# Re: Mixture model simulation

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.
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
>
> 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.
>
> ;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

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