From: Paul Hutson <*prhutson*>

Date: Tue, 07 May 2013 14:12:05 -0500

My thanks to Leonid and Mats. Leonid points out that the equations for

CL were not equivalent in the simulation and estimate runs

SIM

CL=(Z*(CL1 + CLr) + (1.0-Z)*(CL2 + CLr))* EXP(ETA(i)) ; correct

EST

CL=((Z*CL1 + CLr) + ((1.0-Z)*CL2 + CLr))*EXP(ETA(i)) ; wrong

As I approached the model building with only a CLnr and CLr term, I

found the expected bimodal ETA arising from the "undetected" presence of

the mixture model.

When I added the Mixture model, the improperly nested CLr terms

maintained an incorrect bimodal distribution for ETA and led me to doubt

my $MIX code.

Thank you for your troubles.

Paul

On 5/7/2013 1:07 PM, Mats Karlsson wrote:

*> Dear Paul,
*

*>
*

*> I don't think you should expect the same ETA for CL under the two mixtures,
*

*> but estimate two separate ones as shown below.. Note also that the estimate
*

*> of ETA you get in the table file is the one from the most probable mixture
*

*> component (whereas the contribution from both mixture components for each
*

*> subject contributes to the likelihood). To know which the most probably
*

*> mixture is for each subject output EST after stating EST=MIXEST.
*

*>
*

*> I would change the estimation model from
*

*> CL=(Z*(CL1 + CLr) + (1.0-Z)*(CL2 + CLr))* EXP(ETA(1))
*

*> V2 = THETA(4)*(WT/70)*EXP(ETA(2))
*

*> To
*

*> CL=Z*(CL1 + CLr)* EXP(ETA(1))
*

*> CL=(1.0-Z)*(CL2 + CLr)* EXP(ETA(2))
*

*> V2 = THETA(4)*(WT/70)*EXP(ETA(3))
*

*>
*

*> (I'm not sure about your ETA variance structure as it is not entirely
*

*> provided, but if you use a covariance between CL and V use also separate
*

*> ETAs for V between mixtures)
*

*>
*

*> Best regards,
*

*> Mats
*

*> Mats Karlsson, PhD
*

*> Professor of Pharmacometrics
*

*>
*

*> Dept of Pharmaceutical Biosciences
*

*> Faculty of Pharmacy
*

*> Uppsala University
*

*> Box 591
*

*> 75124 Uppsala
*

*>
*

*> Phone: +46 18 4714105
*

*> Fax + 46 18 4714003
*

*>
*

*>
*

*> -----Original Message-----
*

*> From: owner-nmusers *

*> Behalf Of Paul Hutson
*

*> Sent: 07 May 2013 17:32
*

*> To: nmusers *

*> Subject: [NMusers] Mixture model simulation
*

*>
*

*> Dear Users:
*

*> I note the Jan 26, 2013 response to Nick Holford's query about results from
*

*> the use of the $MIX mixture model for simulation. I have created a data set
*

*> of N=100 subjects using R to randomly distribute their covariates, both
*

*> continuous and categorical. I then ran the following sim with SUBPOP=1 to
*

*> generate their corresponding DV values using the following code:
*

*> ; SIMULATION CTL
*

*> $PROBLEM SIM 2COMP
*

*> $INPUT ID TIME AMT DV WT HT BMI BSA GFR AGE SEX TOB EVID $DATA
*

*> MethodSim1.CSV IGNORE=# $SUBROUTINES ADVAN4 TRANS4 $SIMULATION (12345)
*

*> SUBPROBLEMS=1 ONLYSIMULATION
*

*>
*

*> $MIX
*

*> NSPOP=2
*

*> P(1)=THETA(7)
*

*> P(2)=1.0-THETA(7)
*

*>
*

*> $PK
*

*> KA=THETA(1)* EXP(ETA(1)); ETA removed in subsequent fitting of data
*

*> CL1=THETA(2)*((WT/70)**0.75) ; non-renal clearance of subpop1
*

*> CL2=THETA(3)*((WT/70)**0.75); non-renal clearance of subpop1
*

*> CLr=(GFR*60/1000)*0.5 ; renal clearance
*

*>
*

*> Z=1
*

*> IF(MIXNUM.EQ.2) Z=0
*

*> CL=(Z*(CL1 + CLr) + (1.0-Z)*(CL2 + CLr))* EXP(ETA(2))
*

*> V2 = THETA(4)*(WT/70)*EXP(ETA(3))
*

*>
*

*> Q = THETA(5)*(WT/70)**0.75
*

*> V3 =THETA(6)*(WT/70)
*

*> S2=V2
*

*>
*

*> $ERROR
*

*> IPRE = F
*

*> W1=F
*

*> DEL = 0
*

*> IF(IPRE.LT.0.001) DEL = 1
*

*> IRES = DV-IPRE; NEGATIVE TREND IS OVERESTIMATING IPRED WRT DV
*

*> IWRE = IRES/(W1+DEL)
*

*> Y=F*(1+ERR(1))
*

*>
*

*> $THETA (2); KAS
*

*> $THETA (0.1); CL1
*

*> $THETA (5); CL2
*

*> $THETA (5); VC
*

*> $THETA (12); Q
*

*> $THETA (40); VP
*

*> $THETA (0.4); FZ
*

*>
*

*> $OMEGA 0 FIXED; IEKA
*

*> $OMEGA 0 FIXED; IECL
*

*> $OMEGA 0 FIXED; IEV2
*

*>
*

*> $SIGMA 0.03;
*

*>
*

*> $TABLE ID TIME AMT DV WT HT BMI BSA GFR AGE SEX TOB EVID NOPRINT
*

*> NOHEADER NOAPPEND FILE=SimData.txt
*

*>
*

*> However, when I come back and attempt to model the simulated data set,
*

*> my ETA1 on CL (note difference from the simulation ctl above) still
*

*> shows a bimodal distribution. With the incorporation of the $MIXture
*

*> model , I would expect a unimodal distribution of ETA_CL entered on 0.
*

*> Can the community please advise?
*

*>
*

*> ;FITTED CTL
*

*> $MIX
*

*> NSPOP=2
*

*> P(1)=THETA(7)
*

*> P(2)=1.0-THETA(7)
*

*>
*

*> $PK
*

*> KA=THETA(1)
*

*> CL1=THETA(2)*((WT/70)**0.75)
*

*> CL2=THETA(3)*((WT/70)**0.75)
*

*> RS=THETA(8)
*

*> CLr=(GFR*60/1000)*RS
*

*> Z=1
*

*> IF(MIXNUM.EQ.2) Z=0
*

*> CL=((Z*CL1 + CLr) + ((1.0-Z)*CL2 + CLr))*EXP(ETA(1))
*

*> V2 = THETA(4)*(WT/70)*EXP(ETA(2)
*

*> Q = THETA(5)*(WT/70)**0.75
*

*> V3 =THETA(6)*(WT/70)
*

*>
*

*> Thanks
*

*> Paul
*

*>
*

--

Paul R. Hutson, Pharm.D.

Associate Professor

UW School of Pharmacy

T: 608.263.2496

F: 608.265.5421

Received on Tue May 07 2013 - 15:12:05 EDT

Date: Tue, 07 May 2013 14:12:05 -0500

My thanks to Leonid and Mats. Leonid points out that the equations for

CL were not equivalent in the simulation and estimate runs

SIM

CL=(Z*(CL1 + CLr) + (1.0-Z)*(CL2 + CLr))* EXP(ETA(i)) ; correct

EST

CL=((Z*CL1 + CLr) + ((1.0-Z)*CL2 + CLr))*EXP(ETA(i)) ; wrong

As I approached the model building with only a CLnr and CLr term, I

found the expected bimodal ETA arising from the "undetected" presence of

the mixture model.

When I added the Mixture model, the improperly nested CLr terms

maintained an incorrect bimodal distribution for ETA and led me to doubt

my $MIX code.

Thank you for your troubles.

Paul

On 5/7/2013 1:07 PM, Mats Karlsson wrote:

--

Paul R. Hutson, Pharm.D.

Associate Professor

UW School of Pharmacy

T: 608.263.2496

F: 608.265.5421

Received on Tue May 07 2013 - 15:12:05 EDT