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
[EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:+64(9)373-7090
www.health.auckland.ac.nz/pharmacology/staff/nholford
$MIX and $CONTR
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
> [EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:+64(9)373-7090
> www.health.auckland.ac.nz/pharmacology/staff/nholford
Leonid,
Thanks for your thoughtful comments.
I think there are two things to keep separate:
1. Imagine a drug response can be described by a bi-modal distribution when one
examines a sample of subjects who are all children. A mixture model can be used
to identify the parameters of this mixed distribution. One can then categorize
people as being more likely to be in distribution ('responders') than in the
other distribution ('non-responders').
Supposing that we now observe that in a different sample of older subjects that
the mixing probability is different but the two distributions have similar
parameters. We would therefore conclude that the mixing probability changes
with age.
The underlying basis for the distinction between responder and non-responder
may be due to the expression of a gene. The expression of some genes is well
known to vary during human development. Imagine that this gene is either turned
on ('responder') or is turned off ('non-responder'). This would be a biological
explanation of the age dependence of the mixing parameter. If the genotype is
unknown then we would need to use a mixture model to try to decide which
genotype is most likely in an individual. But because the probability of
expression of the gene is also unknown but varies with age then a mixture model
with age as a covariate seems reasonable. If we observed the same subjects as
children and later as adults then we should be able to describe the age related
shift in the probability of being a 'responder' or a 'non-responder'.
It is this kind of situation that I tried to describe using the NM-TRAN code.
2. NONMEM is a particular implementation of a method for describing and
estimating the parameters of mixture model. It seems that NONMEM may only have
a rather simple view of mixtures i.e. an individual always belongs to the same
distribution and this cannot change.
I am not sure yet if it is true that NONMEM assumes a fixed (life long) within
subject assignment to a distribution but I dont see any a priori reason why an
individual should not shift from one distribution to another (as explained in
the example above).
Nick
Leonid Gibiansky wrote:
>
> Nick,
>
> I think you are reading it incorrectly. I would guess that for a long-term
> study you may relate
> probability of response to either baseline age or to the end-of-study age, or
> to any other age in
> between, but this value should be one per subject, not one per record.
> Probability of a subject be
> in one group is assigned based on the entire data set for this subject, and
> not extracted from one
> record. Probability of being a responder may depend on age, but it should be
> 1 value for a subject,
> not 1 value for a record. If you want to simulate subject with same
> covariates but different age,
> give them separate IDs. You may need to simulate ETAs separately (if you want
> patients with the same
> random effects but different ages).
>
> I do not have sufficient experience or knowledge of the nonmem code to be
> more assertive. This is my
> guess only, but guess confirmed by a special treatment of a time dependency
> in the $MIX block (as
> you described).
>
> Leonid
>
> Nick Holford wrote:
> > 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
> >>> [EMAIL PROTECTED] 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
> > [EMAIL PROTECTED] 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
[EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:+64(9)373-7090
www.health.auckland.ac.nz/pharmacology/staff/nholford
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.
[EMAIL PROTECTED]
Phone: 301-398-5356
Fax: 301-398-8356
Quoted reply history
________________________________
From: [EMAIL PROTECTED] 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
> > [EMAIL PROTECTED] 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
[EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:+64(9)373-7090
www.health.auckland.ac.nz/pharmacology/staff/nholford
Hi Nick,
I fully agree with #1. It is a very reasonable model biologically, but the mixture model is not an appropriate tool to describe this model. You may want to describe it with the different procedure: describe probability (not jump, but continuous function of age or something else) of being a responder, and on top of it define different conditional probability of a response for responders and non responders.
P(AGE): probability of being a responder
Presp: probability of response for responders
Pnresp: probability of response for non-responders
Y=P*Presp+(1-P)Pnresp
Of course, each of P, Presp, Pnresp should be expressed via THETAs, ETAs, whatever we need; may depend on gene expression if you like.
I am not sure that I agree with #2: this is not a nonmem implementation deficiency. The biological problem that you describe simply does not fit in the framework of the mixture model, it should be described differently, may be as above (this was only a quick sketch, may not work for you), may be in a more complicated way, but not as a mixture model.
Alternatively, you may assign different IDs to the same subject at age 10 and 50 (it is naive to expect that we stay unchanged for a lifetime): if the person changes so much that it jumps from responders to non-responders, you may expect other changes as well.
Please, let us know if you come up with NONMEM description of your problem.
Leonid
Nick Holford wrote:
> Leonid,
>
> Thanks for your thoughtful comments.
>
> I think there are two things to keep separate:
>
> 1. Imagine a drug response can be described by a bi-modal distribution when one
> examines a sample of subjects who are all children. A mixture model can be used
> to identify the parameters of this mixed distribution. One can then categorize
> people as being more likely to be in distribution ('responders') than in the
> other distribution ('non-responders').
>
> Supposing that we now observe that in a different sample of older subjects that
> the mixing probability is different but the two distributions have similar
> parameters. We would therefore conclude that the mixing probability changes
> with age.
>
> The underlying basis for the distinction between responder and non-responder
> may be due to the expression of a gene. The expression of some genes is well
> known to vary during human development. Imagine that this gene is either turned
> on ('responder') or is turned off ('non-responder'). This would be a biological
> explanation of the age dependence of the mixing parameter. If the genotype is
> unknown then we would need to use a mixture model to try to decide which
> genotype is most likely in an individual. But because the probability of
> expression of the gene is also unknown but varies with age then a mixture model
> with age as a covariate seems reasonable. If we observed the same subjects as
> children and later as adults then we should be able to describe the age related
> shift in the probability of being a 'responder' or a 'non-responder'.
>
> It is this kind of situation that I tried to describe using the NM-TRAN code.
>
> 2. NONMEM is a particular implementation of a method for describing and estimating the parameters of mixture model. It seems that NONMEM may only have a rather simple view of mixtures i.e. an individual always belongs to the same distribution and this cannot change.
>
> I am not sure yet if it is true that NONMEM assumes a fixed (life long) within
> subject assignment to a distribution but I dont see any a priori reason why an
> individual should not shift from one distribution to another (as explained in
> the example above).
>
> Nick
>
> Leonid Gibiansky wrote:
>
> > Nick,
> >
> > I think you are reading it incorrectly. I would guess that for a long-term
> > study you may relate
> > probability of response to either baseline age or to the end-of-study age, or
> > to any other age in
> > between, but this value should be one per subject, not one per record.
> > Probability of a subject be
> > in one group is assigned based on the entire data set for this subject, and not
> > extracted from one
> > record. Probability of being a responder may depend on age, but it should be 1
> > value for a subject,
> > not 1 value for a record. If you want to simulate subject with same covariates
> > but different age,
> > give them separate IDs. You may need to simulate ETAs separately (if you want
> > patients with the same
> > random effects but different ages).
> >
> > I do not have sufficient experience or knowledge of the nonmem code to be more
> > assertive. This is my
> > guess only, but guess confirmed by a special treatment of a time dependency in
> > the $MIX block (as
> > you described).
> >
> > Leonid
> >
> > Nick Holford wrote:
> >
> > > 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
> > > > > [EMAIL PROTECTED] 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
> > > [EMAIL PROTECTED] 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
> [EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:+64(9)373-7090
> www.health.auckland.ac.nz/pharmacology/staff/nholford
Dear Nick,
According to the online manual of ROCM1, the DATA matrix, which is used
in your example to store AGE, changes with each individual record (so
not with each data record of each individual record).
With the statement
"PRINT *, ICALL, DATA(1,1), DATA(2,1)
added to the $MIX code, one may observe that the DATA matrix indeed
contains AGE as is described according to the $MIX help (AGE(i) is
translated to DATA(i,1) by NM-TRAN.) Therefore, the mixture
probabilities may depend on the age data, but only such that each P(.)
has one value for each individual.
But: it seems that with ICALL=4 (during simulation) the DATA matrix does
not hold AGE as described, while with ICALL=2 it does; one may observe
this by removing the ONLYSIM option of the $SIMULATION record...
Best regards,
Erik
Quoted reply history
On Tue, 2007-07-31 at 16:10 +1200, Nick Holford wrote:
> Leonid,
>
> The model you propose is based on the response variable being a binary
> categorical variable - responder or non-responder. Such a likelihood based
> model is straightforward and can easily use age or other time varying
> covariates to help make the prediction.
>
> But the problem I am proposing is based on a continuous scale observation --
> it is not categorical and I do not want to waste information by making some
> kind of categories out of the continuous variable.
>
> You do not describe why "the mixture model is not an appropriate tool to
> describe this model". You also say "The biological problem that you describe
> simply does not fit in the framework of the mixture model". You just say it
> isn't appropriate or does not fit the framework but don't give any reasons
> for your assertions.
>
> I would be interested in you trying to describe exactly why the biological
> problem I proposed is not suitable for a mixture model.
>
> Nick
>
> Leonid Gibiansky wrote:
> >
> > Hi Nick,
> > I fully agree with #1. It is a very reasonable model biologically, but the
> > mixture model is not an
> > appropriate tool to describe this model. You may want to describe it with
> > the different procedure:
> > describe probability (not jump, but continuous function of age or something
> > else) of being a
> > responder, and on top of it define different conditional probability of a
> > response for responders
> > and non responders.
> >
> > P(AGE): probability of being a responder
> >
> > Presp: probability of response for responders
> > Pnresp: probability of response for non-responders
> >
> > Y=P*Presp+(1-P)Pnresp
> >
> > Of course, each of P, Presp, Pnresp should be expressed via THETAs, ETAs,
> > whatever we need; may
> > depend on gene expression if you like.
> >
> > I am not sure that I agree with #2: this is not a nonmem implementation
> > deficiency. The biological
> > problem that you describe simply does not fit in the framework of the
> > mixture model, it should be
> > described differently, may be as above (this was only a quick sketch, may
> > not work for you), may be
> > in a more complicated way, but not as a mixture model.
> >
> > Alternatively, you may assign different IDs to the same subject at age 10
> > and 50 (it is naive to
> > expect that we stay unchanged for a lifetime): if the person changes so
> > much that it jumps from
> > responders to non-responders, you may expect other changes as well.
> >
> > Please, let us know if you come up with NONMEM description of your problem.
> >
> > Leonid
> >
> > Nick Holford wrote:
> > > Leonid,
> > >
> > > Thanks for your thoughtful comments.
> > >
> > > I think there are two things to keep separate:
> > >
> > > 1. Imagine a drug response can be described by a bi-modal distribution
> > > when one examines a sample of subjects who are all children. A mixture
> > > model can be used to identify the parameters of this mixed distribution.
> > > One can then categorize people as being more likely to be in distribution
> > > ('responders') than in the other distribution ('non-responders').
> > >
> > > Supposing that we now observe that in a different sample of older
> > > subjects that the mixing probability is different but the two
> > > distributions have similar parameters. We would therefore conclude that
> > > the mixing probability changes with age.
> > >
> > > The underlying basis for the distinction between responder and
> > > non-responder may be due to the expression of a gene. The expression of
> > > some genes is well known to vary during human development. Imagine that
> > > this gene is either turned on ('responder') or is turned off
> > > ('non-responder'). This would be a biological explanation of the age
> > > dependence of the mixing parameter. If the genotype is unknown then we
> > > would need to use a mixture model to try to decide which genotype is most
> > > likely in an individual. But because the probability of expression of the
> > > gene is also unknown but varies with age then a mixture model with age as
> > > a covariate seems reasonable. If we observed the same subjects as
> > > children and later as adults then we should be able to describe the age
> > > related shift in the probability of being a 'responder' or a
> > > 'non-responder'.
> > >
> > > It is this kind of situation that I tried to describe using the NM-TRAN
> > > code.
> > >
> > > 2. NONMEM is a particular implementation of a method for describing and
> > > estimating the parameters of mixture model. It seems that NONMEM may only
> > > have a rather simple view of mixtures i.e. an individual always belongs
> > > to the same distribution and this cannot change.
> > >
> > > I am not sure yet if it is true that NONMEM assumes a fixed (life long)
> > > within subject assignment to a distribution but I dont see any a priori
> > > reason why an individual should not shift from one distribution to
> > > another (as explained in the example above).
> > >
> > > Nick
> > >
> > > Leonid Gibiansky wrote:
> > >> Nick,
> > >>
> > >> I think you are reading it incorrectly. I would guess that for a
> > >> long-term study you may relate
> > >> probability of response to either baseline age or to the end-of-study
> > >> age, or to any other age in
> > >> between, but this value should be one per subject, not one per record.
> > >> Probability of a subject be
> > >> in one group is assigned based on the entire data set for this subject,
> > >> and not extracted from one
> > >> record. Probability of being a responder may depend on age, but it
> > >> should be 1 value for a subject,
> > >> not 1 value for a record. If you want to simulate subject with same
> > >> covariates but different age,
> > >> give them separate IDs. You may need to simulate ETAs separately (if you
> > >> want patients with the same
> > >> random effects but different ages).
> > >>
> > >> I do not have sufficient experience or knowledge of the nonmem code to
> > >> be more assertive. This is my
> > >> guess only, but guess confirmed by a special treatment of a time
> > >> dependency in the $MIX block (as
> > >> you described).
> > >>
> > >> Leonid
> > >>
> > >> Nick Holford wrote:
> > >>> 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
> > >>>>> [EMAIL PROTECTED] 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
> > >>> [EMAIL PROTECTED] 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
> > > [EMAIL PROTECTED] 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
> [EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:+64(9)373-7090
> www.health.auckland.ac.nz/pharmacology/staff/nholford
The following is a general description of NONMEM's mixture model
feature. During each iteration, after fitting each submodel to an
individual's data, the most probable subpopulation is selected as the
one with the maximum product of "likelihood" X prior where "likelihood"
is an ofv for the individual and the subpopulation and prior is the
current value of P(i) for a subpopulation. At termination of the search
the most probable subpopulation for a given individual from the last
iteration is assigned to that individual. Thus, an individual can only
belong to one subpopulation with this implementation of mixture models.
With simulation, a subpopulation is first chosen based on a uniform
random variable, 0 - 1, and the vector of P(i) values and this submodel
is used to simulate for that individual. As in Nick Holford's example,
P(i) can be a function of covariates but not time-varying covariates.
For simulation or estimation, the MIX subroutine is called only once per
individual record, not with each observation or data record.
There is a bug in the simulation routine (both NONMEM V and VI) that
results in DATA(1,.) containing the last observation record of the
individual record instead of the first when the MIX routine is called
for simulation, as reported by Nick Holford. This is a problem only if
the first and last observation records of an individual record do not
contain the same value(s) for the covariate(s) made available to MIX by
the $DATA statement in the control stream. The fix requires several
changes. We will provide the code changes to Metrum so that they can
add these changes to the next release of NMQUAL and will place a fixed
subroutine on our ftp site in the next day or two. We will delay for a
few days issuing a more formal bug alert because we are working on two
other issues that we would like to include in that alert.
Thanks to Nick Holford for bringing this bug to our attention and for
providing an example that facilitated the debugging procedure and to
Alison Boeckmann for very quickly identifying the specific part of the
NONMEM code that was responsible.
Tom Ludden
Quoted reply history
-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]
On Behalf Of Nick Holford
Sent: Tuesday, July 31, 2007 6:29 AM
To: nmusers
Subject: Re: [NMusers] $MIX and $CONTR
Erik,
Thanks for your detective work. It does seem like there is a problem
with simulation because AGE is not provided to $MIX as described in the
NONMEM documentation i.e. AGE should be the AGE on the first observation
record.
Nick
"Olofsen, E. (ANST)" wrote:
>
> Dear Nick,
>
> According to the online manual of ROCM1, the DATA matrix, which is
used
> in your example to store AGE, changes with each individual record (so
> not with each data record of each individual record).
>
> With the statement
>
> "PRINT *, ICALL, DATA(1,1), DATA(2,1)
>
> added to the $MIX code, one may observe that the DATA matrix indeed
> contains AGE as is described according to the $MIX help (AGE(i) is
> translated to DATA(i,1) by NM-TRAN.) Therefore, the mixture
> probabilities may depend on the age data, but only such that each P(.)
> has one value for each individual.
>
> But: it seems that with ICALL=4 (during simulation) the DATA matrix
does
> not hold AGE as described, while with ICALL=2 it does; one may observe
> this by removing the ONLYSIM option of the $SIMULATION record...
>
> Best regards,
>
> Erik
>
> On Tue, 2007-07-31 at 16:10 +1200, Nick Holford wrote:
> > Leonid,
> >
> > The model you propose is based on the response variable being a
binary categorical variable - responder or non-responder. Such a
likelihood based model is straightforward and can easily use age or
other time varying covariates to help make the prediction.
> >
> > But the problem I am proposing is based on a continuous scale
observation -- it is not categorical and I do not want to waste
information by making some kind of categories out of the continuous
variable.
> >
> > You do not describe why "the mixture model is not an appropriate
tool to describe this model". You also say "The biological problem that
you describe simply does not fit in the framework of the mixture model".
You just say it isn't appropriate or does not fit the framework but
don't give any reasons for your assertions.
> >
> > I would be interested in you trying to describe exactly why the
biological problem I proposed is not suitable for a mixture model.
> >
> > Nick
> >
> > Leonid Gibiansky wrote:
> > >
> > > Hi Nick,
> > > I fully agree with #1. It is a very reasonable model biologically,
but the mixture model is not an
> > > appropriate tool to describe this model. You may want to describe
it with the different procedure:
> > > describe probability (not jump, but continuous function of age or
something else) of being a
> > > responder, and on top of it define different conditional
probability of a response for responders
> > > and non responders.
> > >
> > > P(AGE): probability of being a responder
> > >
> > > Presp: probability of response for responders
> > > Pnresp: probability of response for non-responders
> > >
> > > Y=P*Presp+(1-P)Pnresp
> > >
> > > Of course, each of P, Presp, Pnresp should be expressed via
THETAs, ETAs, whatever we need; may
> > > depend on gene expression if you like.
> > >
> > > I am not sure that I agree with #2: this is not a nonmem
implementation deficiency. The biological
> > > problem that you describe simply does not fit in the framework of
the mixture model, it should be
> > > described differently, may be as above (this was only a quick
sketch, may not work for you), may be
> > > in a more complicated way, but not as a mixture model.
> > >
> > > Alternatively, you may assign different IDs to the same subject at
age 10 and 50 (it is naive to
> > > expect that we stay unchanged for a lifetime): if the person
changes so much that it jumps from
> > > responders to non-responders, you may expect other changes as
well.
> > >
> > > Please, let us know if you come up with NONMEM description of your
problem.
> > >
> > > Leonid
> > >
> > > Nick Holford wrote:
> > > > Leonid,
> > > >
> > > > Thanks for your thoughtful comments.
> > > >
> > > > I think there are two things to keep separate:
> > > >
> > > > 1. Imagine a drug response can be described by a bi-modal
distribution when one examines a sample of subjects who are all
children. A mixture model can be used to identify the parameters of this
mixed distribution. One can then categorize people as being more likely
to be in distribution ('responders') than in the other distribution
('non-responders').
> > > >
> > > > Supposing that we now observe that in a different sample of
older subjects that the mixing probability is different but the two
distributions have similar parameters. We would therefore conclude that
the mixing probability changes with age.
> > > >
> > > > The underlying basis for the distinction between responder and
non-responder may be due to the expression of a gene. The expression of
some genes is well known to vary during human development. Imagine that
this gene is either turned on ('responder') or is turned off
('non-responder'). This would be a biological explanation of the age
dependence of the mixing parameter. If the genotype is unknown then we
would need to use a mixture model to try to decide which genotype is
most likely in an individual. But because the probability of expression
of the gene is also unknown but varies with age then a mixture model
with age as a covariate seems reasonable. If we observed the same
subjects as children and later as adults then we should be able to
describe the age related shift in the probability of being a 'responder'
or a 'non-responder'.
> > > >
> > > > It is this kind of situation that I tried to describe using the
NM-TRAN code.
> > > >
> > > > 2. NONMEM is a particular implementation of a method for
describing and estimating the parameters of mixture model. It seems that
NONMEM may only have a rather simple view of mixtures i.e. an individual
always belongs to the same distribution and this cannot change.
> > > >
> > > > I am not sure yet if it is true that NONMEM assumes a fixed
(life long) within subject assignment to a distribution but I dont see
any a priori reason why an individual should not shift from one
distribution to another (as explained in the example above).
> > > >
> > > > Nick
> > > >
> > > > Leonid Gibiansky wrote:
> > > >> Nick,
> > > >>
> > > >> I think you are reading it incorrectly. I would guess that for
a long-term study you may relate
> > > >> probability of response to either baseline age or to the
end-of-study age, or to any other age in
> > > >> between, but this value should be one per subject, not one per
record. Probability of a subject be
> > > >> in one group is assigned based on the entire data set for this
subject, and not extracted from one
> > > >> record. Probability of being a responder may depend on age, but
it should be 1 value for a subject,
> > > >> not 1 value for a record. If you want to simulate subject with
same covariates but different age,
> > > >> give them separate IDs. You may need to simulate ETAs
separately (if you want patients with the same
> > > >> random effects but different ages).
> > > >>
> > > >> I do not have sufficient experience or knowledge of the nonmem
code to be more assertive. This is my
> > > >> guess only, but guess confirmed by a special treatment of a
time dependency in the $MIX block (as
> > > >> you described).
> > > >>
> > > >> Leonid
> > > >>
> > > >> Nick Holford wrote:
> > > >>> 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
> > > >>>>> [EMAIL PROTECTED] 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
> > > >>> [EMAIL PROTECTED] 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
> > > > [EMAIL PROTECTED] 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
> > [EMAIL PROTECTED] 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
[EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:+64(9)373-7090
www.health.auckland.ac.nz/pharmacology/staff/nholford
_______________________________________________________________________________________________________________________________