R help - Aug 2010 - coxme AIC score and p-value mismatch??

Hi,
I am new to R and AIC scores but what I get from coxme seems wrong. The AIC
score increases as p-values decrease.
Since lower AIC scores mean better models and lower p-values mean stronger
effects or differences then shouldn't they change in the same direction? I
found this happens with the data set rats as well as my own data. Below is
the output for two models constructed with the rats data set.
>library(survival) 
>data(rats)
> str(rats)
'data.frame':   150 obs. of  4 variables:
 $ time  : int  101 104 104 77 89 88 104 96 82 70 ...
 $ tumor : int  0 0 0 0 0 1 1 1 0 1 ...
 $ trt   : int  1 1 1 1 1 1 1 1 1 1 ...
 $ litter: int  1 2 3 4 5 6 7 8 9 10 ...
 
>m1<- coxme(Surv(rats$time, rats$tumor) ~ rats$trt + (1|rats$litter))
>m1
Cox mixed-effects model fit by maximum likelihood
  Data: rats
  events, n = 40, 150
  Iterations= 10 54 
                    NULL Integrated Penalized
Log-likelihood -185.6822   -180.875 -173.7943

                            Chisq    df         p             AIC    BIC
Integrated loglik  9.61  2.00 0.0081708  5.61   2.24
 Penalized loglik 23.78 13.17 0.0356440 -2.57 -24.82

Model:  Surv(rats$time, rats$tumor) ~ rats$trt + (1 | rats$litter) 
Fixed coefficients
              coef exp(coef)  se(coef)    z      p
rats$trt 0.9124426  2.490398 0.3226733 2.83 0.0047

Random effects
 Group       Variable  Std Dev   Variance 
 rats.litter Intercept 0.6526484 0.4259500
>m2<- coxme(Surv(rats$time, rats$tumor) ~ rats$litter + (1|rats$trt) )
>m2
Cox mixed-effects model fit by maximum likelihood
  Data: rats
  events, n = 40, 150
  Iterations= 5 28 
                    NULL Integrated Penalized
Log-likelihood -185.6822  -182.3795 -181.3178

                            Chisq   df        p            AIC   BIC
Integrated loglik  6.61 2.00 0.036785 2.61 -0.77
 Penalized loglik  8.73 1.88 0.011091 4.97  1.79

Model:  Surv(rats$time, rats$tumor) ~ rats$litter + (1 | rats$trt) 
Fixed coefficients
                  coef exp(coef)   se(coef)    z    p
rats$litter 0.01425045  1.014352 0.01088983 1.31 0.19

Random effects
 Group    Variable  Std Dev   Variance 
 rats.trt Intercept 0.6081659 0.3698658

Teresa Iglesias
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You noticed that the AIC increases while the p-value decreases as you 
change the model and hold the data fixed. There would be more indication 
of a problem if you instead noticed the same relationship between the 
AIC and the p-value as you changed the data and held the model fixed.

David


On 22/08/2010 1:04 AM, Teresa Iglesias wrote:
> Hi,
> I am new to R and AIC scores but what I get from coxme seems wrong. The AIC
> score increases as p-values decrease.
> Since lower AIC scores mean better models and lower p-values mean stronger
> effects or differences then shouldn't they change in the same
direction? I
> found this happens with the data set rats as well as my own data. Below is
> the output for two models constructed with the rats data set.

The AICs do not seem right to me either. Unless I am missing something, it
appears that the formula:

AIC= -2x logLik -2k

is being applied, rather than:

AIC= -2x logLik +2k

Meaning models with fewer degrees of freedom are being penalised.
So in your example I make the degrees of freedom
9.61 +2*2= 13.61 for Integrated logLik
23.78 +2*13.7 for Penalised logLik.

Someone please let me know if I am mistaken here!
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