[R] covariate selection in cox model (counting process)

[Thomas Lumley]

On Mon, 26 Jul 2004, Mayeul KAUFFMANN wrote:

> Hello everyone,
> I am searching for a covariate selection procedure in a cox model
> formulated
> as a counting process.
> I use intervals, my formula looks like coxph(Surv(start,stop,status)~
> x1+x2+...+cluster(id),robust=T) where id is a country code (I study
> occurence of civil wars from 1962 to 1997).
> I'd like something not based on p-values, since they have several flaws
> for
> this purpose.

You may be out of luck.  In the case of recurrent events coxph() is not
using maximum likelihood or even maximum partial likelihood. It is
maximising the quantity that (roughly speaking) would be the partial
likelihood if the covariates explained all the cluster differences.

Partial likelihood for single events does have an AIC analogue that works
reasonably well (not surprisingly, since the partial likelihood is also a
perfectly valid marginal likelihood for the ranks of the survival times).
For recurrent events this isn't going to work.

If you absolutely have to do covariate selection you may need to look for
a maximum likelihood approach, such as a parametric model with random
effects to describe the dependence.  You might be able to use survreg()
with frailty() terms.

	-thomas

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