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st: comparing survival models: Cox vs AFT


From   "Moran, John (NWAHS)" <John.Moran@nwahs.sa.gov.au>
To   "Statalist (E-mail)" <statalist@hsphsun2.harvard.edu>
Subject   st: comparing survival models: Cox vs AFT
Date   Thu, 22 Aug 2002 16:18:13 +0930

Dear Statalisters

I am not quite sure as to direction here; any advice would be most welcome.

I have a multi-record per patient survival data set with 28 day (from acute
diagnosis)  mortality as the outcome. A Cox model with (significant)
time-varying covariates gives a "good" fit , by conventional means (residual
analysis etc) . 

A log normal AFT model (parameterized in the time-ratio sense) seems to do a
"good" job as well (again, by conventional diagnostics). The shape of the
baseline Cox model hazard (using stkerhaz, recently posted) certainly has a
log-normal profile.

Apart from "intrinsic" scientific sense of what drives the model, are there
any "objective" criteria to select the better model; the following have
occurred to me

visual inspection of residual plots has a certain subjective element

plotting survival curves from the 2 models against K-M estimates to give an
"observed-predicted" comparison

AIC / BIC comparisons are OK for comparing parametric models, but seems not
to be appropriate for the Cox, in a cross-comparison sense, where there is a
partial-likelihood. This begs the question of the status of the likelihood
in the Cox model, as per page 126-128 in the green-book (An introduction to
survival analysis using Stata);  is it possible to recover the "full"
likelihood or is it OK to use the partial likelihood?

This problem arose in the context of a certain bias in the medical
literature towards the Cox model.

Thanks in advance for any contribution on this matter


john moran


John L Moran 
Intensive Care Unit
The Queen Elizabeth Hospital
28 Woodville Road Woodville
SA 5011
Australia
Tel  61 08 8222 6463
Fax 61 08 8222 6045
E-mail: john.moran@nwahs.sa.gov.au

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