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Re: AW: Simulations with/without residual error

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.
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>
>

--
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

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