Modeling of two time-to-event outcomes

> -----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)sehosp*exp(Bcholhosp*chol(t)) > h(death)sedeath*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

> -----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

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!

> > 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

-----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Nick Holford Sent: Friday, July 24, 2009 8:09 AM To: nmusers Subject: Re: [NMusers] Modeling of two time-to-event outcomes Steve, Stephen Duffull wrote: > Nick > > >> "Obviously we (implicitly) use copulas all the time when we model >> interval data since a multivariate normal is a specific example of a >> copula of two marginal normal distributions and we do this when >> modelling bivariate continuous measure responses such as parent- >> metabolite data." >> >> Why is a model for interval data an example? >> > > Only because for continuous normally distributed data we have an automatic > solution in the use of a multivariate normal and we implement this in NONMEM > wit $SIGMA BLOCK and the L1 L2 data item flags. > > I still don't understand what this has to do with 'interval data'. >> I think of a parent-metabolite model as being a fixed effect model >> connecting parent with metabolite in just the same way as my earlier >> example of using chol(t) as a fixed effect affecting the hazard >> functions for time to hospitalization and time to death. Putting aside >> any random effect correlations between the parent and metabolite >> structural model parameters in what way does a parent-metabolite model >> involve an implicit copula? >> > > This is an important point. There are two scenarios here: > 1) The fixed effect doesn't fully explain the correlation structure in the > data (i.e. all models are wrong) > 2) There is correlation in the residual random effects, e.g. both assay: > parent and metabolite are assayed in the same run and both are affected by > process errors: recording errors with wrong dose & wrong time > > I think most agree that we would account for correlated observations when > considering parent-metabolite and concentration-effect modelling and that a > fixed effect alone may not be sufficient to handle this correlation. > The correlation between parent and metabolite collected at the same time is indeed a theoretical possibility but I've not had much success in showing it has any importance in improving the description of real data sets. The fixed effect part of the model seems to dominate this kind of process. > For empirical models, e.g. logistic regression and survival, there is even > more reason to believe our model is wrong and we cannot hope to account for > co-dependence structure based on fixed effects only. > Here I agree with you. Time to event models are very tough to diagnose and typically use very empirical fixed effect structures. Finding some way to account for some kind of random effect would be very nice but I still have no idea how to it. Nick > >> Stephen Duffull wrote: >> >>> Hi Nick >>> >>> >>> >>>> 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. >>>> >>>> >>> This is a good point. I have seen very few applications of copulas >>> >> outside of statistics or actuary processes in the specific sense of >> joining two or more parametric distributions together to form a >> multivariate distribution. >> >>> Obviously we (implicitly) use copulas all the time when we model >>> >> interval data since a multivariate normal is a specific example of a >> copula of two marginal normal distributions and we do this when >> modelling bivariate continuous measure responses such as parent- >> metabolite data. >> >>> Explicit use of copulas are considered when joining distributions >>> >> that either don't have multivariate forms (e.g. a multivariate Poisson) >> or distributions that aren't of the same form (e.g. logistic-normal). >> >>> Part of the complexity is there are many types of copulas and it >>> >> seems important to match the copula type to the marginal distribution >> type. >> >>> >>>> 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? >>>> >>>> >>> Yes. Most copulas seem to be parameterised with an "alpha" parameter >>> >> that describes the amount of co-dependence between the observations. >> Note that the values of alpha are not necessarily interchangeable >> between copulas and are mostly bounded on -inf to +inf or 0 to +inf. >> >>> >>>> 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? >>>> >>>> >>> Yes. I would expect that the degree of co-dependence would decrease. >>> >>> >>> >>>> It would be helpful to me and perhaps to others if you could give >>>> >> some >> >>>> specific example of what copulas contribute. >>>> >>>> >>> I haven't seen a PKPD estimation application (yet). >>> >>> Steve >>> -- >>> Professor Stephen Duffull >>> Chair of Clinical Pharmacy >>> School of Pharmacy >>> University of Otago >>> PO Box 913 Dunedin >>> New Zealand >>> E: [email protected] >>> P: +64 3 479 5044 >>> F: +64 3 479 7034 >>> >>> Design software: www.winpopt.com >>> >>> >>> >> -- >> 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 >> > > -- 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