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Re: Modeling of two time-to-event outcomes

From: Nick Holford <n.holford>
Date: Wed, 22 Jul 2009 08:22:33 +0200

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: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 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<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 Zealand
n.holford
mobile: +33 64 271-6369 (Apr 6-Jul 20 2009)
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
Received on Wed Jul 22 2009 - 02:22:33 EDT

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