R help - Apr 2007 - Approaches of Frailty estimation: coxme vs coxph(...frailty(id, dist='gauss'))

Dear List,


In documents (Therneau, 2003 : On mixed-effect cox
models, ...), as far as I came to know, coxme penalize
the partial likelihood (Ripatti, Palmgren, 2000) where
as frailtyPenal (in frailtypack package) uses  the
penalized the full likelihood approach (Rondeau et al,
2003).

How, then, coxme and coxph(...frailty(id,
dist='gauss')) differs? Just the coding algorithm, or
in approach too?

coxph(...frailty(id, dist='gamma')) estimates by means
of the penalized likelihood approach (Hougaard, 2000).
Same for coxph(...frailty(id, dist='gauss'))?

How these are related with nltm(...model="GFT") in
nltm package done in the approach of Non-linear
transformation (Tsodikov, 2003)?

Also, is the 3 stage approach (Hougaard, 2000, pp.267)
implimented anywhere in R?

Finally, Is there a R version of the Frailty.stable (A
set of Splus function to estimate parameters of a
positive stable frailty model) by  Wassell et al
(1999)?


Thanks for your valuable time.
Thanks in advance.


Mohammad Ehsanul Karim
Institute of Statistical Research and Training, 
University of Dhaka

M Karim asked about the difference between
	coxme(..., random= ~1|id)  and 
	coxph( ... frailty(id, dist='gauss')
	
 1. coxme is the later routine, with more sophisticated and reliable 
optimization, and a wider range of models.  If I get the abstract done in
time, there will be a presentation at the R conference about a next
release of the survival package which folds in coxme, improvements in coxme,
and suggestion of depreciated status for the frailty() function.  There are
data sets where frailty() gets lost in searching for the optimum and coxme
does not.

 2. McGilchrist suggested an "REML" estimator for Cox models with a
Gaussian
frailty; but it was motivated by analogy with linear models and not by
a direct EM argument.  Later work by Cortinas (PhD thesis, 2004) showed cases
where it performed more poorly than the ML estimate, which does have a formal
derivation due to Ripatti and Palmgren.  The coxme function uses the ML,
the frailty(, dist='gauss') the proposed 'reml' estimate.  \

 I don't have answers for Karim's further questions about existence of a
routine for the positive stable distribution, or comparisons to the nltm()
or frailtypack routines.

	Terry Therneau