[R] Question regarding significance of a covariate in a coxme survival model

[C. Peng]

The likelihood ratio test is more reliable when one model is nested in the
other. This true for your case. 
AIC/SBC are usually used when two models are in a hiearchical structure.
Please also note that any decision made made based on AIC/SBC scores are
very subjective since no sampling distribution can be used to make a
"rigorous" decision. Regarding the magnitutes between the loglikelihood and
AIC/SBC, I would say the author must used a modified version in coxme()
since several different modified AIC/SBC scores are running in practice. 


My suggestion would be to use LR test for your case: 

For the integrated likelihhod: 

LL.small.model = - 467.3549    (including lifedxm) 
LL.large.model = - 471.3333    (excluding lifedxm) 
DF.diff = 3 - 1 = 2 

LR: -2*(- 471.3333 + 467.3549) = 7.9568 
p-value: 1-pchisq(7.9568,2) = 0.01871556 


For the penalized likelihhod: 

LPL.small.model = -435.2096     (including lifedxm) 
LPL.large.model = -436.0478     (excluding lifedxm) 
DF.diff = 3 - 1 = 2 

PLR: -2*(- 436.0478 + 435.2096 ) = 1.6764 
p-value: 1-pchisq(1.6764,2) = 0.4324883 

Two different likehood methods produce different results, which one you
should use depends 
on which likelihood makes more sense to you (or which likehood is better). 

HTH 

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