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

[Cheng 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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