R help - Jan 2011 - coxme and random factors

Hi

I would really appreciate some help with my code for coxme...

My data set
I'm interested in survival of animals after an experiment with 4  
treatments, which was performed on males and females. I also have two  
random factors:

Response variable: 	survival (death)
Factor 1: 			treatment (4 levels)
Factor 2:				sex (male / female)
Random effects 1: 	person nested within day (2 people did the  
experiment over 2 	days)
Random effects 2: 	box nested within treatment (animals were kept in  
boxes in groups of 6, and there were multiple boxes per treatment)

I've read the introductions to coxme by Terry Therneau, and something  
like the following is what I think I should use:

model1<-coxme(Surv(death,censor)~treatment*sex+(1|day/person)+(1| 
treatment/box))

Which gives me the following:
Cox mixed-effects model fit by maximum likelihood

   events, n = 154, 291
   Iterations= 57 305
                    NULL Integrated Penalized
Log-likelihood -823.276  -795.2354 -784.4807

                   			Chisq    	df          	p   			AIC       BIC
Integrated loglik 	56.08 	11.00 	4.9096e-08	 34.08   0.67
  Penalized loglik 	77.59 	17.91 	2.0958e-09 	41.78 -12.60

Model:  Surv(death, censor) ~ treatment * sex + (1 | day/person) + (1  
|      treatment/box)
Fixed coefficients
                            				coef 		    exp(coef)   se(coef)        
z        p
teratmentb            				-0.0838877 0.9195345 0.3744511 -0.22 0.8200
treatmentb2           			-0.4731922 0.6230103 0.3136199 -1.51 0.1300
treatmentn         				-1.0154149 0.3622521 0.4097754 -2.48 0.0130
sexmale              				-0.1838885 0.8320286 0.2602169 -0.71 0.4800
treatmentb:sexmale    			-0.3905856 0.6766605 0.2132936 -1.83 0.0670
treatmentb2:sexmale    		0.6742202 1.9625020 0.3836907  1.76 0.0790
treatmentn:sexmale  			1.2628977 3.5356520 0.4603589  2.74 0.0061

Random effects
  Group        			Variable    Std Dev    		Variance
  day/person   		(Intercept) 0.32690104 	0.10686429
  day          			(Intercept) 0.49516113 	0.24518455
  treatment/box 		(Intercept) 0.26837158 	0.07202330
  treatment       		(Intercept) 0.29263637 	0.08563604


My questions
(1) Does anyone know how I can test the significance of each of the  
random effects in turn? For example, to find the significance of (1| 
treatment/box) can I compare the results of the above model to one  
without this term? (i.e. by subtracting the integrated loglikelihood  
values of the model without (1|treatment/box) from the model with  
that term).

(2) Can I include 'treatment' as a factor as well as including it as  
part of a nested term? (incidentally I did wonder if I should include  
it as (treatment|box), but an error message comes back that factors  
cannot be used as a covariate within a random effect)

(3) Is it possible to test the proportionality assumption within  
coxme. Previously I used  >cox.zph(model1) with coxph, but that does  
not work with coxme.

Very many thanks to anyone who can offer me some advice!

Sophie


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--- begin inclusion ---
Response variable: 	survival (death)
Factor 1: 			treatment (4 levels)
Factor 2:				sex (male / female)
Random effects 1: 	person nested within day (2 people did the  
experiment over 2 	days)
Random effects 2: 	box nested within treatment (animals were kept in  
boxes in groups of 6, and there were multiple boxes per treatment)

I've read the introductions to coxme by Terry Therneau, and something  
like the following is what I think I should use:

model1<-coxme(Surv(death,censor)~treatment*sex+(1|day/person)+(1| 
treatment/box))

--- End inclusion ---

That looks right to me.  Your questions:
1: How to test: As you guessed, fit the model without one of the random
effects and compare the integrated likelihood for the two fits.  The
usual "is it a chisq or sum of chisquares" question from random
effects
models applies -- the simple chisq test will be conservative.

2: (treatment |box) term.  For a factor variable such as treatment a
term (1 | treatment/box) specifies a (random) coefficient for each
treatment by box combination.  The term (treatment|box) is asking for
exactly the same thing, but coxme currently does not support asking for
it in that way.

3. I do not have an extension of cox.zph to the mixed effects model, in
either theory or code.  Residuals methods for coxme would be an
important addition and is on my to-do list. (But as my wife would point
out, so is a bathroom remodel and she isn't holding her breath.)