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From: Eleveld-Ufkes, DJ <d.j.eleveld_at_umcg.nl>

Date: Wed, 23 Oct 2019 18:11:35 +0000

Hi Ruben,

As I understand it the way you seem to intend it that CL takes value THETA(=

1)*EXP(ETA(2)) when IOV1=1 (thus IOV2=0) from 0 to 24h, and THETA(1)*EX=

P(ETA(3)) when IOV2=1 (thus IOV1=0) from 24h onwards. These are separat=

e occasions and do not overlap, so ETA(2) has no meaning (no influence on a=

ny predictions or likelihood or anything) after 24 hours. The opposite mean=

ing is for ETA(3). So in my view only A) makes sense and B) and C) dont. At=

least as far as I understand your code style.

When you say algebraic equations do you mean the closed-form solutions for =

particular mammilary models? You only have to know the equations which can =

handle non-zero initial conditions which you would need starting at 24h to =

do the prediction at 30h. I dont know what structures you need, if you have=

unusual structures then DES is the only way I think. For some normal struc=

tures take a look at: Abuhelwa, A.Y., Foster, D.J. and Upton, R.N., 2015. A=

DVAN-style analytical solutions for common pharmacokinetic models. Journal =

of pharmacological and toxicological methods, 73, pp.42-48. In the suppleme=

nts is R code I believe. I have gotten some of the models to work in C just=

by cut-paste-compile and fix errors, so they should work in R as well.

I hope this helps.

Warm regards,

Douglas Eleveld

________________________________

From: owner-nmusers_at_globomaxnm.com <owner-nmusers_at_globomaxnm.com> on behalf=

of Ruben Faelens <ruben.faelens_at_gmail.com>

Sent: Wednesday, October 23, 2019 5:59:04 PM

To: nmusers_at_globomaxnm.com

Subject: [NMusers] Algebraic equations and IOV

Dear colleagues,

I am implementing my own simulation engine for non-linear mixed-effects mod=

els in R. To ensure that I can reproduce models estimated in NONMEM or Mono=

lix, I was wondering how IOV is treated in those software.

Usually, IOV is implemented as follows (NONMEM code):

IOV1=0

IOV2=0

IF(OCC.EQ.1) IOV1=1

IF(OCC.EQ.2) IOV2=1

CL = THETA(1) * EXP( ETA(1) + IOV1*ETA(2) + IOV2*ETA(3) )

Assume a data-set with the following items:

TIME;OCC;EVID;AMT

0;1;1;50

24;2;1;50

We will then use CL1=THETA*EXP(ETA1 + ETA2) from 0 to 24h, and CL2=THET=

A*EXP(ETA1+ETA3) from 24h onwards.

When using differential equations, the implementation is clear. We integrat=

e the ODE system using CL1 until time 24h. We then continue to integrate fr=

om 24h onwards, but using CL2.

My question is how this works when we use algebraic equations. Let's define=

CONC_tmt1(CL, X) to represent the concentration at time X due to treatment=

1 at time 0. For tmt2 (which happens at t=24), we write CONC_tmt2(CL, X-=

24).

Suppose we need a prediction at times 5h and 30h. Without IOV, we would cal=

culate this as follows:

CONC(5) = CONC_tmt1(CL, 5)

CONC(30) = CONC_tmt1(CL, 30) + CONC_tmt2(CL, 30-24)

There are multiple options to do this with IOV:

A) Approximate what an ODE implementation would do:

CONC(5) = CONC_tmt1(CL1, 5)

INIT_24 = CONC_tmt1(CL1, 24)

CONC(30) = CONC_virtualTreatment( Dose=INIT_24, CL2, 30-24 ) + CONC_tm=

t2(CL2, 30-24)

We calculate the elimination of the remaining drug amounts in each compartm=

ent, and calculate the elimination of them into occasion 2.

Are these equations available somewhere?

B) We ignore overlap in dosing profiles. The full profile of tmt1 (even the=

part in occasion 2) is calculated using CL1.

CONC(5) = CONC_tmt1(CL1, 5)

CONC(30) = CONC_tmt1(CL1, 30) + CONC_tmt2(CL2, 30-24)

C) We can ignore continuity in concentrations. The contribution of tmt1 in =

occasion 2 is calculated as if the full treatment occurred under CL2.

CONC(5) = CONC_tmt1(CL1, 5)

CONC(30) = CONC_tmt1(CL2, 30) + CONC_tmt2(CL2, 30-24)

Which technique does NONMEM and Monolix use for simulating PK concentration=

using algebraic equations with IOV?

This is important for numerical validation between my framework and NONMEM =

/ Monolix.

Best regards,

Ruben Faelens

________________________________

De inhoud van dit bericht is vertrouwelijk en alleen bestemd voor de geadre=

sseerde(n). Anderen dan de geadresseerde(n) mogen geen gebruik maken van di=

t bericht, het niet openbaar maken of op enige wijze verspreiden of vermeni=

gvuldigen. Het UMCG kan niet aansprakelijk gesteld worden voor een incomple=

te aankomst of vertraging van dit verzonden bericht.

The contents of this message are confidential and only intended for the eye=

s of the addressee(s). Others than the addressee(s) are not allowed to use =

this message, to make it public or to distribute or multiply this message i=

n any way. The UMCG cannot be held responsible for incomplete reception or =

delay of this transferred message.

Received on Wed Oct 23 2019 - 14:11:35 EDT

Date: Wed, 23 Oct 2019 18:11:35 +0000

Hi Ruben,

As I understand it the way you seem to intend it that CL takes value THETA(=

1)*EXP(ETA(2)) when IOV1=1 (thus IOV2=0) from 0 to 24h, and THETA(1)*EX=

P(ETA(3)) when IOV2=1 (thus IOV1=0) from 24h onwards. These are separat=

e occasions and do not overlap, so ETA(2) has no meaning (no influence on a=

ny predictions or likelihood or anything) after 24 hours. The opposite mean=

ing is for ETA(3). So in my view only A) makes sense and B) and C) dont. At=

least as far as I understand your code style.

When you say algebraic equations do you mean the closed-form solutions for =

particular mammilary models? You only have to know the equations which can =

handle non-zero initial conditions which you would need starting at 24h to =

do the prediction at 30h. I dont know what structures you need, if you have=

unusual structures then DES is the only way I think. For some normal struc=

tures take a look at: Abuhelwa, A.Y., Foster, D.J. and Upton, R.N., 2015. A=

DVAN-style analytical solutions for common pharmacokinetic models. Journal =

of pharmacological and toxicological methods, 73, pp.42-48. In the suppleme=

nts is R code I believe. I have gotten some of the models to work in C just=

by cut-paste-compile and fix errors, so they should work in R as well.

I hope this helps.

Warm regards,

Douglas Eleveld

________________________________

From: owner-nmusers_at_globomaxnm.com <owner-nmusers_at_globomaxnm.com> on behalf=

of Ruben Faelens <ruben.faelens_at_gmail.com>

Sent: Wednesday, October 23, 2019 5:59:04 PM

To: nmusers_at_globomaxnm.com

Subject: [NMusers] Algebraic equations and IOV

Dear colleagues,

I am implementing my own simulation engine for non-linear mixed-effects mod=

els in R. To ensure that I can reproduce models estimated in NONMEM or Mono=

lix, I was wondering how IOV is treated in those software.

Usually, IOV is implemented as follows (NONMEM code):

IOV1=0

IOV2=0

IF(OCC.EQ.1) IOV1=1

IF(OCC.EQ.2) IOV2=1

CL = THETA(1) * EXP( ETA(1) + IOV1*ETA(2) + IOV2*ETA(3) )

Assume a data-set with the following items:

TIME;OCC;EVID;AMT

0;1;1;50

24;2;1;50

We will then use CL1=THETA*EXP(ETA1 + ETA2) from 0 to 24h, and CL2=THET=

A*EXP(ETA1+ETA3) from 24h onwards.

When using differential equations, the implementation is clear. We integrat=

e the ODE system using CL1 until time 24h. We then continue to integrate fr=

om 24h onwards, but using CL2.

My question is how this works when we use algebraic equations. Let's define=

CONC_tmt1(CL, X) to represent the concentration at time X due to treatment=

1 at time 0. For tmt2 (which happens at t=24), we write CONC_tmt2(CL, X-=

24).

Suppose we need a prediction at times 5h and 30h. Without IOV, we would cal=

culate this as follows:

CONC(5) = CONC_tmt1(CL, 5)

CONC(30) = CONC_tmt1(CL, 30) + CONC_tmt2(CL, 30-24)

There are multiple options to do this with IOV:

A) Approximate what an ODE implementation would do:

CONC(5) = CONC_tmt1(CL1, 5)

INIT_24 = CONC_tmt1(CL1, 24)

CONC(30) = CONC_virtualTreatment( Dose=INIT_24, CL2, 30-24 ) + CONC_tm=

t2(CL2, 30-24)

We calculate the elimination of the remaining drug amounts in each compartm=

ent, and calculate the elimination of them into occasion 2.

Are these equations available somewhere?

B) We ignore overlap in dosing profiles. The full profile of tmt1 (even the=

part in occasion 2) is calculated using CL1.

CONC(5) = CONC_tmt1(CL1, 5)

CONC(30) = CONC_tmt1(CL1, 30) + CONC_tmt2(CL2, 30-24)

C) We can ignore continuity in concentrations. The contribution of tmt1 in =

occasion 2 is calculated as if the full treatment occurred under CL2.

CONC(5) = CONC_tmt1(CL1, 5)

CONC(30) = CONC_tmt1(CL2, 30) + CONC_tmt2(CL2, 30-24)

Which technique does NONMEM and Monolix use for simulating PK concentration=

using algebraic equations with IOV?

This is important for numerical validation between my framework and NONMEM =

/ Monolix.

Best regards,

Ruben Faelens

________________________________

De inhoud van dit bericht is vertrouwelijk en alleen bestemd voor de geadre=

sseerde(n). Anderen dan de geadresseerde(n) mogen geen gebruik maken van di=

t bericht, het niet openbaar maken of op enige wijze verspreiden of vermeni=

gvuldigen. Het UMCG kan niet aansprakelijk gesteld worden voor een incomple=

te aankomst of vertraging van dit verzonden bericht.

The contents of this message are confidential and only intended for the eye=

s of the addressee(s). Others than the addressee(s) are not allowed to use =

this message, to make it public or to distribute or multiply this message i=

n any way. The UMCG cannot be held responsible for incomplete reception or =

delay of this transferred message.

Received on Wed Oct 23 2019 - 14:11:35 EDT