Re: Modeling of two time-to-event outcomes
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-----
Quoted reply history
> > 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