From: Nick Holford <*n.holford*>

Date: Thu, 09 Jul 2009 11:51:20 +0200

Andreas K,

It is not strictly true to say you cannot specify the parameter

uncertainties from a previous run to be included in a simulation.

If you take the variance-covariance matrix of the estimate from a

previous run ('the uncertainty matrix') you can add it as an additional

OMEGA matrix and use it to obtain parameter samples with uncertainty.

e.g. with a very simple example with just two parameters. This will

simulate 100 data sets and uncertainty to the THETA values for CL and V.

$SIM (20090709) ONLYSIM SUBPROBLEMS=100

; estimates of THETA and OMEGA from previous run

$THETA

1 ; POP_CL theta1

10 ; POP_V theta2

$OMEGA

0.5 ; PPV_CL eta1

0.5 ; PPV_V eta2

;variance-covariance matrix of the THETA estimates from previous run

$OMEGA BLOCK(2)

0.2 ; UNC_POP_CL eta3

0.1 3 ; UNC_POP_V eta 4

$PK

; get CL and V uncertainties

IF (NEWIND.EQ.0) THEN ; do this just once per subproblem

UNCCL=THETA(1)+ETA(3)

UNCV=THETA(2)+ETA(4)

ENDIF

CL=UNCCL*EXP(ETA(1)) ; with uncertainty for CL

V =UNCV*EXP(ETA(2)) ; with uncertainty for V

...

Nick

andreas.krause

*> Andreas,
*

*>
*

*> I guess you are hinting at the difference between simulation of a large
*

*> population and simulation of a study.
*

*>
*

*> The latter incorporates the added uncertainty of the parameter estimates,
*

*> as you point out.
*

*> You would simulate the population parameters with their uncertainties first
*

*> (from the "big covariance matrix" in nonmem) and then simulate the study
*

*> with these sampled population parameters (both steps many times).
*

*> Nonmem can only do the latter directly since you cannot specify the
*

*> parameter uncertainties from a previous run to be included in the
*

*> simulation.
*

*> It is fairly straightforward though since the matrix reflects a
*

*> multivariate Normal distribution.
*

*>
*

*> Andreas
*

*>
*

*> -----
*

*>
*

*> Andreas Krause, PhD
*

*> Lead Scientist Modeling and Simulation
*

*>
*

*> Actelion Pharmaceuticals Ltd / Gewerbestrasse 16 / CH-4123 Allschwil /
*

*> Switzerland
*

*> andreas.krause *

*>
*

*>
*

*>
*

*> -----owner-nmusers *

*>
*

*>
*

*> To: <nmusers *

*> From: "andreas lindauer" <lindauer *

*> Sent by: owner-nmusers *

*> Date: 2009-07-09 09:42
*

*> Subject: AW: [NMusers] Simulations with/without residual error
*

*>
*

*> Nick,
*

*> Thank you very much for your comments.
*

*> Indeed for VPC et al. i always simulate with residual error.
*

*> I understand that when one wants to simulate the 'true' value residual
*

*> error
*

*> is not needed. But what if one wants to simulate 'real' values which will
*

*> be
*

*> observed in a future study. For example, you have a PK/PD model for an
*

*> anti-hypertensive drug and want to predict how many subjects will attain a
*

*> blood pressure below a pre-defined value. Wouldn't a simulation without
*

*> residual error result in an overoptimistic prediction because in reality
*

*> blood pressure is measured with error?
*

*> On the other hand, the estimated residual error does not only reflect
*

*> measurement error but also model misspecification etc.. So, might it be an
*

*> option to simulate not with the estimated residual error but rather with a
*

*> residual error set to the imprecision of the measurement method?
*

*> Best regards, Andreas.
*

*>
*

*>
*

*> .
*

*>
*

*> -----Ursprüngliche Nachricht-----
*

*> Von: owner-nmusers *

*> Auftrag von Nick Holford
*

*> Gesendet: Mittwoch, 8. Juli 2009 15:39
*

*> An: nmusers
*

*> Betreff: Re: [NMusers] Simulations with/without residual error
*

*>
*

*> Andreas,
*

*>
*

*> My suggestion:
*

*>
*

*> If you want to compare your simulations with actual observations then
*

*> you should include residual error in the simulation. The observations
*

*> will include noise as well as the 'true' value so in order to compare
*

*> observations with simulated observations you need the residual error.
*

*>
*

*> If you want to use the simulation to describe the 'true' value then dont
*

*> include the residual error. Residual error is assumed to have a mean of
*

*> zero around the 'true' value so there is no point in adding this kind of
*

*> noise if you are trying to predict the 'true' value.
*

*>
*

*> Your examples suggest to me that you are trying to predict the 'true'
*

*> value -- not trying to match simulations directly with measured values.
*

*> If my guess is correct then you dont need to include residual error.
*

*>
*

*> However, if you are using simulations for some kind of predictive check
*

*> (visual, numerical, statistical) that will be compared to distribution
*

*> statistics of the observations then you should include residual error.
*

*>
*

*> Nick
*

*>
*

*> andreas lindauer wrote:
*

*>
*

*>> Dear NMUSERS,
*

*>>
*

*>>
*

*>>
*

*>> The recent discussion about simulation with a nonparametric method
*

*>> brought a general question concerning monte-carlo simulations into my
*

*>> mind. When should simulations be performed with residual error and
*

*>> when not. I am especially interested in comments regarding the
*

*>> following scenarios when the result of the simulation should be
*

*>> reported as mean or median and 90% prediction interval:
*

*>>
*

*>> 1. Simulated response at a particular time point (eg. Trough values)
*

*>>
*

*>> 2. Simulated response at a particular time point (x) relative to
*

*>> baseline response (IPRED(t=x)/IPRED(t=0) vs. DV(t=x)/DV(t=0) )
*

*>>
*

*>> 3. Simulated time of maximal response (eg. Tmax)
*

*>>
*

*>>
*

*>>
*

*>>
*

*>>
*

*>> Thanks and best regards, Andreas.
*

*>>
*

*>>
*

*>>
*

*>>
*

*>>
*

*>> ____________________________
*

*>>
*

*>>
*

*>>
*

*>> Andreas Lindauer
*

*>>
*

*>>
*

*>>
*

*>> Department of Clinical Pharmacy
*

*>>
*

*>> Institute of Pharmacy
*

*>>
*

*>> University of Bonn
*

*>>
*

*>> An der Immenburg 4
*

*>>
*

*>> D-53121 Bonn
*

*>>
*

*>>
*

*>>
*

*>> phone: + 49 228 73 5781
*

*>>
*

*>> fax: + 49 228 73 9757
*

*>>
*

*>>
*

*>>
*

*>>
*

*>
*

*> --
*

*> Nick Holford, Professor Clinical Pharmacology
*

*> Dept Pharmacology & Clinical Pharmacology
*

*> University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
*

*> Zealand
*

*> n.holford *

*> mobile: +33 64 271-6369 (Apr 6-Jul 20 2009)
*

*> 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.
*

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*

*> 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

n.holford

mobile: +33 64 271-6369 (Apr 6-Jul 20 2009)

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

Received on Thu Jul 09 2009 - 05:51:20 EDT

Date: Thu, 09 Jul 2009 11:51:20 +0200

Andreas K,

It is not strictly true to say you cannot specify the parameter

uncertainties from a previous run to be included in a simulation.

If you take the variance-covariance matrix of the estimate from a

previous run ('the uncertainty matrix') you can add it as an additional

OMEGA matrix and use it to obtain parameter samples with uncertainty.

e.g. with a very simple example with just two parameters. This will

simulate 100 data sets and uncertainty to the THETA values for CL and V.

$SIM (20090709) ONLYSIM SUBPROBLEMS=100

; estimates of THETA and OMEGA from previous run

$THETA

1 ; POP_CL theta1

10 ; POP_V theta2

$OMEGA

0.5 ; PPV_CL eta1

0.5 ; PPV_V eta2

;variance-covariance matrix of the THETA estimates from previous run

$OMEGA BLOCK(2)

0.2 ; UNC_POP_CL eta3

0.1 3 ; UNC_POP_V eta 4

$PK

; get CL and V uncertainties

IF (NEWIND.EQ.0) THEN ; do this just once per subproblem

UNCCL=THETA(1)+ETA(3)

UNCV=THETA(2)+ETA(4)

ENDIF

CL=UNCCL*EXP(ETA(1)) ; with uncertainty for CL

V =UNCV*EXP(ETA(2)) ; with uncertainty for V

...

Nick

andreas.krause

--

Nick Holford, Professor Clinical Pharmacology

Dept Pharmacology & Clinical Pharmacology

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

n.holford

mobile: +33 64 271-6369 (Apr 6-Jul 20 2009)

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

Received on Thu Jul 09 2009 - 05:51:20 EDT