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st: Interpretation of shared frailty model


From   Christian Schnier <christian.schnier@helsinki.fi>
To   statalist@hsphsun2.harvard.edu
Subject   st: Interpretation of shared frailty model
Date   Wed, 9 Jul 2003 16:36:16 +0300

Hi!

I have some difficulties to properly interpret a gamma shared frailty 
model, and I hope someone could help.

The idea is to analyse the time-to-first-service in cattle from 200 
different farms. Every cow is measured only once, but cows from the same 
farm are correlated. The main predictor variable is the type of farm (so it 
is measured on the group level) and potential confounding factors are 
measured on the cow-level (breed, 2 levels).
For the analysis I have used an Accelerated failure time model with Weibull-
distributed failure times and a gamma-shared frailty effect. In STATA this 
looks like:
xi: streg i.type i.breed, d(weibull) frailty(gamma) shared(farm) time

Now, the question:
I would like to predict the length of the period when the first, second and 
third quartile of the cows are inseminated (fail) in both farm-types. 
For the median of a cow in farm-type1 I would use:
[-ln(0.5)]^(1/e(aux_p))*exp(_b[_cons]+_b_[I_type1]) 
which should work for Weibull-AFT models without frailty (Hosmer and 
Lemeshow).
But: can I use the 'normal' formula and ignore the estimated shared frailty 
(theta=0.3)? Is that a prediction for a farm with zero-frailty?


Thanks for your help!

Christian

-- 
\ Christian Schnier
 \ University of Helsinki
  \ Faculty of Veterinary Medicine
   \ Department of Clinical Veterinary Sciences
   | P.O.Box 57 (Hämeentie 57)
   | 00014 University of Helsinki
   | Finland
    \ Phone: +358 9 191 49571

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Efficacy of Prayers'. He examined the longevity of royal families - 
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ROYALTY FARED WORSE than did people of humbler birth.
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