RE: COX Proportional Hazard Model with Time DependentCovariate
Nick,
I would argue that parametric survival models are dependent on the
"structural model" (Weibull, Exponential, Gompertz etc.) that you choose
for the hazard function and so suffer the same issues as standard PK
model building where the choice of covariates, error structures etc.
depend on the correct choice of hazard model. The choice of model is
still an assumption...
On the other hand my understanding of Proportional Hazards models is
that we don't necessarily care what the parametric form of the hazard
is. We assume that the hazards changes proportionately with changes in
the covariates (hence the name). Treatment, dose or exposure variable
could be a covariate and although it is usually added in a linear form
it doesn't have to. In many cases the form or "shape" of the hazard
function itself is a bit of a "nuisance variable" and what we want to
know is the influencing factors on survival rates. In this case the
proportional hazards model does just fine.
I'm hoping that your last paragraph was written at least partly
tongue-in-cheek... I would argue that if the range of parametric hazard
models you may have tried do not capture features in your data then you
may want to examine proportional hazards models. There's a fairly huge
statistical literature on these topics (and I have to confess I'm not an
expert by any means!).
A good reference book is by D. Collett: "Modelling Survival Data in
Medical Research", Chapman & Hall / CRC Press. 2003.
http://www.amazon.co.uk/Modelling-Survival-Medical-Research-Statistical/
dp/1584883251/ref=pd_bowtega_3/026-9223339-1525240?ie=UTF8&s=books&qid=1
183564051&sr=1-3
Mike
Quoted reply history
-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]
On Behalf Of Nick Holford
Sent: 03 July 2007 22:59
To: [email protected]
Subject: Re: [NMusers] COX Proportional Hazard Model with Time
DependentCovariate
Jeff,
<EDIT>
The parametric approach does not require the restrictive assumption that
the underlying hazard is the same for both treatments (which is
analogous to having to assume clearance is the same for a bioequivalence
analysis).
So it depends what you want -- if you just want to collect P values then
use the semiparametric method. But if you want to understand the biology
of the disease and the effects of drug treatments you need to seriously
consider the parametric method.
Nick