Re: [R] Proportional Hazard Function and Competing risks

From: Ravi Varadhan <>
Date: Wed 12 Jul 2006 - 01:21:50 EST


If you are interested in building regression models for the sub-distribution functions (or cumulative incidence function), then you may want to look at the "cmprsk" package by Gray. It is based on the article: Fine and Gray (JASA 1999). There is also the approach based on multi-state models (see the work of the Danish group led by Andersen) for modeling state probabilities.

If you are interested only in the cause-specific hazard models, then you don't need anything other than the standard Cox relative risk model or something like that, where events from other causes are simply treated as censoring.

If, however, you are interested in the net hazard or net probabilities, then you enter the dangerous and highly controversial realm of the "classical" competing risk problem. You have to overcome a lot of conceptual, philosophical, and statistical (e.g. identifiability) issues, before attempting to model it using latent failure time models. For a cogent critique of this approach, see Prentice et al. (Biometrics 1978). Crowder's (2001) book presents a somewhat more pragmatic view of the classical competing risks problem.

Hope this helps,

Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health Division of Geriatric Medicine and Gerontology Johns Hopkins University
Ph: (410) 502-2619
Fax: (410) 614-9625

> -----Original Message-----
> From: [mailto:r-help-
>] On Behalf Of Thomas Lumley
> Sent: Tuesday, July 11, 2006 10:56 AM
> To:
> Cc:
> Subject: Re: [R] Proportional Hazard Function and Competing risks
> On Tue, 11 Jul 2006, wrote:
> > How can I model coxph() in combination with competing risks
> >
> > i.e. I have two events and for event the object will leave the data set.
> > So :
> >
> > Coxph(Surv(time,event)~....) the event is for all my objects 1.
> >
> > How can I model this?
> There is nothing built in. Some proposals for competing risks analysis
> involve Cox models and generalized linear models and so can be implemented
> in R. It depends on what you want to do -- there isn't a standard
> solution because a lot of what people want to do with competing risks is
> provably impossible.
> -thomas
> Thomas Lumley Assoc. Professor, Biostatistics
> University of Washington, Seattle
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> guide.html mailing list PLEASE do read the posting guide! Received on Wed Jul 12 01:27:45 2006

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