The `parametric survival models' in S-PLUS are accelerated life and not
proportional hazard models. That's one part of the difficulties, such as
they are. Another is that the `partial likelihood' used for Cox models
avoids some integrations. (If you have a time-dependent covariate the
pdf is no longer a simple function of the hazard and you need to know the
CDF or cumulative hazard.)
On Fri, 31 Jan 2003, Robert Dodier wrote:
> Hello,
>
> I am looking for information about parametric
> survival models with time dependent covariates.
> The only reference I can find specifically devoted
> to parametric survival (as opposed to Cox models)
> seems to imply that it is not easy to incorporate
> time dependent covariates into a parametric
> survival model. (See this message dated April 17,
> 2001, in the s-news archive:
> http://www.biostat.wustl.edu/mailinglists/s-news/200104/msg00154.html)
>
> So, I wonder where the difficulty lies. If I can
> better understand the problem, perhaps I will be able
> to formulate a workable approximation or some such.
> What is it about time dependent covariates that makes
> the extension of the Cox model straightforward, yet
> parametric survival models more difficult? Is there
> a "brute force" approach which will give the correct
> answer at the price of burdensome computations?
Yes: compute the likelihood and maximize it.
--
Brian D. Ripley, ripley@stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272860 (secr)
Oxford OX1 3TG, UK Fax: +44 1865 272595
|