[R] coxme and random factors

[Terry Therneau]

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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))

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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.)