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


From   Brigham Whitman <brighamj@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: Cox proportional hazard model and the number of parameters for AICc
Date   Tue, 6 Dec 2011 13:26:19 -0500

Thank you for the information, Paul.  This helps.

-Brigham Whitman



On Tue, Dec 6, 2011 at 4:00 AM, Silcocks, Paul
<Paul.Silcocks@liverpool.ac.uk> wrote:
> 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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