# Re: Modeling of two time-to-event outcomes

From: A.J. Rossini <blindglobe>
Date: Wed, 22 Jul 2009 09:21:35 +0200

Nick -

The point of copulas is to write a pair of survival (or distribution)
functions in a way that you can add parameters to link them together
to describe the correlation structure. It's reasonably flexible.

Check out the stats literature, it's quite common, even in the applied
journals.

I'm sure it can be implemented in NONMEM, just a matter of programming
up the correlation component as a different parameter.

Next time we get something like that here (number of bivariate models,
but not joint survival recently), I'll see if we can code it up.

best,
-tony

On Wed, Jul 22, 2009 at 8:22 AM, Nick Holford<n.holford
te:
> Steve,
>
> I've been hearing about copulas for a couple of years now but haven't see=
n
> 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 de=
ath
> 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 effec=
t,
> 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:blindglobe
>>> 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 som=
e
>>> 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<stephen.duffull
>>>
>>>>
>>>> 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: owner-nmusers
>>>>> nmusers
>>>>> 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
>>>>> n.holford
>>>>> mobile: +33 64 271-6369 (Apr 6-Jul 20 2009)
>>>>> http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
>>>>>
>>>>
>>>>
>>>
>>> --
>>> best,
>>> -tony
>>>
>>> blindglobe
>>> 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 Zeal=
and
> n.holford
> mobile: +33 64 271-6369 (Apr 6-Jul 20 2009)
> http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
>
>

--
best,
-tony

blindglobe
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!
Received on Wed Jul 22 2009 - 03:21:35 EDT

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