# Re: st: comparing survival models: Cox vs AFT

 From Ronan Conroy To statalist@hsphsun2.harvard.edu Subject Re: st: comparing survival models: Cox vs AFT Date Thu, 22 Aug 2002 10:52:12 +0100

```on 22/8/02 7:48 AM, Moran, John (NWAHS) at John.Moran@nwahs.sa.gov.au wrote:

> 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.

With 28-day survival, you will have complete data (or you will have in less
than a month...). For this reason, you might consider logistic regression
or, indeed, -binreg- as the first options. With 28-day survival, the shape
of the survival distribution is generally of little interest (I am guessing
that this is something like acute coronary syndrome, where there is a
significant hazard in the first 28 days). Logistic regression allows you to
estimate the effects of risk factors as odds ratios. -binreg-, on the other
hand, will try to estimate risk ratios, which are easier to interpret, since
a risk ratio is simply the ratio of two probabilities, but you aren't
guaranteed that any model will converge.

Both Cox regression and AFT models can give you hazard ratios, which are
also useful measures of the effect of risk factors, though harder to explain
properly than risk ratios.

The advantage of AFT models, and other parametric approaches such as
fractional polynomials, is that you can characterise the shape of the hazard
function. Cox regression, on the other hand, treats the shape as a high
dimensional nuisance parameter - something that just has to be got out of
the way before we do the interesting work parametrising the risk factors.

In general, if you are interested in factors which predict outcome, I would
go for simple binary models using -logistic- or -binreg- and the hell with
the shape of the survival function.

If the survival function's shape is actually interesting, then parametric
approaches allow you to characterise it, while Cox regression simply takes
it as a given, so I would opt first for simple parametric methods, and then
investigate the gain from using something like fractional polynomials. I
would beware of making a model that is more complex than the underlying
theory!

Ronan M Conroy (rconroy@rcsi.ie)
Lecturer in Biostatistics
Royal College of Surgeons
Dublin 2, Ireland
+353 1 402 2431 (fax 2329)

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