[R] parametric proportional hazard regression

Thomas Lumley tlumley at u.washington.edu
Mon Jul 10 16:12:54 CEST 2006

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

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