RE: COX Proportional Hazard Model with Time DependentCovariate Nick Holford
Nick
I've come in at the end of this email exchange but felt I had to 'defend' the
extremely widely used method of Cox regression and the proportional hazards
model. There are several advantages which you don't spell out in you email and
a couple of inaccuracies as well.
1. There is both a non-parametric version of the proportional hazards model
(the widely used Cox regression model) and a parametric version which assumes a
parametric form for the survival times but still retains the proportionality
assumption.
2. The hazard function in the proportional hazards model is NOT assumed to be
the same for each treatment group they are assumed to be proportional, pedantic
maybe but needed to be spelt out for clarity. The proportionality assumption is
often valid for survival data. There are extensions to the Cox model which
allows different hazard functions between subgroups or strata.
3. The choice of survival time distribution is often difficult to justify with
parametric models. That said, when this is possible the parametric model allows
a greater degree of interpretation and provides more precise parameter
estimates.
4. Whereas a parametric survival model is limited by the flexibility of the
chosen survival distribution (and corresponding shape of the hazard function)
the semi-parametric Cox method estimates this in a non-parametric way and so is
extremely flexible.
5. "So it depends what you want -- if you just want to collect P values then
use the semi parametric 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." I would suggest that Professor Sir David Cox the
originator of this method would have a few choice words to say about this
remark :-) By the way he has written over 300 papers or books and the original
paper has now been cited over 22,000 times.
Finally (and I might be opening myself up to a torrent of emails here, but why
would you want to analysis survival data in NONMEM when this is covered so
comprehensively in other software packages and many scripts are available to
use in R/Splus??
Mike
____________________________________________
Michael Cole, CStat FSS
Statistician
Northern Institute for Cancer Research,
Paul O'Gorman Building,
Medical School,
University of Newcastle Upon Tyne,
Framlington Place,
Newcastle Upon Tyne,
NE2 4HH
Email: [EMAIL PROTECTED]
____________________________________________
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,
Thanks for highlighting the time to event analysis terminology issue. I think
nmusers need to pay particular attention to a major difference between two
classes of methods.
1. The Cox proportional hazards model is a semiparametric method that is used
to describe the difference between treatments. It assumes the underlying hazard
for both treatments is the same.
2. Parametric methods (e.g. using the Weibull distribution) try to describe the
undelying hazard for each treatment and do not require the assumption that the
underlying hazard is the same.
The semiparametric method is somewhat similar to doing a bioequivalence
analysis with NCA. It can tell you about the difference between the two
formulations under the assumption that the clearance is the same but it doesnt
tell you the underlying PK parameters (clearance, volume, absorption rate
constant etc) and cannot make predictions of the time course of concentration.
The parametric time to event method describes the full hazard function but is
dependent on assuming a particular model -- just like assuming a specific
compartmental model and input function in compartmental PK.
As nmusers will appreciate, one can learn and understand much more from a
compartmental model than one can from doing a bioequivalence analysis. 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
[EMAIL PROTECTED] wrote:
>
> Liang - There are some examples of NONMEM code in the following link. I have
> used this in the past as a good starting point for specifying time-dependent
> hazard models.
>
> http://anesthesia.stanford.edu/pkpd/NONMEM%20Repository/
>
> A note on nomenclature, I always felt a bit confused about these models till
> I realized the level of ambiguity in the literature. The following words are
> often used in an apparent mosaic fashion to describe different analyses that
> are actually quite similar.
> Survival analysis
> Failure analysis
> Event modeling
> Hazard regression
> Cox proportional hazards model
> Cox model
> Proportional hazards model.
> Weibull (...or insert your favorite function here...) proportional hazards
> model
> Parametric proportional hazards models
> Semi-parametric proportional hazards models
> Cox regression
> Poisson regression, etc...
>
> For more check out: http://en.wikipedia.org/wiki/Proportional_hazards_models
>
> Regards, Jeff
>
>
> "Nick Holford" <[EMAIL PROTECTED]>
>
> Sent by: [EMAIL PROTECTED]
>
> œj¬72Z·ÌG{»%Ù·—ÿ±
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:[EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/