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Re: Credible range for the variance of a frailty term in a penalized Cox

To: s-news@lists.biostat.wustl.edu, lawrence-hunsicker@uiowa.edu
Subject: Re: Credible range for the variance of a frailty term in a penalized Cox model
From: Terry Therneau <therneau@mayo.edu>
Date: Thu, 28 Aug 2008 17:10:03 -0500 (CDT)
Reply-to: Terry Therneau <therneau@mayo.edu>
> Hi, folks.  Another question.

> If I do a coxph with a frailty term, the summary tells me that the
> variance of the frailty term is 0.0305.  But I am not sure what the
> credible range is for this variance.  The 'intervals' function doesn't
> work on a penalized Cox model, apparently.  Is there a good way to test ...

  First, use coxme for the models.  It is superior to coxph + frailty.
  
  To test for significance of the random effect, compare the integrated 
likelihood from a coxme model to the model without a random effect, i.e., to a 
coxph result with the same variables.  A standard LR test.
  
  To get a confidence interval you need to use the profile likelihood.  Use the 
variance= argument of coxme to get the likelihood for various trial values of 
the variance, and find the values such that 2*(difference in likelihood) = 
chisq 
on one df.  Confidence intervals for this parameter are often aysmmetric.
  
        Terry Therneau


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