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st: stratified Cox proportional hazards model and AIC


From   Brigham Whitman <brighamj@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: stratified Cox proportional hazards model and AIC
Date   Tue, 1 Nov 2011 00:23:18 -0400

I am using the stcox command to perform a Cox proportional hazards
model, and using the log likelihood in the output, I am computing AICc
values to determine the best model.  If anybody has ever done this, I
am trying to find out if I can compare the AICc value for a model that
is stratified (in this case by sex) with the AICc value of a different
model that does not stratify by sex.  Can I do this?  Or do I need to
compare stratified models together as one suite of models, and
non-stratified models as a different suite of models?

Results from a non-stratified model and a stratified model are below.

Thank you,

Brigham Whitman



 stcox velo_log10_ra14 velo_log10_ra14squared sex , nohr

         failure _d:  event == 3
   analysis time _t:  (mydate-origin)
             origin:  time d(01Jan2006)
  enter on or after:  event==1
  exit on or before:  event==3 4
                 id:  id

Iteration 0:   log likelihood = -37.949901
Iteration 1:   log likelihood = -36.376963
Iteration 2:   log likelihood = -35.219183
Iteration 3:   log likelihood = -33.895999
Iteration 4:   log likelihood = -32.808219
Iteration 5:   log likelihood =  -32.71276
Iteration 6:   log likelihood =  -32.71274
Refining estimates:
Iteration 0:   log likelihood =  -32.71274

Cox regression -- Breslow method for ties

No. of subjects =           34                     Number of obs   =      2406
No. of failures =           14
Time at risk    =         2744
                                                   LR chi2(3)      =     10.47
Log likelihood  =    -32.71274                     Prob > chi2     =    0.0149

------------------------------------------------------------------------------
          _t |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
velo_log1~14 |  -10.92228    8.79507    -1.24   0.214     -28.1603    6.315739
velo_log10.. |   2.799857    2.81852     0.99   0.321    -2.724341    8.324055
         sex |   1.418398   .6191127     2.29   0.022     .2049591    2.631836
------------------------------------------------------------------------------

. stcox velo_log10_ra14 velo_log10_ra14squared , nohr strata(sex)

         failure _d:  event == 3
   analysis time _t:  (mydate-origin)
             origin:  time d(01Jan2006)
  enter on or after:  event==1
  exit on or before:  event==3 4
                 id:  id

Iteration 0:   log likelihood = -26.357427
Iteration 1:   log likelihood = -25.001699
Iteration 2:   log likelihood = -24.947868
Iteration 3:   log likelihood = -24.947775
Refining estimates:
Iteration 0:   log likelihood = -24.947775

Stratified Cox regr. -- no ties

No. of subjects =           34                     Number of obs   =      2406
No. of failures =           14
Time at risk    =         2744
                                                   LR chi2(2)      =      2.82
Log likelihood  =   -24.947775                     Prob > chi2     =    0.2442

------------------------------------------------------------------------------
          _t |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
velo_log1~14 |  -6.248969   9.205174    -0.68   0.497    -24.29078    11.79284
velo_log10.. |   1.329912   2.974208     0.45   0.655    -4.499429    7.159252
------------------------------------------------------------------------------
                                                             Stratified by sex
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