From: Perez Ruixo, Juan Jose <*juanjose*>

Date: Fri, 10 Jul 2009 13:56:44 +0200

Dears,

Another option, especially if you are interested in accounting for the unce=

rtainties in OMEGA and SIGMA (and their correlations), is to use a bootstra=

p distribution rather than a multivariate normal distribution. Then, each s=

imulation can be performed with a different vector of THETA, OMEGA and SIGM=

A coming out from the bootstrap distribution.

The only potential problem of using the bootstrap distribution to account f=

or uncertainty is the run time of the bootstrap analysis, especially if the=

model run time is long and/or the number of BS replicates requested is lar=

ge (for instance 1000). In my experience, the confidence and predictions in=

tervals obtained when using the uncertainty in THETA, OMEGA and SIGMA from =

a bootstrap distribution of 1000 replicates are similar to those obtained w=

hen using a bootstrap distribution of 30 replicates. I also understand that=

for other metrics the effect of the number of replicates might become more=

critical.

In addition, if you are interested in predicting the future observations an=

d your uncertainty is relatively low compared with the variability, then yo=

u should know that the effect of the uncertainty in the predictions interva=

ls is limited (see Samtani et al. JCP 2009;49:336-350).

For further discussion on uncertainty you may want to check a previous post=

ing:

http://www.cognigencorp.com/nonmem/nm/98jun142005.html

Best Regards,

Juan Jose Perez Ruixo.

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

From: owner-nmusers

Behalf Of Nick Holford

Sent: Friday, July 10, 2009 12:35 AM

To: nmusers

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

Andreas,

Thanks for your comments. I am sorry I did not explain everything that

NONMEM was doing in this simple example. It does not shave my face (!)

but it does recognize the covariance between the uncertainty estimates

UNC_POP_CL and UNC_POP_V when the values of ETA(3) and ETA(4) are

sampled -- so the covariance of 0.1 in the OMEGA block defining

parameter uncertainty is not ignored. NONMEM is doing exactly the same

thing you describe in R -- it is sampling from multivariate normal

distributions.

The code I gave was just a simple example showing the idea. Of course,

you can include the full variance-covariance matrix of the estimate from

a previous run including the uncertainties in THETA, OMEGA and SIGMA

(and their correlations).

You can also apply the uncertainties to the random effect parameters,

OMEGA and SIGMA, but it may not be so simple as for THETA. I personally

have no experience of this. I am sure there are others who have done it

who may wish to comment.

Best wishes,

Nick

andreas.krause

*>
*

*> Nick,
*

*>
*

*> your example shows there is almost nothing you can not do with nonmem
*

*> (maybe except shaving your face).
*

*> On the other hand, even in the simple two parameter example you have
*

*> off-diagonal covariance terms.
*

*> In your example code the value of 0.1 in the $OMEGA block seems
*

*> ignored (covariance pop CL and pop Vol).
*

*>
*

*> There would typically also be covariances between the pop parameters
*

*> and the OMEGA and SIGMA blocks.
*

*> The latter are often small compared to other variance terms but the
*

*> proper way would be to draw from the full variance-covariance matrix.
*

*> For now it seems best to draw multivariate Normals with full
*

*> covariance matrices in some other environment like R and write the
*

*> generated population parameters to nonmem control streams.
*

*> Unless you find a way again of doing it all in nonmem.
*

*>
*

*> Best regards,
*

*>
*

*> Andreas
*

*>
*

*> PS. Specifying the variance-covariance matrix to use it with $SIM
*

*> might actually be a good candidate for the to-do list for nonmem VIII.
*

*>
*

*>
*

*> -----
*

*>
*

*> Andreas Krause, PhD
*

*> Lead Scientist Modeling and Simulation
*

*>
*

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

*> Switzerland
*

*> andreas.krause *

*>
*

*>
*

*>
*

*> *Nick Holford <n.holford *

*> Sent by: owner-nmusers *

*>
*

*> 07/09/2009 11:51 AM
*

*>
*

*>
*

*> To
*

*> nmusers <nmusers *

*> cc
*

*>
*

*> Subject
*

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

*>
*

*>
*

*>
*

*>
*

*>
*

*>
*

*>
*

*>
*

*>
*

*> 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 stud=
*

y

*> > 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 realit=
*

y

*> > 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 *

*> [mailto: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 don=
*

t

*> > 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 o=
*

f

*> > 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.
*

*> > 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
*

*> >
*

*> >
*

*>
*

*> --
*

*> 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 stri=
*

ctly confidential and may be legally privileged.

*> It is intended solely for the addressee. If you are not the intended reci=
*

pient, any copying, distribution or any other use of this email is prohibit=

ed and may be unlawful. In such case, you should please notify the sender i=

mmediately and destroy this email.

*> The content of this email is not legally binding unless confirmed by lett=
*

er.

*> Any views expressed in this message are those of the individual sender, e=
*

xcept where the message states otherwise and the sender is authorised to st=

ate them to be the views of the sender's company. For further information a=

bout 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 Zealan=

d

n.holford

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

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

Received on Fri Jul 10 2009 - 07:56:44 EDT

Date: Fri, 10 Jul 2009 13:56:44 +0200

Dears,

Another option, especially if you are interested in accounting for the unce=

rtainties in OMEGA and SIGMA (and their correlations), is to use a bootstra=

p distribution rather than a multivariate normal distribution. Then, each s=

imulation can be performed with a different vector of THETA, OMEGA and SIGM=

A coming out from the bootstrap distribution.

The only potential problem of using the bootstrap distribution to account f=

or uncertainty is the run time of the bootstrap analysis, especially if the=

model run time is long and/or the number of BS replicates requested is lar=

ge (for instance 1000). In my experience, the confidence and predictions in=

tervals obtained when using the uncertainty in THETA, OMEGA and SIGMA from =

a bootstrap distribution of 1000 replicates are similar to those obtained w=

hen using a bootstrap distribution of 30 replicates. I also understand that=

for other metrics the effect of the number of replicates might become more=

critical.

In addition, if you are interested in predicting the future observations an=

d your uncertainty is relatively low compared with the variability, then yo=

u should know that the effect of the uncertainty in the predictions interva=

ls is limited (see Samtani et al. JCP 2009;49:336-350).

For further discussion on uncertainty you may want to check a previous post=

ing:

http://www.cognigencorp.com/nonmem/nm/98jun142005.html

Best Regards,

Juan Jose Perez Ruixo.

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

From: owner-nmusers

Behalf Of Nick Holford

Sent: Friday, July 10, 2009 12:35 AM

To: nmusers

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

Andreas,

Thanks for your comments. I am sorry I did not explain everything that

NONMEM was doing in this simple example. It does not shave my face (!)

but it does recognize the covariance between the uncertainty estimates

UNC_POP_CL and UNC_POP_V when the values of ETA(3) and ETA(4) are

sampled -- so the covariance of 0.1 in the OMEGA block defining

parameter uncertainty is not ignored. NONMEM is doing exactly the same

thing you describe in R -- it is sampling from multivariate normal

distributions.

The code I gave was just a simple example showing the idea. Of course,

you can include the full variance-covariance matrix of the estimate from

a previous run including the uncertainties in THETA, OMEGA and SIGMA

(and their correlations).

You can also apply the uncertainties to the random effect parameters,

OMEGA and SIGMA, but it may not be so simple as for THETA. I personally

have no experience of this. I am sure there are others who have done it

who may wish to comment.

Best wishes,

Nick

andreas.krause

y

y

t

f

ctly confidential and may be legally privileged.

pient, any copying, distribution or any other use of this email is prohibit=

ed and may be unlawful. In such case, you should please notify the sender i=

mmediately and destroy this email.

er.

xcept where the message states otherwise and the sender is authorised to st=

ate them to be the views of the sender's company. For further information a=

bout 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 Zealan=

d

n.holford

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

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

Received on Fri Jul 10 2009 - 07:56:44 EDT