From: Jian Xu <*alanub*>

Date: Fri, 10 Jul 2009 06:11:10 -0700 (PDT)

Hi, Nick, This may work. In order to account for uncertainty to the ra=

ndom effect parameters, we can fix OMEGA and SIGMA to 1, and reparametrize =

them as THETA. Your example modified: $SIM (20090709) ONLYSIM SU=

BPROBLEMS=100 ; estimates of THETA and OMEGA from previous run $THE=

TA 1 ; POP_CL theta1 10 ; POP_V =

theta2 0.2 ; Coefficient on CL ETA theta3 0.5 ; Coefficient on =

V ETA theta4 0.3 ; PROP_RV theta5 $OMEGA 1 ;FIX=

; PPV_CL eta1 1 ;FIX; PPV_V eta2 $S=

IGMA 1 ;FIX; PROP RV eps1 ;variance-covariance matrix o=

f the THETA estimates from previous run $OMEGA BLOCK(5) 0.2 ; UNC_POP=

_CL eta3 0.1 3 ; UNC_POP_V eta 4 0.08 0.2 0.7 ; UNC Coef_CL eta5 =

PROP RV eta7 $PK ; get CL and V uncertainties IF (NEWIND.EQ.0) TH=

EN ; do this just once per subproblem UNCCL=THETA(1)+ETA(3) UNC=

V=THETA(2)+ETA(4) UNCLE=THETA(3)+ETA(5) UNVE=THETA(4)+ ETA(6)=

h uncertainty for CL and OMEGA V =UNCV*EXP(UNVE*ETA(2)) ; with =

uncertainty for V and OMEGA PROP=UNRV $ERROR IPRE=F Y=

=F*(1+PROP*EPS(1)) Cheers, Jian _________________=

_______________ From: Nick Holford <n.holford

rs <nmusers

ect: Re: AW: [NMusers] Simulations with/without residual error Andreas=

, Thanks for your comments. I am sorry I did not explain everything th=

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

ut it does recognize the covariance between the uncertainty estimates UNC_P=

OP_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 w=

as just a simple example showing the idea. Of course, you can include the f=

ull variance-covariance matrix of the estimate from a previous run includin=

g the uncertainties in THETA, OMEGA and SIGMA (and their correlations). =

EGA 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

n.com wrote: > > Nick, > > your example shows there is almost not=

hing you can not do with nonmem (maybe except shaving your face). > On th=

e other hand, even in the simple two parameter example you have off-diagona=

l 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 te=

rms but the proper way would be to draw from the full variance-covariance m=

atrix. > For now it seems best to draw multivariate Normals with full cov=

ariance matrices in some other environment like R and write the generated p=

opulation parameters to nonmem control streams. > Unless you find a way a=

gain of doing it all in nonmem. > > Best regards, > > And=

reas > > 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.=

ng and Simulation > > Actelion Pharmaceuticals Ltd / Gewerbestrasse 16=

/ CH-4123 Allschwil / Switzerland > andreas.krause

telion.com > > > > *Nick Holford <n.holford

Sent by: owner-nmusers

*>
> To
> nmusers <nmusers *

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

t is not strictly true to say you cannot specify the parameter > uncertai=

nties from a previous run to be included in a simulation. > > If you t=

ake 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. wit=

h a very simple example with just two parameters. This will > simulate 10=

0 data sets and uncertainty to the THETA values for CL and V. > > $SIM=

(20090709) ONLYSIM SUBPROBLEMS=100 > ; estimates of THETA and OMEGA fr=

om previous run > $THETA > 1 ; POP_CL theta1 > 10 ; POP_V theta2 >=

$OMEGA > 0.5 ; PPV_CL eta1 > 0.5 ; PPV_V eta2 > ;variance-covarianc=

e 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 subpr=

oblem > UNCCL=THETA(1)+ETA(3) > UNCV=THETA(2)+ETA(4) > ENDIF=

A(2)) ; with uncertainty for V > ... > > Nick > > > > =

andreas.krause

re hinting at the difference between simulation of a large > > population=

and simulation of a study. > > > > The latter incorporates the added u=

ncertainty of the parameter estimates, > > as you point out. > > You wo=

uld simulate the population parameters with their uncertainties first > >=

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

*> > 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 refl=

ects a > > multivariate Normal distribution. > > > > Andreas > >=

and Simulation > > > > Actelion Pharmaceuticals Ltd / Gewerbestrasse 16=

/ CH-4123 Allschwil / > > Switzerland > > andreas.krause

www.actelion.com > > > > > > > > -----owner-nmusers

wrote: ----- > > > > > > To: <nmusers

ndreas lindauer" <lindauer

axnm.com > > Date: 2009-07-09 09:42 > > Subject: AW: [NMusers] Simulati=

ons with/without residual error > > > > Nick, > > Thank you very much=

for your comments. > > Indeed for VPC et al. i always simulate with resi=

dual error. > > I understand that when one wants to simulate the 'true' v=

alue residual > > error > > is not needed. But what if one wants to sim=

ulate 'real' values which will > > be > > observed in a future study. F=

or 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 res=

ult in an overoptimistic prediction because in reality > > blood pressure=

is measured with error? > > On the other hand, the estimated residual er=

ror does not only reflect > > measurement error but also model misspecifi=

cation etc.. So, might it be an > > option to simulate not with the estim=

ated residual error but rather with a > > residual error set to the impre=

cision of the measurement method? > > Best regards, Andreas. > > > >=

musers

g von Nick Holford > > Gesendet: Mittwoch, 8. Juli 2009 15:39 > > An: n=

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

compare your simulations with actual observations then > > you should in=

clude residual error in the simulation. The observations > > will include=

noise as well as the 'true' value so in order to compare > > observation=

s with simulated observations you need the residual error. > > > > If y=

ou 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=
*

r examples suggest to me that you are trying to predict the 'true' > > va=

lue -- not trying to match simulations directly with measured values. > >=

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

eck > > (visual, numerical, statistical) that will be compared to distrib=

ution > > statistics of the observations then you should include residual=

error. > > > > Nick > > > > andreas lindauer wrote: > > >> Dear=

NMUSERS, > >> > >> > >> > >> The recent discussion about simulatio=

n with a nonparametric method > >> brought a general question concerning =

monte-carlo simulations into my > >> mind. When should simulations be per=

formed 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 (e=

g. Trough values) > >> > >> 2. Simulated response at a particular time =

point (x) relative to > >> baseline response (IPRED(t=x)/IPRED(t=0) v=

s. DV(t=x)/DV(t=0) ) > >> > >> 3. Simulated time of maximal respons=

e (eg. Tmax) > >> > >> > >> > >> > >> > >> Thanks and best rega=

rds, Andreas. > >> > >> > >> > >> > >> > >> ___________________=

_________ > >> > >> > >> > >> Andreas Lindauer > >> > >> > >>=

*> >>
> >> fax: + 49 228 73 9757
> >>
> >>
> >>
> >> >
>=
*

* > --
> > Nick Holford, Professor Clinical Pharmacology
> > Dept Pharma=
*

cology & Clinical Pharmacology > > University of Auckland, 85 Park Rd, Pr=

ivate Bag 92019, Auckland, New > > Zealand > > n.holford

tel:+64(9)923-6730 fax:+64(9)373-7090 > > mobile: +33 64 271-6369 (Apr 6=

-Jul 20 2009) > > http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford=

smitted with it is strictly confidential and may be legally privileged. >=

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

ipient, any copying, distribution or any other use of this email is prohibi=

ted 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 th=

is message are those of the individual sender, except where the message sta=

tes 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 ou=

r website at http://www.actelion.com > > > > > -- Nick Holford, Pro=

fessor Clinical Pharmacology > Dept Pharmacology & Clinical Pharmacology=

ealand > n.holford

nd.ac.nz/sms/pharmacology/holford > > > > The information of thi=

s email and in any file transmitted with it is strictly confidential and ma=

y be legally privileged. > It is intended solely for the addressee. If yo=

u are not the intended recipient, any copying, distribution or any other us=

e of this email is prohibited and may be unlawful. In such case, you should=

please notify the sender immediately and destroy this email. > The conte=

nt 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 t=

hem to be the views of the sender's company. For further information about =

Actelion please see our website at http://www.actelion.com -- Nick H=

olford, Professor Clinical Pharmacology Dept Pharmacology & Clinical Phar=

macology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland,=

New Zealand n.holford

90 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 - 09:11:10 EDT

Date: Fri, 10 Jul 2009 06:11:10 -0700 (PDT)

Hi, Nick, This may work. In order to account for uncertainty to the ra=

ndom effect parameters, we can fix OMEGA and SIGMA to 1, and reparametrize =

them as THETA. Your example modified: $SIM (20090709) ONLYSIM SU=

BPROBLEMS=100 ; estimates of THETA and OMEGA from previous run $THE=

TA 1 ; POP_CL theta1 10 ; POP_V =

theta2 0.2 ; Coefficient on CL ETA theta3 0.5 ; Coefficient on =

V ETA theta4 0.3 ; PROP_RV theta5 $OMEGA 1 ;FIX=

; PPV_CL eta1 1 ;FIX; PPV_V eta2 $S=

IGMA 1 ;FIX; PROP RV eps1 ;variance-covariance matrix o=

f the THETA estimates from previous run $OMEGA BLOCK(5) 0.2 ; UNC_POP=

_CL eta3 0.1 3 ; UNC_POP_V eta 4 0.08 0.2 0.7 ; UNC Coef_CL eta5 =

PROP RV eta7 $PK ; get CL and V uncertainties IF (NEWIND.EQ.0) TH=

EN ; do this just once per subproblem UNCCL=THETA(1)+ETA(3) UNC=

V=THETA(2)+ETA(4) UNCLE=THETA(3)+ETA(5) UNVE=THETA(4)+ ETA(6)=

h uncertainty for CL and OMEGA V =UNCV*EXP(UNVE*ETA(2)) ; with =

uncertainty for V and OMEGA PROP=UNRV $ERROR IPRE=F Y=

=F*(1+PROP*EPS(1)) Cheers, Jian _________________=

_______________ From: Nick Holford <n.holford

rs <nmusers

ect: Re: AW: [NMusers] Simulations with/without residual error Andreas=

, Thanks for your comments. I am sorry I did not explain everything th=

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

ut it does recognize the covariance between the uncertainty estimates UNC_P=

OP_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 w=

as just a simple example showing the idea. Of course, you can include the f=

ull variance-covariance matrix of the estimate from a previous run includin=

g the uncertainties in THETA, OMEGA and SIGMA (and their correlations). =

EGA 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

n.com wrote: > > Nick, > > your example shows there is almost not=

hing you can not do with nonmem (maybe except shaving your face). > On th=

e other hand, even in the simple two parameter example you have off-diagona=

l 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 te=

rms but the proper way would be to draw from the full variance-covariance m=

atrix. > For now it seems best to draw multivariate Normals with full cov=

ariance matrices in some other environment like R and write the generated p=

opulation parameters to nonmem control streams. > Unless you find a way a=

gain of doing it all in nonmem. > > Best regards, > > And=

reas > > 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.=

ng and Simulation > > Actelion Pharmaceuticals Ltd / Gewerbestrasse 16=

/ CH-4123 Allschwil / Switzerland > andreas.krause

telion.com > > > > *Nick Holford <n.holford

Sent by: owner-nmusers

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

t is not strictly true to say you cannot specify the parameter > uncertai=

nties from a previous run to be included in a simulation. > > If you t=

ake 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. wit=

h a very simple example with just two parameters. This will > simulate 10=

0 data sets and uncertainty to the THETA values for CL and V. > > $SIM=

(20090709) ONLYSIM SUBPROBLEMS=100 > ; estimates of THETA and OMEGA fr=

om previous run > $THETA > 1 ; POP_CL theta1 > 10 ; POP_V theta2 >=

$OMEGA > 0.5 ; PPV_CL eta1 > 0.5 ; PPV_V eta2 > ;variance-covarianc=

e 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 subpr=

oblem > UNCCL=THETA(1)+ETA(3) > UNCV=THETA(2)+ETA(4) > ENDIF=

A(2)) ; with uncertainty for V > ... > > Nick > > > > =

andreas.krause

re hinting at the difference between simulation of a large > > population=

and simulation of a study. > > > > The latter incorporates the added u=

ncertainty of the parameter estimates, > > as you point out. > > You wo=

uld simulate the population parameters with their uncertainties first > >=

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

simulation. > > It is fairly straightforward though since the matrix refl=

ects a > > multivariate Normal distribution. > > > > Andreas > >=

and Simulation > > > > Actelion Pharmaceuticals Ltd / Gewerbestrasse 16=

/ CH-4123 Allschwil / > > Switzerland > > andreas.krause

www.actelion.com > > > > > > > > -----owner-nmusers

wrote: ----- > > > > > > To: <nmusers

ndreas lindauer" <lindauer

axnm.com > > Date: 2009-07-09 09:42 > > Subject: AW: [NMusers] Simulati=

ons with/without residual error > > > > Nick, > > Thank you very much=

for your comments. > > Indeed for VPC et al. i always simulate with resi=

dual error. > > I understand that when one wants to simulate the 'true' v=

alue residual > > error > > is not needed. But what if one wants to sim=

ulate 'real' values which will > > be > > observed in a future study. F=

or 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 res=

ult in an overoptimistic prediction because in reality > > blood pressure=

is measured with error? > > On the other hand, the estimated residual er=

ror does not only reflect > > measurement error but also model misspecifi=

cation etc.. So, might it be an > > option to simulate not with the estim=

ated residual error but rather with a > > residual error set to the impre=

cision of the measurement method? > > Best regards, Andreas. > > > >=

musers

g von Nick Holford > > Gesendet: Mittwoch, 8. Juli 2009 15:39 > > An: n=

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

compare your simulations with actual observations then > > you should in=

clude residual error in the simulation. The observations > > will include=

noise as well as the 'true' value so in order to compare > > observation=

s with simulated observations you need the residual error. > > > > If y=

ou 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 >=

r examples suggest to me that you are trying to predict the 'true' > > va=

lue -- not trying to match simulations directly with measured values. > >=

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

eck > > (visual, numerical, statistical) that will be compared to distrib=

ution > > statistics of the observations then you should include residual=

error. > > > > Nick > > > > andreas lindauer wrote: > > >> Dear=

NMUSERS, > >> > >> > >> > >> The recent discussion about simulatio=

n with a nonparametric method > >> brought a general question concerning =

monte-carlo simulations into my > >> mind. When should simulations be per=

formed 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 (e=

g. Trough values) > >> > >> 2. Simulated response at a particular time =

point (x) relative to > >> baseline response (IPRED(t=x)/IPRED(t=0) v=

s. DV(t=x)/DV(t=0) ) > >> > >> 3. Simulated time of maximal respons=

e (eg. Tmax) > >> > >> > >> > >> > >> > >> Thanks and best rega=

rds, Andreas. > >> > >> > >> > >> > >> > >> ___________________=

_________ > >> > >> > >> > >> Andreas Lindauer > >> > >> > >>=

cology & Clinical Pharmacology > > University of Auckland, 85 Park Rd, Pr=

ivate Bag 92019, Auckland, New > > Zealand > > n.holford

tel:+64(9)923-6730 fax:+64(9)373-7090 > > mobile: +33 64 271-6369 (Apr 6=

-Jul 20 2009) > > http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford=

smitted with it is strictly confidential and may be legally privileged. >=

ipient, any copying, distribution or any other use of this email is prohibi=

ted 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 th=

is message are those of the individual sender, except where the message sta=

tes 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 ou=

r website at http://www.actelion.com > > > > > -- Nick Holford, Pro=

fessor Clinical Pharmacology > Dept Pharmacology & Clinical Pharmacology=

ealand > n.holford

nd.ac.nz/sms/pharmacology/holford > > > > The information of thi=

s email and in any file transmitted with it is strictly confidential and ma=

y be legally privileged. > It is intended solely for the addressee. If yo=

u are not the intended recipient, any copying, distribution or any other us=

e of this email is prohibited and may be unlawful. In such case, you should=

please notify the sender immediately and destroy this email. > The conte=

nt 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 t=

hem to be the views of the sender's company. For further information about =

Actelion please see our website at http://www.actelion.com -- Nick H=

olford, Professor Clinical Pharmacology Dept Pharmacology & Clinical Phar=

macology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland,=

New Zealand n.holford

90 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 - 09:11:10 EDT