Re: [NMusers] $MIX and $CONTR

Katya,

Overall I agree with what you say. But we don't have to assume that ETAs have to stay constant in an individual with time e.g. you can describe between occasion variability without using the SAME option which means the ETA for that subject can vary depending on the occasion.

So why should we assume (without thinking specifically of NONMEM) that there is a time invariant restriction on the ETA distribution described using a mixture model?

I have attempted to explain in another email that it may be quite plausible to assume that a subject does not remain in the same subpopulation for life. In theory this is possible to describe in terms of a mixture model but it remains to be seen if it possible to get NONMEM to estimate the parameters.

Nick

"Gibiansky, Ekaterina" wrote:
>
> Nick,
>
> As I understand the mixture model, it allows to describe multimodal distributions of random effects (ETAs). In the context of the mixed-effect model these distributions (and individual ETAs) do not change with time. It is similar to $PK or $PRED where individual ETAs do not change with time while the parameters itself (CL, V, etc) can depend on time. In $MIX, each subject is classified into one of the subpopulations, based on estimated mixing probabilities, population parameter estimates and subject's individual data. Once classified, predictions for that subject are based on the submodel for that population.
>
> Katya
> ---
> Ekaterina Gibiansky
> Director, PK/PD
> MedImmune, Inc.
> GibianskyE_at_MedImmune.com
> Phone: 301-398-5356
> Fax: 301-398-8356
>
> ________________________________
>
> From: owner-nmusers_at_globomaxnm.com on behalf of Nick Holford
> Sent: Mon 7/30/2007 5:14 PM
> To: nmusers
> Subject: Re: [NMusers] $MIX and $CONTR
>
> Leonid,
>
> I dont see why a proportion should not change with time. The documentation for $MIX says this:
>
> "Then AGE may be used on the right in $MIX. ...
> AGE(i) refers to the value of AGE on the i-th. observation record of the individual record."
>
> This clearly shows that it was anticipated that one might wish to use AGE from any observation record in the individual record. If the records represent a time series (which is 100% necessary if AGE varies!) then this implies that a time varying covariate can be used to model the mixing probability.
>
> In my example I propose that the probability of being a responder changes with age. E.g. children tend to respond to amphetamine like drugs by being less active while adults tend to be stimulated.
>
> This seems like a very plausible way to describe the response in a population. I dont think there is any a priori reason why there should not be a within subject variation in a mixing fraction.
>
> My view of a mixing fraction is that it is a substitute for a missing covariate. If one has a time varying covariate then the mixing fraction would be time varying. In the example proposed in the NONMEM help the covariate proposed for use in $MIX is AGE. If AGE is properly recorded in the data set then AGE is guaranteed to be a time varying covariate!
>
> Nick
>
> Leonid Gibiansky wrote:
> >
> > Nick,
> > I am not sure that the entire idea is correct: subject can only belong to one population, it cannot
> > jump from population to population. Therefore, time dependent P() should not be allowed.
> > Record-number dependence in $MIX was probably invented to have an option of defining the Ps either
> > by the baseline values, or by the values at the end of the study, but not for time-dependence. This
> > could explains differences with the PK block approach.
> > Thanks
> > Leonid
> >
> > > First question: Why is the proportion of simulated subjects different from what I expected? It
> > seems like all the values are being simulated with AGE=50 instead of AGE=0.
> > >
> > > Second question: More generally, if we used AGE in other subroutines (e.g. $PK, $PRED) then AGE
> > would change depending on the value in the current event record. Why doesn't this happen with $MIX?
> > >
> > > Third question: Is there a way to know the index of the observation record that is being used by
> > $MIX? If I wanted to use AGE like I do in $PK it seems I must give the index of the current
> > observation record.
> >
> > Nick Holford wrote:
> > > I wonder if someone can explain this item in the online NONMEM help guide for $MIX.
> > >
> > > $INPUT ... AGE ...
> > > $CONTR DATA=(AGE)
> > > Then AGE may be used on the right in $MIX. AGE and AGE(1) both
> > > refer to the value of AGE on the first observation record of the
> > > individual record. AGE(i) refers to the value of AGE on the i-
> > > th. observation record of the individual record.
> > >
> > > Assume there are 2 records for each subject like this
> > >
> > > ID AGE DV
> > > 1 0 10.506
> > > 1 50 10.331
> > > 2 0 10.039
> > > 2 50 10.99
> > > 3 0 9.3782
> > > 3 50 9.9395
> > > 4 0 98.438
> > > 4 50 99.411
> > > 5 0 10.598
> > > 5 50 9.6335
> > >
> > > and this code is used to simulate with a different mixing fraction if AGE is less than 25 compared with AGE greater than or equal to 25:
> > >
> > > $PROB MIX
> > > $DATA agemix.csv
> > > $INPUT ID AGE DV
> > > $SIM (20070730) ONLYSIM NSUB=1
> > > $THETA
> > > 0.25 ; PLT25 25% of young are non-responder
> > > 0.75 ; PGE25 75% of older are non-responder
> > > 10 ; NONRESPONDER
> > > 100 ; RESPONDER
> > > $OMEGA 0.01
> > > $OMEGA 0.1
> > > $SIGMA 1
> > >
> > > $PRED
> > > IF (MIXNUM.EQ.1) THEN ; non-responder
> > > Y=THETA(3) + ETA(1) + EPS(1)
> > > ELSE ; responder
> > > Y=THETA(4) + ETA(2) + EPS(1)
> > > ENDIF
> > >
> > > $CONTR DATA=(AGE)
> > > $MIX
> > > NSPOP=2
> > > IF (AGE.LT.25) THEN
> > > P(1)=THETA(1) ; young non-responder
> > > P(2)=1-THETA(1)
> > > ELSE
> > > P(1)=THETA(2) ; older non-responder
> > > P(2)=1-THETA(2)
> > > ENDIF
> > >
> > > $TABLE ID AGE DV
> > > NOAPPEND NOPRINT ONEHEADER FILE=agemix.fit
> > >
> > > I choose to define a response > 50 as a responder and <=50 as a non-responder.
> > > The simulated DV values (10,000 subjects) had 75% of non-responders (with the same proportion at both ages). I had expected 25% because AGE in $MIX is supposed to be the AGE on the first obs record i.e. AGE=0. I got identical results with NONMEM VI and NONMEM V.
> > >
> > > First question: Why is the proportion of simulated subjects different from what I expected? It seems like all the values are being simulated with AGE=50 instead of AGE=0.
> > >
> > > Second question: More generally, if we used AGE in other subroutines (e.g. $PK, $PRED) then AGE would change depending on the value in the current event record. Why doesn't this happen with $MIX?
> > >
> > > Third question: Is there a way to know the index of the observation record that is being used by $MIX? If I wanted to use AGE like I do in $PK it seems I must give the index of the current observation record.
> > >
> > > Nick
> > >
> > > --
> > > Nick Holford, Dept Pharmacology & Clinical Pharmacology
> > > University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
> > > n.holford_at_auckland.ac.nz tel:+64(9)373-7599x86730 fax:+64(9)373-7090
> > > www.health.auckland.ac.nz/pharmacology/staff/nholford
> > >
> > >
>
> --
> Nick Holford, Dept Pharmacology & Clinical Pharmacology
> University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
> n.holford_at_auckland.ac.nz tel:+64(9)373-7599x86730 fax:+64(9)373-7090
> www.health.auckland.ac.nz/pharmacology/staff/nholford

--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
n.holford_at_auckland.ac.nz tel:+64(9)373-7599x86730 fax:+64(9)373-7090
www.health.auckland.ac.nz/pharmacology/staff/nholford
Received on Mon Jul 30 2007 - 23:59:17 EDT