RE: [NMusers] $MIX and $CONTR

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


Received on Mon Jul 30 2007 - 23:04:10 EDT