From: Christian Hennig <fm3a004_at_math.uni-hamburg.de>

Date: Mon 14 Mar 2005 - 23:22:53 EST

Christian Hennig

Fachbereich Mathematik-SPST/ZMS, Universitaet Hamburg hennig_at_math.uni-hamburg.de, http://www.math.uni-hamburg.de/home/hennig/

>From 1 April 2005: Department of Statistical Science, UCL, London

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Mon Mar 14 23:28:18 2005

Date: Mon 14 Mar 2005 - 23:22:53 EST

Dear list, dear Frank,

I try to fit a Weibull survival regression model with package Design:

sclear <- psm(sobj~V1+V2,dist="weibull")

sobj is a one-dimensional survival object (no event indicators), V1 and V2 are factors.

I get the following result:

Parametric Survival Model: Weibull Distribution

psm(formula = sobj ~ V1 + V2, dist = "weibull")

Obs Events Model L.R. d.f. P R2 120 120 30.96 3 0 0.23 Value Std. Error z p (Intercept) 2.6161 0.0639 40.94 0.00e+00 V1=2 0.3098 0.0748 4.14 3.47e-05 V1=3 0.0911 0.0741 1.23 2.19e-01 V2=2 -0.2212 0.0613 -3.61 3.09e-04 Log(scale) -1.1060 0.0704 -15.70 1.52e-55

Scale= 0.331

I wonder how to relate the estimated parameters to the Weibull regression model. Here is the model specification from Harrel, Regression Modeling Strategies, p. 422:

S(t|X)=exp[-\alpha*t^\gamma exp(X\beta)]

This is the model without intercept, and it is indicated that \alpha can be replaced by exp(\beta_0) in the model with intercept.

Now I am puzzled by the fact that \alpha (or \alpha exp(X\beta))
is usually referred to as

"scale parameter" in the context of the Weibull distribution. If this would
be the case, I could get the Weibull scale from the \beta/\beta_0 estimators
and I would need an estimator for \gamma. But only one further estimator is
given which is called "scale". This is definitely not the \gamma estimator,
because if I compute, say, median estimators, I get a result outside the
value range. From survplot I know that the model fit of the survival
function is OK, so in principle it seems that I did the right thing.

But how do I relate the output to the parameters \alpha,\gamma,\beta in the model?

Thanks,

Christian

Christian Hennig

Fachbereich Mathematik-SPST/ZMS, Universitaet Hamburg hennig_at_math.uni-hamburg.de, http://www.math.uni-hamburg.de/home/hennig/

>From 1 April 2005: Department of Statistical Science, UCL, London

#######################################################################ich empfehle www.boag-online.de

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Mon Mar 14 23:28:18 2005

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