From: Mats Karlsson <*mats.karlsson*>

Date: Mon, 21 Dec 2009 11:31:26 +0100

Jia,

I don't see any indication that your first model is problematic. A strong

correlation between BSV and BOV ETA for CL is to be expected when you have

shrinkage in your individual etas (see e.g. Savic & Karlsson AAPS J. 2009

Sep;11(3):558-69). This does not mean that the population model should

include such a correlation. If shrinkage is high (>20% or so) I would tend

to use simulation-based or CWRES based diagnostics instead of posthoc eta's.

Best regards,

Mats

Mats Karlsson, PhD

Professor of Pharmacometrics

Dept of Pharmaceutical Biosciences

Uppsala University

Box 591

751 24 Uppsala Sweden

phone: +46 18 4714105

fax: +46 18 471 4003

-----Original Message-----

From: owner-nmusers

Behalf Of andreas.krause

Sent: Monday, December 21, 2009 10:41 AM

To: Nick Holford

Cc: nmusers

Subject: Re: [NMusers] BSV and BOV interaction

Nick,

overparameterization refers to the parameters, the variances play only an

indirect role. Putting the SAME constraint on the covariance thus

restricts the set of random effects but not necessarily the set of random

effects for, say, subject i.

The SAME option thus might keep the estimation process a bit more under

control but I still think there is an overparameterization problem for

each individual subject.

It should be interesting to take out those ETA values containing the SAME

lines by specifying 0.0 FIX instead of SAME and comparing the results.

Andreas

PS. Shouldn't we all be off for some holidays?

Nick Holford <n.holford

Sent by: owner-nmusers

12/21/2009 09:52 AM

To

nmusers <nmusers

cc

Subject

Re: [NMusers] BSV and BOV interaction

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

The information of this email and in any file transmitted with it is

strictly confidential and may be legally privileged.

It is intended solely for the addressee. If you are not the intended

recipient, any copying, distribution or any other use of this email is

prohibited and may be unlawful. In such case, you should please notify the

sender immediately and destroy this email.

The content of this email is not legally binding unless confirmed by

letter.

Any views expressed in this message are those of the individual sender,

except where the message states otherwise and the sender is authorised to

state them to be the views of the sender's company. For further

information about Actelion please see our website at

http://www.actelion.com

--

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

The information of this email and in any file transmitted with it is

strictly confidential and may be legally privileged.

It is intended solely for the addressee. If you are not the intended

recipient, any copying, distribution or any other use of this email is

prohibited and may be unlawful. In such case, you should please notify the

sender immediately and destroy this email.

The content of this email is not legally binding unless confirmed by letter.

Any views expressed in this message are those of the individual sender,

except where the message states otherwise and the sender is authorised to

state them to be the views of the sender's company. For further information

about Actelion please see our website at http://www.actelion.com

Received on Mon Dec 21 2009 - 05:31:26 EST

Date: Mon, 21 Dec 2009 11:31:26 +0100

Jia,

I don't see any indication that your first model is problematic. A strong

correlation between BSV and BOV ETA for CL is to be expected when you have

shrinkage in your individual etas (see e.g. Savic & Karlsson AAPS J. 2009

Sep;11(3):558-69). This does not mean that the population model should

include such a correlation. If shrinkage is high (>20% or so) I would tend

to use simulation-based or CWRES based diagnostics instead of posthoc eta's.

Best regards,

Mats

Mats Karlsson, PhD

Professor of Pharmacometrics

Dept of Pharmaceutical Biosciences

Uppsala University

Box 591

751 24 Uppsala Sweden

phone: +46 18 4714105

fax: +46 18 471 4003

-----Original Message-----

From: owner-nmusers

Behalf Of andreas.krause

Sent: Monday, December 21, 2009 10:41 AM

To: Nick Holford

Cc: nmusers

Subject: Re: [NMusers] BSV and BOV interaction

Nick,

overparameterization refers to the parameters, the variances play only an

indirect role. Putting the SAME constraint on the covariance thus

restricts the set of random effects but not necessarily the set of random

effects for, say, subject i.

The SAME option thus might keep the estimation process a bit more under

control but I still think there is an overparameterization problem for

each individual subject.

It should be interesting to take out those ETA values containing the SAME

lines by specifying 0.0 FIX instead of SAME and comparing the results.

Andreas

PS. Shouldn't we all be off for some holidays?

Nick Holford <n.holford

Sent by: owner-nmusers

12/21/2009 09:52 AM

To

nmusers <nmusers

cc

Subject

Re: [NMusers] BSV and BOV interaction

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

The information of this email and in any file transmitted with it is

strictly confidential and may be legally privileged.

It is intended solely for the addressee. If you are not the intended

recipient, any copying, distribution or any other use of this email is

prohibited and may be unlawful. In such case, you should please notify the

sender immediately and destroy this email.

The content of this email is not legally binding unless confirmed by

letter.

Any views expressed in this message are those of the individual sender,

except where the message states otherwise and the sender is authorised to

state them to be the views of the sender's company. For further

information about Actelion please see our website at

http://www.actelion.com

--

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

The information of this email and in any file transmitted with it is

strictly confidential and may be legally privileged.

It is intended solely for the addressee. If you are not the intended

recipient, any copying, distribution or any other use of this email is

prohibited and may be unlawful. In such case, you should please notify the

sender immediately and destroy this email.

The content of this email is not legally binding unless confirmed by letter.

Any views expressed in this message are those of the individual sender,

except where the message states otherwise and the sender is authorised to

state them to be the views of the sender's company. For further information

about Actelion please see our website at http://www.actelion.com

Received on Mon Dec 21 2009 - 05:31:26 EST