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st: RE: Cox proportional hazard model and the number of parameters for AICc


From   "Silcocks, Paul" <Paul.Silcocks@liverpool.ac.uk>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Cox proportional hazard model and the number of parameters for AICc
Date   Tue, 6 Dec 2011 09:00:13 +0000

Firstly, AICc was derived for Gaussian linear models and doesn't directly apply to generalised linear models or Cox models.  Provided you have a "reasonable" events/parameter ratio to begin with,  AIC should be ok for model selection.  What is "reasonable" is often cited as an events/parameter ratio of 10:1 if you are developing a prediction model from scratch, this ratio can be surprising high (50:1) see Steyerberg EW "Clinical Prediction models" Springer 2009, p198.

If the stratification variables are the same from model to model then the strata won't count when calculating AIC, which will just be based on the number of parameters fitted to the (stratified) Cox model.


Paul Silcocks BM BCh, MSc , FRCPath, FFPH, CStat
Senior statistician,
Cancer Research UK Liverpool Cancer Trials Unit 
University of Liverpool
Block C Waterhouse Building
1-3 Brownlow Street
L69 3GL 

email:  paul.silcocks@liverpool.ac.uk
tel: 0151 7948802
mob: 0794 983 2775


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Brigham Whitman
Sent: 05 December 2011 21:40
To: statalist@hsphsun2.harvard.edu
Subject: st: Cox proportional hazard model and the number of parameters for AICc

I am using the stcox command to perform a stratified Cox proportional
hazard model in Stata.  I want to use AICc to determine the best model
of a set of candidate models and I cannot figure out how to determine
the number of parameters ("K") to use for each model.  The models are
stratified by sex (male or female) and use 1, 2, or 3 variables.  I
don't know how to consider a dichotomous variable that the model is
being stratified by when determining "K" for the AICc calculation.  I
would appreciate any help on this subject.

I am using Stata/ MP 9.2 and there is an example below of one model
(which has 2 variables ("velo_log10" and "dst_to_cover_m")) and its
output.

Thank you,

Brigham Whitman
SUNY ESF




. stcox velo_log10 dst_to_cover_m, nohr robust 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 pseudolikelihood = -24.512423
Iteration 1:   log pseudolikelihood = -20.631007
Iteration 2:   log pseudolikelihood = -20.563058
Iteration 3:   log pseudolikelihood = -20.562172
Iteration 4:   log pseudolikelihood = -20.562171
Refining estimates:
Iteration 0:   log pseudolikelihood = -20.562171

Stratified Cox regr. -- no ties

No. of subjects      =           34                Number of obs   =      2304
No. of failures      =           13
Time at risk         =         2597
                                                   Wald chi2(2)    =      9.26
Log pseudolikelihood =   -20.562171                Prob > chi2     =    0.0097

                                    (Std. Err. adjusted for 34 clusters in id)
------------------------------------------------------------------------------
             |               Robust
          _t |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
  velo_log10 |  -1.608069   .7634565    -2.11   0.035    -3.104417   -.1117222
dst_to_cov~m |  -.0123516   .0126958    -0.97   0.331     -.037235    .0125318
------------------------------------------------------------------------------
                                                             Stratified by sex
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