From: Ribbing, Jakob <*Jakob.Ribbing*>

Date: Mon, 21 Dec 2009 09:21:35 -0000

Andreas,

The code snippet you picked out is not overparameterized, since the

assumption is made that the variance of eta 5 and 6 are the same:

$OMEGA BLOCK(1) 0.05

$OMEGA BLOCK(1) SAME

This first equation that you suggest is this:

IOV2=0

IF (DESC.EQ.2) IOV2=1

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

As you note the equation you suggest implies that the between-subject

variability in CL will be larger for the first occasion than the second.

Unless inclusion criteria resulted in weird data that forced me to make

that assumption I would not feel comfortable using this

parameterisation. Also I do not fully understand this "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." Both eta 1

and eta 5 may be negative and positive, so if you are hoping for only

positive eta5 values it seems something is wrong with the structural

model. Or did you mean that you hope the variance of eta5 is positive

(ie. OMEGA(5,5))?

Finally, I also have my doubts about your last suggestion regarding how

to combine eta 1 and 5: "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." How would you interpret that model?

Subjects that have abnormally high CL at occasion 1 are likely to have

either abnormally high, or abnormally low CL at occasion 2. I think

simulations would give you patterns you do not see in real life with

such assumptions. Also, if data supports such a model, it may be more a

reflection of the error model. If some subjects have more error in their

observations a simple eta on epsilon may be more appropriate.

I hope everyone will have a nice break, both from nmusers and from work!

Best regards

Jakob

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

From: owner-nmusers

On Behalf Of andreas.krause

Sent: 21 December 2009 08:18

To: Jia Ji

Cc: nmusers

Subject: Re: [NMusers] BSV and BOV interaction

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

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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

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

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information about Actelion please see our website at

http://www.actelion.com

Received on Mon Dec 21 2009 - 04:21:35 EST

Date: Mon, 21 Dec 2009 09:21:35 -0000

Andreas,

The code snippet you picked out is not overparameterized, since the

assumption is made that the variance of eta 5 and 6 are the same:

$OMEGA BLOCK(1) 0.05

$OMEGA BLOCK(1) SAME

This first equation that you suggest is this:

IOV2=0

IF (DESC.EQ.2) IOV2=1

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

As you note the equation you suggest implies that the between-subject

variability in CL will be larger for the first occasion than the second.

Unless inclusion criteria resulted in weird data that forced me to make

that assumption I would not feel comfortable using this

parameterisation. Also I do not fully understand this "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." Both eta 1

and eta 5 may be negative and positive, so if you are hoping for only

positive eta5 values it seems something is wrong with the structural

model. Or did you mean that you hope the variance of eta5 is positive

(ie. OMEGA(5,5))?

Finally, I also have my doubts about your last suggestion regarding how

to combine eta 1 and 5: "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." How would you interpret that model?

Subjects that have abnormally high CL at occasion 1 are likely to have

either abnormally high, or abnormally low CL at occasion 2. I think

simulations would give you patterns you do not see in real life with

such assumptions. Also, if data supports such a model, it may be more a

reflection of the error model. If some subjects have more error in their

observations a simple eta on epsilon may be more appropriate.

I hope everyone will have a nice break, both from nmusers and from work!

Best regards

Jakob

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

From: owner-nmusers

On Behalf Of andreas.krause

Sent: 21 December 2009 08:18

To: Jia Ji

Cc: nmusers

Subject: Re: [NMusers] BSV and BOV interaction

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

Received on Mon Dec 21 2009 - 04:21:35 EST