From: Gastonguay, Marc <*marcg*>

Date: Thu, 16 Jul 2009 13:58:41 -0400

(Apologies for the delayed posting.. this apparently didn't make it to

nmusers on the initial attempt).

Dear Nick, Andreas, Andreas and nmusers,

Here are a couple of additional methods for including uncertainty in

parameters at the inter-trial (or inter-replicate) level, when

simulating with NONMEM:

1. You can take advantage the PRIOR subroutine in NONMEM VI (and VII -

although I haven't tried it yet) simulations, to generate random

variates from a Multi-Variate Normal distribution for THETA and an

Inverse Wishart distribution for OMEGA. This works fine if your prior

uncertainty distributions are adequately described by these

distributions. Of course the MVN assumption is consistent with the var-

covar matrix of the estimates in NONMEM, but you'll have to translate

the uncertainty in OMEGA into the required parameters of an Inv.

Wishart (e.g. mode and degrees of freedom). This method does not

directly allow for prior uncertainty on SIGMA.

2. If you'd like to simulate from other distributions, or pull-in

uncertainty in parameter estimates from other sources, such as the

resulting parameter estimates from bootstrap replicates or MCMC

Bayesian posterior distributions, you'll need to use an external tool

with NONMEM. As Andreas points out, R is a useful choice. Leonid

Gibiasnky and I had developed a toolkit of R functions called NMSUDS

to facilitate these types of simulations in NONMEM. These functions

have been extended and are now part of the broader MIfuns package (http://cran.r-project.org/

).

There's another important issue to consider... Be careful that the

specification of the prior uncertainty distribution is consistent with

reality for the parameters in your model. This point has been

discussed by Pascal Girard and others in past nmusers threads. For

example, a MVN uncertainty distribution for THETA is not realistic for

PK parameters and is never realistic for OMEGA and SIGMA, in that MVN

allows for simulation of negative values. To work-around this problem

for THETA, you could choose to log-transform typical values of PK

parameters to constrain resulting replicates within a physiologically

realistic range.

For example:

Instead of:

CL = THETA(1)*(WT/70)**THETA(2)*EXP(ETA(1))

Parameterize as:

LNCL = THETA(1)+THETA(2)*(WT/70)+ETA(1)

CL = EXP(LNCL)

This sort of transformation is a useful thing to do for NONMEM

simulation and estimation in general, because it creates a parameter

uncertainty distribution that is consistent (for THETA) with the MVN

assumption implicit in Maximum Likelihood methods for continuous data.

This means that confidence intervals (for THETA) from NONMEM's

asymptotic standard errors ($COV) should be more realistic. You may

also find improved stability in estimation runs.

Best regards,

Marc

Marc R. Gastonguay, Ph.D. < marcg

President & CEO, Metrum Research Group LLC < metrumrg.com >

Scientific Director, Metrum Institute < metruminstitute.org >

2 Tunxis Rd, Suite 112, Tariffville, CT 06081 Direct:

+1.860.670.0744 Main: +1.860.735.7043 Fax: +1.860.760.6014

Received on Thu Jul 16 2009 - 13:58:41 EDT

Date: Thu, 16 Jul 2009 13:58:41 -0400

(Apologies for the delayed posting.. this apparently didn't make it to

nmusers on the initial attempt).

Dear Nick, Andreas, Andreas and nmusers,

Here are a couple of additional methods for including uncertainty in

parameters at the inter-trial (or inter-replicate) level, when

simulating with NONMEM:

1. You can take advantage the PRIOR subroutine in NONMEM VI (and VII -

although I haven't tried it yet) simulations, to generate random

variates from a Multi-Variate Normal distribution for THETA and an

Inverse Wishart distribution for OMEGA. This works fine if your prior

uncertainty distributions are adequately described by these

distributions. Of course the MVN assumption is consistent with the var-

covar matrix of the estimates in NONMEM, but you'll have to translate

the uncertainty in OMEGA into the required parameters of an Inv.

Wishart (e.g. mode and degrees of freedom). This method does not

directly allow for prior uncertainty on SIGMA.

2. If you'd like to simulate from other distributions, or pull-in

uncertainty in parameter estimates from other sources, such as the

resulting parameter estimates from bootstrap replicates or MCMC

Bayesian posterior distributions, you'll need to use an external tool

with NONMEM. As Andreas points out, R is a useful choice. Leonid

Gibiasnky and I had developed a toolkit of R functions called NMSUDS

to facilitate these types of simulations in NONMEM. These functions

have been extended and are now part of the broader MIfuns package (http://cran.r-project.org/

).

There's another important issue to consider... Be careful that the

specification of the prior uncertainty distribution is consistent with

reality for the parameters in your model. This point has been

discussed by Pascal Girard and others in past nmusers threads. For

example, a MVN uncertainty distribution for THETA is not realistic for

PK parameters and is never realistic for OMEGA and SIGMA, in that MVN

allows for simulation of negative values. To work-around this problem

for THETA, you could choose to log-transform typical values of PK

parameters to constrain resulting replicates within a physiologically

realistic range.

For example:

Instead of:

CL = THETA(1)*(WT/70)**THETA(2)*EXP(ETA(1))

Parameterize as:

LNCL = THETA(1)+THETA(2)*(WT/70)+ETA(1)

CL = EXP(LNCL)

This sort of transformation is a useful thing to do for NONMEM

simulation and estimation in general, because it creates a parameter

uncertainty distribution that is consistent (for THETA) with the MVN

assumption implicit in Maximum Likelihood methods for continuous data.

This means that confidence intervals (for THETA) from NONMEM's

asymptotic standard errors ($COV) should be more realistic. You may

also find improved stability in estimation runs.

Best regards,

Marc

Marc R. Gastonguay, Ph.D. < marcg

President & CEO, Metrum Research Group LLC < metrumrg.com >

Scientific Director, Metrum Institute < metruminstitute.org >

2 Tunxis Rd, Suite 112, Tariffville, CT 06081 Direct:

+1.860.670.0744 Main: +1.860.735.7043 Fax: +1.860.760.6014

Received on Thu Jul 16 2009 - 13:58:41 EDT