As mentioned below, I also find that parametric survival models
are much easier to work with for getting survival curves and
cumulative hazard functions with time-dependent covariables. See
@ARTICLE{her95res,
author = {Herndon, James E. and Harrell, Frank E.},
year = 1995,
title = {The restricted cubic spline as baseline hazard in the
proportional
hazards model with step function time-dependent covariables},
journal = Stat in Med,
volume = 14,
pages = {2119-2129},
annote = {spline; restricted cubic spline; time-dependent covariables;
PH
model}
}
I always meant to incorporate the Fortran program used in that
paper into S-Plus but never got around to it. If anyone is
interested in doing this that would be wonderful.
Frank Harrell
longhow.lam@nl.abnamro.com wrote:
>
> Hi,
>
> My original question:
>
> I am analyzing survival data with time varying covariates. I am using the
> coxph function with counting process format for the data. I have quit a lot
> of data, fitting the model is not a problem but when I calculate an
> expected survival for one individual with a certain covariate path this
> takes a lot of memory and time. And I need to calculate the expected
> survival for a lot of individuals each with a specific covariath path.
>
> Would switching to parametric models help? I believe that these models are
> not implemented in S-PLUS, does anyone have experiences with fitting and
> analyzing parametric survival models (in S-PLUS) ?
>
> ***********************************************************
>
> Parametric models for survival analyis are available in S-PLUS but not with
> time varying covariates. It seems that you can do it with eiter Stata or
> Limdep.
>
> Thanks to those who responded,
> cheers
> Longhow.
>
> Responses I had so far:
>
> Parametric survival models are implimented in Splus (survReg or censorReg).
> They don't handle time-dependent covariates: I am not aware of any
> parametric
> model that does. (It leads to a programming/bookkeeping morass, which no
> one
> seems to have had the energy to tackle).
>
> Terry Therneau
>
> **************************************
>
> I'm pretty sure that survreg does standard parametric survival regression,
> but I'm not sure whether it can cope with time-varying covariates. If not,
> then the solution could lie in using GLMs to fit the survival analysis,
> this is covered in a Chapter in McCullagh and Nelder. The idea is to model
> the counting process data as a Poisson process with a log link and linear
> predictor function of the form
>
> offset(hazard(time))+coeff%*%covariates(time) .
>
> Where hazard(time), is the baseline hazard function which you want to use
> in your parametric model. This is justified by examining the two
> likelihood functions and observing that they are proportional. In the case
> of Cox proportional hazards, the offset(hazard(time)) is replaced by
> factor(time), as no assumptions are made about the baseline hazard.
>
> However, going back to your original problem, I've no reason to see why
> this should be any more computationally efficient than coxph.
>
> regards,
>
> Simon Bond
>
> ********************************************
> Parametric survival can be done using the censorReg function in
> S-PLUS. There is a chapter or 5 on survivial analysis in the free
> documentation that you can download from Insightful.
>
> http://www.insightful.com/resources/doc/default.html
>
> The survival stuff is in "Guide to statistics volume 2", the survival
> stuff starts in chapter 8 and the parametric survival is in chapter 11.
>
> hope this helps,
>
> Greg Snow, PhD
>
> *****************************************************
>
> I believe they are, perhaps depending on what version of Splus you have.
> Look for a function named censorReg(). It's in unix versions 5 and 6 for
> sure.
>
> -Don
>
> Hi Longhow,
>
> I use discrete-time models, eg binomial regressions with a cloglog link.
> See: Prentice RL, Gloeckler LA, 1978. Regression analysis of grouped
> survival data with application to breast cancer data. Biometrics, 34:
> 57-67.
> It's straighforward to use and you won't have problems with predictions
> (I guess !). The biggest problem is to turn the data into an appropriate
> format. Moreover, you can't use a continuous time-dependent covariate,
> or you will have to discretize it.
>
> Hope this helps,
>
> Renaud
>
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--
Frank E Harrell Jr Prof. of Biostatistics & Statistics
Div. of Biostatistics & Epidem. Dept. of Health Evaluation Sciences
U. Virginia School of Medicine http://hesweb1.med.virginia.edu/biostat
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