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

Teresa Iglesias tliglesias at ucdavis.edu
Mon Sep 6 00:09:36 CEST 2010

David Winsemius wrote:
> That is different than my understanding of AIC. I thought that the AIC  
> and BIC both took as input the difference in -2LL and then adjusted  
> those differences for the differences in number of degrees of freedom. 

David! Your words make sense to me now. Sorry for the lapse.
A very smart professor took the time out to school me. I misunderstood the
output from coxme. I see now that it's giving the LL for the NULL model and
for the model I have specified and the AIC output is the difference between
the full model and the NULL. So the numbers all make sense to me and in fact
the p-values are "in agreement" in that they decrease as the specified model
is an improvement over the NULL. I am using only the AIC values and akaike
weights in my analyses so the p-values are not my basis for reaching a
conclusion. I was distressed over the seeming disagreement between the AIC,
the p-values and my results using lmer (ignoring that the data were
censored), and bar graphs illustrating a clear difference when coxme was
telling me "otherwise".  To spell it out for others like me that need to see
the numbers add up...

Given this output from coxme:
                              NULL     Integrated   Penalized
Log-likelihood -119.8470  -112.1598   -108.1663

                            Chisq   df          p                AIC   BIC
Integrated loglik 15.37 2.00 0.00045863 11.37  8.05
Penalized loglik 23.36 7.06 0.00153710  9.25 -2.49

-2(LL) + (2*df) = AIC

NULL:        -2(-119.8470) = 239.694
Integrated: -2(-112.1598) + (2 * 2) = 228.3196
Penalized: -2(-108.1663) + (2 * 7.06) = 230.4526

subtract the integrated model's AIC from the NULL model's AIC, you
get the stated AIC for the integrated model in the output (same for
penalized model).

239.694 - 228.3196  =    11.3744

So the larger (positive range) the AIC, in the coxme output, the better that
model does compared to the NULL model. Incidentally, we see that the p-value
decreases with an increase in the coxme AIC and so there is no

Thank you very smart professor! 

-Teresa Iglesias
Davis, Ca
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