[R] Approaches of Frailty estimation: coxme vs coxph(...frailty(id, dist='gauss'))

[Terry Therneau]

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