From: Nick Holford <*n.holford*>

Date: Mon, 21 Dec 2009 21:52:46 +1300

Andreas,

The code is not overparameterized because the SAME option is used for

the OMEGA block defining ETA(6). This means that there is only one

parameter being estimated for the variance of the distribution from

which ETA(5) and ETA(6) are sampled i.e. ETA(5) and ETA(6) come from an

eta distribution with the SAME variance.

Best wishes,

Nick

andreas.krause

*> Jia,
*

*>
*

*> you are overparameterized. Take this snippet from your code:
*

*>
*

*> IOV2=0
*

*> IF (DESC.EQ.1) IOV2=ETA(5)
*

*> IF (DESC.EQ.2) IOV2=ETA(6)
*

*>
*

*> ETCL = ETA(1)+IOV1
*

*>
*

*> Now consider the two possibilites:
*

*> a) DESC.EQ.1: ETCL = ETA(1) + ETA(5)
*

*> b) DESC.EQ2.2: ETCL = ETA(1) + ETA(6)
*

*>
*

*> In other words, you have two equations to identify 3 parameters.
*

*> Usually you associate the "base" random effect with one case and add a
*

*> deviation parameter to the other case.
*

*> An example would be
*

*>
*

*> IOV2=0
*

*> IF (DESC.EQ.2) IOV2=1
*

*> ETCL = ETA(1)+IOV2*ETA(5)
*

*>
*

*> Thus, ETA(1) estimates your random effect variation for the case DESC.EQ.1
*

*> and ETA(1) + ETA(5) is the random effect variation for the case DESC.EQ.2.
*

*> ETA(5) is thus the additional random effect variation for the second case
*

*> compared to the first.
*

*> Watch out that this implies that the random effect variation is larger for
*

*> DESC.EQ.2 than for DESC.EQ.1 since ETA(5) is (hopefully) not negative.
*

*> You could multiply the two to allow for the variation being smaller or
*

*> larger in the latter case but multiplication makes the estimation more
*

*> unstable.
*

*>
*

*> Why do you see the need to link the two? Why don't you define
*

*> IF(DESC.EQ.1) ETCL=ETA(5)
*

*> IF(DESC.EQ.2) ETCL=ETA(6)
*

*> CL=THETA(1)*EXP(ETCL)
*

*>
*

*> and get rid of ETA(1)? That decouples the two estimates entirely.
*

*>
*

*> Andreas
*

*>
*

*>
*

*>
*

*>
*

*>
*

*>
*

*>
*

*> Jia Ji <jackie.j.ji *

*> Sent by: owner-nmusers *

*> 12/19/2009 12:32 AM
*

*>
*

*> To
*

*> nmusers *

*> cc
*

*>
*

*> Subject
*

*> [NMusers] BSV and BOV interaction
*

*>
*

*>
*

*>
*

*>
*

*>
*

*>
*

*> Dear All,
*

*>
*

*> I am trying to model our data with a two-compartment model now. In our
*

*> trial, some patients received escalated dose at the second cycle so they
*

*> have one more set of kinetics data. So there were BSV and BOV on PK
*

*> parameters in the model. Objective function value is
*

*> significantly improved (compared with the model not having BOV) and SE of
*

*> ETAs are around 40% or less. The code is as below:
*

*>
*

*> $PK
*

*> DESC=1
*

*> IF (TIME.GE.100) DESC=2
*

*> IOV1=0
*

*> IF (DESC.EQ.1) IOV1=ETA(2)
*

*> IF (DESC.EQ.2) IOV1=ETA(3)
*

*>
*

*> IOV2=0
*

*> IF (DESC.EQ.1) IOV2=ETA(5)
*

*> IF (DESC.EQ.2) IOV2=ETA(6)
*

*>
*

*> ETCL = ETA(1)+IOV1
*

*> ETQ = ETA(4)+IOV2
*

*> ETV2 = ETA(7)
*

*>
*

*> CL=THETA(1)*EXP(ETCL)
*

*> V1=THETA(2)
*

*> Q=THETA(3)*EXP(ETQ)
*

*> V2=THETA(4)*EXP(ETV2)
*

*>
*

*> ;OMEGA initial estimates
*

*> $OMEGA 0.0529
*

*> $OMEGA BLOCK(1) 0.05
*

*> $OMEGA BLOCK(1) SAME
*

*> $OMEGA 0.318
*

*> $OMEGA BLOCK(1) 0.05
*

*> $OMEGA BLOCK(1) SAME
*

*> $OMEGA 0.711
*

*>
*

*> When I looked at scatterplot of ETA, I found that there is strong
*

*> correlation between ETA(1) and ETA(2), which is BSV and BOV of CL. And the
*

*> same thing happened to BSV and BOV of Q. Worrying about
*

*> over-parameterization (I am not NONMEM 7 user), I tried to define a THETA
*

*> for this correlation as the code below (just test on CL only first):
*

*>
*

*> $PK
*

*> DESC=1
*

*> IF (TIME.GE.100) DESC=2
*

*> IOV1=0
*

*> IF (DESC.EQ.1) IOV1=THETA(1)*ETA(1)
*

*> IF (DESC.EQ.2) IOV1=THETA(1)*ETA(1)
*

*>
*

*> ETCL = ETA(1)+IOV1
*

*> ETQ = ETA(2)
*

*> ETV2 = ETA(3)
*

*>
*

*> CL=THETA(2)*EXP(ETCL)
*

*> V1=THETA(3)
*

*> Q=THETA(4)*EXP(ETQ)
*

*> V2=THETA(5)*EXP(ETV2)
*

*>
*

*> The objective function value is exactly the same as the model not having
*

*> IOV. BSV of CL is decreased and SE of THETAs are also improved,
*

*> though. The same thing happend to Q when tested individually. Then I tried
*

*> another way to account for this correlation:
*

*>
*

*> $PK
*

*> DESC=1
*

*> IF (TIME.GE.100) DESC=2
*

*> IOV1=0
*

*> IF (DESC.EQ.1) IOV1=ETA(2)
*

*> IF (DESC.EQ.2) IOV1=ETA(3)
*

*>
*

*> ETCL = ETA(1)+IOV1
*

*> ETQ = ETA(4)
*

*> ETV2 = ETA(5)
*

*>
*

*> CL=THETA(1)*EXP(ETCL)
*

*> V1=THETA(2)
*

*> Q=THETA(3)*EXP(ETQ)
*

*> V2=THETA(4)*EXP(ETV2)
*

*>
*

*> ;OMEGA initial estimates
*

*> $OMEGA BLOCK(2) 0.0529 0.01 0.05
*

*> $OMEGA BLOCK(1) 0.05 ;BTW, I don't know how to do SAME here, it's
*

*> not working when putting SAME here
*

*> $OMEGA 0.318
*

*> $OMEGA 0.711
*

*>
*

*> This time I got significantly decreased objective function value, compared
*

*> with the model not having IOV. But, SE of ETA(1), ETA(2) and ETA(3) are
*

*> huge!
*

*>
*

*> All together, does it mean that there is no need to have BOV on CL and Q?
*

*> Or I don't get the right solution to solve correlation problem? Any
*

*> suggestion is highly appreciated! Thank you so much!
*

*>
*

*> Happy Holidays!
*

*>
*

*> Jia
*

*>
*

*>
*

*>
*

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*>
*

*>
*

--

Nick Holford, Professor Clinical Pharmacology

Dept Pharmacology & Clinical Pharmacology

University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand

tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53

email: n.holford

http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford

Received on Mon Dec 21 2009 - 03:52:46 EST

Date: Mon, 21 Dec 2009 21:52:46 +1300

Andreas,

The code is not overparameterized because the SAME option is used for

the OMEGA block defining ETA(6). This means that there is only one

parameter being estimated for the variance of the distribution from

which ETA(5) and ETA(6) are sampled i.e. ETA(5) and ETA(6) come from an

eta distribution with the SAME variance.

Best wishes,

Nick

andreas.krause

--

Nick Holford, Professor Clinical Pharmacology

Dept Pharmacology & Clinical Pharmacology

University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand

tel:+64(9)923-6730 fax:+64(9)373-7090 mobile:+64(21)46 23 53

email: n.holford

http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford

Received on Mon Dec 21 2009 - 03:52:46 EST