From: Leonid Gibiansky <*lgibiansky*>

Date: Thu, 24 Oct 2019 13:15:09 -0400

We have to be careful with data structure. When Nonmem advances from

time T1=0 to time T2=24 (whether with DES or exact solution), covariate

values (OCC in this case) at time T2=24 are used. So for the data file

presented, 0 to 24 hours will be treated as OCC=2

* > will then use CL1=THETA*EXP(ETA1 + ETA3) from 0 to 24h (NOT ETA2)
*

Value of CL for time > 24 will depend on OCC value of the next record

(not presented in the data file)

Leonid

On 10/23/2019 2:11 PM, Eleveld-Ufkes, DJ wrote:

*> 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)*EXP(ETA(3)) when IOV2=1 (thus IOV1=0) from 24h onwards. These
*

*> are separate occasions and do not overlap, so ETA(2) has no meaning (no
*

*> influence on any predictions or likelihood or anything) after 24 hours.
*

*> The opposite meaning 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 structures take a look at: Abuhelwa, A.Y.,
*

*> Foster, D.J. and Upton, R.N., 2015. ADVAN-style analytical solutions for
*

*> common pharmacokinetic models. /Journal of pharmacological and
*

*> toxicological methods/, /73/, pp.42-48. In the supplements 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 *

*> behalf of Ruben Faelens <ruben.faelens *

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

*> *To:* nmusers *

*> *Subject:* [NMusers] Algebraic equations and IOV
*

*> Dear colleagues,
*

*>
*

*> I am implementing my own simulation engine for non-linear mixed-effects
*

*> models in R. To ensure that I can reproduce models estimated in NONMEM
*

*> or Monolix, 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=THETA*EXP(ETA1+ETA3) from 24h onwards.
*

*>
*

*> When using differential equations, the implementation is clear. We
*

*> integrate the ODE system using CL1 until time 24h. We then continue to
*

*> integrate from 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
*

*> calculate 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_tmt2(CL2, 30-24)
*

*> We calculate the elimination of the remaining drug amounts in each
*

*> compartment, 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
*

*> ------------------------------------------------------------------------
*

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*

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*

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*

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*

*>
*

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Received on Thu Oct 24 2019 - 13:15:09 EDT

Date: Thu, 24 Oct 2019 13:15:09 -0400

We have to be careful with data structure. When Nonmem advances from

time T1=0 to time T2=24 (whether with DES or exact solution), covariate

values (OCC in this case) at time T2=24 are used. So for the data file

presented, 0 to 24 hours will be treated as OCC=2

Value of CL for time > 24 will depend on OCC value of the next record

(not presented in the data file)

Leonid

On 10/23/2019 2:11 PM, Eleveld-Ufkes, DJ wrote:

Received on Thu Oct 24 2019 - 13:15:09 EDT