[R] How to use the whole dataset (including between events) in Cox model (time-varying covariates) ?

Thomas Lumley tlumley at u.washington.edu
Fri Aug 13 16:21:00 CEST 2004

On Fri, 13 Aug 2004, Mayeul KAUFFMANN wrote:

> > you can always use parametric models and a
> > full likelihood (but you may have to program them yourself).
> > Prof Brian Ripley
> I started trying this but I could not make the counting process notation
> work on this.
> (Andersen, P.K. and Gill, R.D. (1982). Cox's regression model for counting
> processes: A large sample study. Ann. stat. 10 , 1100-1120).
> I think it is only (currently) available for Cox model with R.
> survreg(Surv(start, stop,status)~  x1,data=data )
> Error in survreg(Surv(start, stop, status) ~ x1, data = data) :
>  Invalid survival type

Yes. survreg() fits parametric accelerated failure models, not
proportional hazards models, and time-varying covariates present more
difficulties for accelerated failure models.

However, you were concerned about bias because the covariates at event
times are not representative.   If this is the case, the bias will still
be present in a parametric proportional hazards model, and you do not have
proportional hazards.  The Cox model gives consistent estimates whenever a
parametric proportional hazards model does, and the loss of efficiency is
typically very small.

To recover inter-event information, and especially if it is needed to
remove bias, you probably need a joint model for the event process and the
covariate process.


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