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I'm trying to fit a parametric survival model using the survreg function
with a Weibull distribution.
I'm studying the time to death of individuals from different families
and I would like to fit different shape parameters (ie 1/scale in R) for
each of the families. I looked it up in the help pdf and on the
internet, but I couldn't find anything.
Would it be possible to do such a thing ?

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Yes it is possible -- but clearly I need to add one more example to the help 
page; use a strata() term.  

   Terry Therneau

> survreg(Surv(time, status) ~ ph.ecog + age + strata(sex), lung)
Coefficients:
(Intercept)     ph.ecog         age 
 6.73234505 -0.32443043 -0.00580889 

Scale:
    sex=1     sex=2 
0.7834211 0.6547830 

Loglik(model)= -1137.3   Loglik(intercept only)= -1146.2
        Chisq= 17.8 on 2 degrees of freedom, p= 0.00014 
n=227 (1 observation deleted due to missingness)

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