function of
t, and thus S a decreasing one. The key thing to note is that H or S depend on the entire
covariate history for a subject. If you have a subject whose value of "x" changes from 1
to 2 at time 10, when computing their survival at time 15 you cannot just use a value of
"2" all the way from 0 to 15 in the formula.
Many Cox model programs (e.g.SAS) allow for time dependent covariates when computing the
Cox fit, but then only allow for fixed covariates when computing a curve. You can only do
predictions for people whose covariates never change. (For some diseases I work with such
people do not exist, e.g. in PBC your bilirubin WILL rise with time. So such a curve is
useless). This adds to the confusion.
Terry T.
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
