Steve,
I've been hearing about copulas for a couple of years now but haven't
seen anything which reveals how they can be translated into the real world.
If we take the example I gave of hospitalization for heart disease and
death as being two 'correlated' events. Is there something like a
correlation coefficient that you can get from a copula to describe the
assocation between the two event time distributions? If one then added a
fixed effect, such as cholesterol in the example I proposed, would you
then see a fall in this correlation coefficient?
It would be helpful to me and perhaps to others if you could give some
specific example of what copulas contribute.
Nick
Stephen Duffull wrote:
Anthony
We've been working with extreme value Copula functions for conjoining survival analyses in MATLAB. I wasn't sure, however, whether these could be implemented easily in NONMEM.
Steve
-----Original Message-----
From: A.J. Rossini [mailto:[email protected]]
Sent: Wednesday, 22 July 2009 5:31 p.m.
To: Stephen Duffull
Cc: Nick Holford; nmusers
Subject: Re: [NMusers] Modeling of two time-to-event outcomes
For 2 event-time responses, without regression, copula models are the
common way of handling bivariate event time models. There are some
extensions for regression approaches with them, but I havn't been
following that literature.
Another approach would be the Weissfield-Wei-Lin (not sure I got the
first name correct) extensions to the cox model, but that is more like
the GEE/Population average approach, which handles and accomodates the
correlation structure indirectly rather than being specific about it
as in the mixed-effects literature.
The above are implemented in R, along with many variations. Check
CRAN.
On Wed, Jul 22, 2009 at 3:36 AM, Stephen
Duffull<[email protected]> wrote:
Nick
Your approach is an important first step. However, there remains the
possibility of co-dependence in the marginal distribution of the data
once you have included a common fixed effect in your models.
I'm not sure that this can be specifically implemented in NONMEM for
odd-type data. If it can then I'm keen to learn more.
Steve
--
-----Original Message-----
From: [email protected] [mailto:owner-
[email protected]] On Behalf Of Nick Holford
Sent: Wednesday, 22 July 2009 8:08 a.m.
To: nmusers
Subject: Re: [NMusers] Modeling of two time-to-event outcomes
Manisha,
It might be helpful if you could be more specific about what you
mean
by
correlated event times e.g. one could image that the time to event
for
hospitalization for a heart attack and the time to event for death
might
be correlated because they both depend on the the status of
atherosclerotic heart disease.
A parametric approach would be to specify the hazards for the two
events
and include a common covariate (e.g. serum cholesterol time course,
chol(t)) in the hazard e.g.
h(hosp)=basehosp*exp(Bcholhosp*chol(t))
h(death)=basedeath*exp(Bcholdeath*chol(t))
The common covariate, chol(t), would introduce some degree of
correlation between the event times.
Nick
Manisha Lamba wrote:
Dear NMusers,
If anyone in the user group aware of approaches on developing
semi-parametric or parametric models for (joint modeling of) two
time-to-event endpoints, which are highly correlated?
Any suggestions/references/codes(NONMEM, R etc.) would be very
much
appreciated!
Many thanks!
Manisha
--
Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
[email protected] tel:+64(9)923-6730 fax:+64(9)373-7090
mobile: +33 64 271-6369 (Apr 6-Jul 20 2009)
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
--
best,
-tony
[email protected]
Muttenz, Switzerland.
"Commit early,commit often, and commit in a repository from which we
can easily roll-back your mistakes" (AJR, 4Jan05).
Drink Coffee: Do stupid things faster with more energy!
--
Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
[email protected] tel:+64(9)923-6730 fax:+64(9)373-7090
mobile: +33 64 271-6369 (Apr 6-Jul 20 2009)
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
