Re: [R] parametric proportional hazard regression

From: Thomas Lumley <tlumley_at_u.washington.edu>
Date: Tue 11 Jul 2006 - 00:12:54 EST

On Fri, 7 Jul 2006, Valentin Dimitrov wrote:
>
> I do not need a accelerated failure model, but a
> proportional hazard model with a f0= weibull,
> exponential, loglogistic or lognormal baseline
> distribution. The hazard function is
> lambda(t)=exp(Xi*beta)*lambda0(t),
> where lambda0 is the baseline hazard
> lambda0(t)=f0(t)/(1-F0(t)) where f0 and F0 are the
> baseline density and cumulative distribution
> functions.
> This is a proportional hazard model since the ratio
> lambda(t|Xi)/lambda(t|Xj)=exp(Xi*beta)/exp(Xj*beta)
> does not depend on t.
>

For a weibull (including exponential) model you can do this with survreg. For the other models you would have to maximize the likelihood directly. This will involve writing the likelihood directly in terms of the hazard and cumulative hazard, since a proportional hazards model that is gaussian at X=0 is not gaussian at any other X.

         -thomas

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

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