RE: [NMusers] Parameter uncertainty

[Leander, Jacob]

Hi Fanny, Marc

I was thinking in the same direction as Marc. If you use MCMC (BAYES method in 
NONMEM) the algorithm will provide you with samples from the posterior density 
(posterior = likelihood * prior). From these samples you can then investigate 
different statistics, for example variance of your parameters. Be caution about 
convergence of the algorithm, since these algorithms are not guaranteed to 
sample uncorrelated samples.

On the same topic, are there any good comparisons out there comparing the 
standard covariance matrix approach, bootstrap, profiling and MCMC?

/Jacob
From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On 
Behalf Of Marc Gastonguay
Sent: den 16 februari 2017 13:23
To: Fanny Gallais <gallais.fa...@gmail.com>
Cc: Williams, Jason <jason.willi...@pfizer.com>; nmusers@globomaxnm.com
Subject: Re: [NMusers] Parameter uncertainty

Dear Fanny,

One additional method to obtain the parameter uncertainty, which I don't 
believe was mentioned, is Bayesian estimation using Markov-Chain Monte Carlo 
(MCMC) simulation. This method provides a full joint posterior distribution 
(e.g. uncertainty distribution) of the parameters and any predicted quantities, 
and is really the gold standard for this type of goal. It is possible to 
implement this method in NONMEM (with some limitations on the prior 
distributions), or you could use BUGS or Stan with associated PK model 
libraries. You can also extract the samples from the posterior distribution and 
simulate using the methods already described in this thread.

Marc

On Thu, Feb 16, 2017 at 6:01 AM, Fanny Gallais 
<gallais.fa...@gmail.com<mailto:gallais.fa...@gmail.com>> wrote:
Thank you all for your responses. It is going to be very useful for my work.

Best regards,

F.G.

2017-02-15 17:35 GMT+01:00 Williams, Jason 
<jason.willi...@pfizer.com<mailto:jason.willi...@pfizer.com>>:
Dear Fanny,

Another useful tool you may want to try is using the mrgsolve package available 
in R, developed by Kyle Baron at Metrum Research Group. I have found mrgsolve 
to be very efficient for PKPD simulation and sensitivity analysis in R. There 
is an example of incorporating parameter uncertainty (from $COV step in NONMEM) 
in Section 9 of the example on Probability of Technical Success (link below).

https://github.com/mrgsolve/examples/blob/master/PrTS/pts.pdf

Best regards,

Jason

From: owner-nmus...@globomaxnm.com<mailto:owner-nmus...@globomaxnm.com> 
[mailto:owner-nmus...@globomaxnm.com<mailto:owner-nmus...@globomaxnm.com>] On 
Behalf Of Fanny Gallais
Sent: Wednesday, February 15, 2017 2:55 AM
To: nmusers@globomaxnm.com<mailto:nmusers@globomaxnm.com>
Subject: [NMusers] Parameter uncertainty

Dear NM users,

I would like to perform a simulation (on R) incorporating parameter 
uncertainty. For now I'm working on a simple PK model. Parameters were 
estimated with NONMEM. I'm trying to figure out what is the best way to assess 
parameter uncertainty. I've read about using the standard errors reported by 
NONMEM and assume a normal distribution. The main problem is this can lead to 
negative values. Another approach would be a more computational non-parametric 
method like bootstrap. Do you know other methods to assess parameter 
uncertainty?


Best regards

F. Gallais









--
Marc R. Gastonguay, Ph.D.<mailto:ma...@metrumrg.com>
CEO
Metrum Research Group LLC<http://metrumrg.com>
2 Tunxis Rd., Ste 112, Tariffville, CT 06081 USA
Tel: +1.860.735.7043 ext. 101, Mobile: +1.860.670.0744, Fax: +1.860.760.6014



Confidentiality Notice: This message is private and may contain confidential 
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Re: [NMusers] Parameter uncertainty

[Marc Gastonguay]

Dear Fanny,

One additional method to obtain the parameter uncertainty, which I don't
believe was mentioned, is Bayesian estimation using Markov-Chain Monte
Carlo (MCMC) simulation. This method provides a full joint posterior
distribution (e.g. uncertainty distribution) of the parameters and any
predicted quantities, and is really the gold standard for this type of
goal. It is possible to implement this method in NONMEM (with some
limitations on the prior distributions), or you could use BUGS or Stan with
associated PK model libraries. You can also extract the samples from the
posterior distribution and simulate using the methods already described in
this thread.

Marc

On Thu, Feb 16, 2017 at 6:01 AM, Fanny Gallais <gallais.fa...@gmail.com>
wrote:

> Thank you all for your responses. It is going to be very useful for my
> work.
>
> Best regards,
>
> F.G.
>
> 2017-02-15 17:35 GMT+01:00 Williams, Jason <jason.willi...@pfizer.com>:
>
>> Dear Fanny,
>>
>>
>>
>> Another useful tool you may want to try is using the mrgsolve package
>> available in R, developed by Kyle Baron at Metrum Research Group. I have
>> found mrgsolve to be very efficient for PKPD simulation and sensitivity
>> analysis in R. There is an example of incorporating parameter uncertainty
>> (from $COV step in NONMEM) in Section 9 of the example on Probability of
>> Technical Success (link below).
>>
>>
>>
>> https://github.com/mrgsolve/examples/blob/master/PrTS/pts.pdf
>>
>>
>>
>> Best regards,
>>
>>
>> Jason
>>
>>
>>
>> *From:* owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com]
>> *On Behalf Of *Fanny Gallais
>> *Sent:* Wednesday, February 15, 2017 2:55 AM
>> *To:* nmusers@globomaxnm.com
>> *Subject:* [NMusers] Parameter uncertainty
>>
>>
>>
>> Dear NM users,
>>
>>
>>
>> I would like to perform a simulation (on R) incorporating parameter
>> uncertainty. For now I'm working on a simple PK model. Parameters were
>> estimated with NONMEM. I'm trying to figure out what is the best way to
>> assess parameter uncertainty. I've read about using the standard errors
>> reported by NONMEM and assume a normal distribution. The main problem is
>> this can lead to negative values. Another approach would be a more
>> computational non-parametric method like bootstrap. Do you know other
>> methods to assess parameter uncertainty?
>>
>>
>>
>>
>>
>> Best regards
>>
>>
>>
>> F. Gallais
>>
>>
>>
>>
>>
>>
>>
>
>


-- 
Marc R. Gastonguay, Ph.D. <ma...@metrumrg.com>
CEO
Metrum Research Group LLC <http://metrumrg.com>
2 Tunxis Rd., Ste 112, Tariffville, CT 06081 USA
Tel: +1.860.735.7043 ext. 101, Mobile: +1.860.670.0744, Fax: +1.860.760.6014

Re: [NMusers] Parameter uncertainty

[Fanny Gallais]

Thank you all for your responses. It is going to be very useful for my
work.

Best regards,

F.G.

2017-02-15 17:35 GMT+01:00 Williams, Jason <jason.willi...@pfizer.com>:

> Dear Fanny,
>
>
>
> Another useful tool you may want to try is using the mrgsolve package
> available in R, developed by Kyle Baron at Metrum Research Group. I have
> found mrgsolve to be very efficient for PKPD simulation and sensitivity
> analysis in R. There is an example of incorporating parameter uncertainty
> (from $COV step in NONMEM) in Section 9 of the example on Probability of
> Technical Success (link below).
>
>
>
> https://github.com/mrgsolve/examples/blob/master/PrTS/pts.pdf
>
>
>
> Best regards,
>
>
> Jason
>
>
>
> *From:* owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com]
> *On Behalf Of *Fanny Gallais
> *Sent:* Wednesday, February 15, 2017 2:55 AM
> *To:* nmusers@globomaxnm.com
> *Subject:* [NMusers] Parameter uncertainty
>
>
>
> Dear NM users,
>
>
>
> I would like to perform a simulation (on R) incorporating parameter
> uncertainty. For now I'm working on a simple PK model. Parameters were
> estimated with NONMEM. I'm trying to figure out what is the best way to
> assess parameter uncertainty. I've read about using the standard errors
> reported by NONMEM and assume a normal distribution. The main problem is
> this can lead to negative values. Another approach would be a more
> computational non-parametric method like bootstrap. Do you know other
> methods to assess parameter uncertainty?
>
>
>
>
>
> Best regards
>
>
>
> F. Gallais
>
>
>
>
>
>
>

RE: [NMusers] Parameter uncertainty

[Williams, Jason]

Dear Fanny,

Another useful tool you may want to try is using the mrgsolve package available 
in R, developed by Kyle Baron at Metrum Research Group. I have found mrgsolve 
to be very efficient for PKPD simulation and sensitivity analysis in R. There 
is an example of incorporating parameter uncertainty (from $COV step in NONMEM) 
in Section 9 of the example on Probability of Technical Success (link below).

https://github.com/mrgsolve/examples/blob/master/PrTS/pts.pdf

Best regards,

Jason

From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On 
Behalf Of Fanny Gallais
Sent: Wednesday, February 15, 2017 2:55 AM
To: nmusers@globomaxnm.com
Subject: [NMusers] Parameter uncertainty

Dear NM users,

I would like to perform a simulation (on R) incorporating parameter 
uncertainty. For now I'm working on a simple PK model. Parameters were 
estimated with NONMEM. I'm trying to figure out what is the best way to assess 
parameter uncertainty. I've read about using the standard errors reported by 
NONMEM and assume a normal distribution. The main problem is this can lead to 
negative values. Another approach would be a more computational non-parametric 
method like bootstrap. Do you know other methods to assess parameter 
uncertainty?


Best regards

F. Gallais

Re: FW: [NMusers] Parameter uncertainty

[Leonid Gibiansky]

One of the tools available for simulations is Metrum R package

metrumrg

install.packages("metrumrg", repos="http://R-Forge.R-project.org;)

Example of applications can be found here:

http://www.page-meeting.org/page/page2006/P2006III_11.pdf

Since the time it was written (2005-2006), Nonmem enhanced the 
simulations options, so now you can simulate from the model-estimated 
uncertainty directly from Nonmem. The R package could be useful if you 
do it from the bootstrap results.


Leonid



*From:*owner-nmus...@globomaxnm.com
[mailto:owner-nmus...@globomaxnm.com] *On Behalf Of *Fanny Gallais
*Sent:* Wednesday, February 15, 2017 5:55 AM
*To:* nmusers@globomaxnm.com
*Subject:* [NMusers] Parameter uncertainty

Dear NM users,



I would like to perform a simulation (on R) incorporating parameter
uncertainty. For now I'm working on a simple PK model. Parameters were
estimated with NONMEM. I'm trying to figure out what is the best way to
assess parameter uncertainty. I've read about using the standard errors
reported by NONMEM and assume a normal distribution. The main problem is
this can lead to negative values. Another approach would be a more
computational non-parametric method like bootstrap. Do you know other
methods to assess parameter uncertainty?





Best regards



F. Gallais









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RE: [NMusers] Parameter uncertainty

[Martin Bergstrand]

Dear Fanny and Bill,



The sampling importance resampling (SIR) approach [1] to characterize the
parameter uncertainty address the aspects pointed out Bill. In my opinion
this is currently in general the most widely applicable and accurate method
to characterize parameter uncertainty for NLMEM (bootstrap is likely
approximately as good for large datasets and balanced designs). The method
is implemented in PsN [2] and ready to use together with NONMEM.



[1] Dosne A-G, Bergstrand M, Harling K, Karlsson MO. Improving the
estimation of parameter uncertainty distributions in nonlinear mixed
effects models using sampling importance resampling. J Pharmacokinet
Pharmacodyn. 2016 Oct 11.

http://link.springer.com/article/10.1007/s10928-016-9487-8

[2] SIR user guide, PsN 4.6.0:
http://psn.sourceforge.net/pdfdocs/sir_userguide.pdf



Best regards,



Martin Bergstrand, Ph.D.

Senior Consultant

Pharmetheus AB



+46(0)709 994 396

martin.bergstr...@pharmetheus.com

www.pharmetheus.com



+46(0)18 513 328

U-A Science Park, Dag Hammarskjölds v. 52b

752 37 Uppsala, Sweden



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*From:* owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] *On
Behalf Of *William Denney
*Sent:* Wednesday, February 15, 2017 1:01 PM
*To:* Fanny Gallais <gallais.fa...@gmail.com>
*Cc:* nmusers@globomaxnm.com
*Subject:* Re: [NMusers] Parameter uncertainty



Hi Fanny,



It is often good practice to fit parameters that must be positive on the
log scale (by exponentiating them).  That will ensure that when sampling
from a normal distribution (and then exponentiating the sample) you will
have a positive value.



LLP was suggested, but it won't assess correlation between your parameters
which is often important when running simulations.



Bootstrap is another good alternative as has already been suggested.



Thanks,



Bill


On Feb 15, 2017, at 5:55 AM, Fanny Gallais <gallais.fa...@gmail.com> wrote:

Dear NM users,



I would like to perform a simulation (on R) incorporating parameter
uncertainty. For now I'm working on a simple PK model. Parameters were
estimated with NONMEM. I'm trying to figure out what is the best way to
assess parameter uncertainty. I've read about using the standard errors
reported by NONMEM and assume a normal distribution. The main problem is
this can lead to negative values. Another approach would be a more
computational non-parametric method like bootstrap. Do you know other
methods to assess parameter uncertainty?





Best regards



F. Gallais

RE: [NMusers] Parameter uncertainty

[Pieter Colin]

Hi Fanny,

As I understand it, you’re looking for ways to produce predictions according to 
your model taking into account parameter uncertainty.
We’ve recently published on the importance of parameter uncertainty when 
considering probability of target attainment for antibiotic dosing regimens.
(Colin et al. J Antimicrob Chemother (2016) 71 (9): 2502-2508)

The online supplement to this paper holds an R-script which you can use to 
simulate (and calculate PTA, if relevant) taking into account parameter 
uncertainty. For this, the script uses the variance-covariance matrix that is 
produced by the $COV step in NONMEM. Of course other techniques which generate 
a var-cov matrix could be used as input for the script as well.

Kind regards,

Pieter Colin

From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On 
Behalf Of Fanny Gallais
Sent: woensdag 15 februari 2017 11:55
To: nmusers@globomaxnm.com
Subject: [NMusers] Parameter uncertainty

Dear NM users,

I would like to perform a simulation (on R) incorporating parameter 
uncertainty. For now I'm working on a simple PK model. Parameters were 
estimated with NONMEM. I'm trying to figure out what is the best way to assess 
parameter uncertainty. I've read about using the standard errors reported by 
NONMEM and assume a normal distribution. The main problem is this can lead to 
negative values. Another approach would be a more computational non-parametric 
method like bootstrap. Do you know other methods to assess parameter 
uncertainty?


Best regards

F. Gallais

Re: [NMusers] Parameter uncertainty

[William Denney]

Hi Fanny,

It is often good practice to fit parameters that must be positive on the log 
scale (by exponentiating them).  That will ensure that when sampling from a 
normal distribution (and then exponentiating the sample) you will have a 
positive value.

LLP was suggested, but it won't assess correlation between your parameters 
which is often important when running simulations.

Bootstrap is another good alternative as has already been suggested.

Thanks,

Bill

> On Feb 15, 2017, at 5:55 AM, Fanny Gallais  wrote:
> 
> Dear NM users,
> 
> I would like to perform a simulation (on R) incorporating parameter 
> uncertainty. For now I'm working on a simple PK model. Parameters were 
> estimated with NONMEM. I'm trying to figure out what is the best way to 
> assess parameter uncertainty. I've read about using the standard errors 
> reported by NONMEM and assume a normal distribution. The main problem is this 
> can lead to negative values. Another approach would be a more computational 
> non-parametric method like bootstrap. Do you know other methods to assess 
> parameter uncertainty?
> 
> 
> Best regards
> 
> F. Gallais
> 
> 
> 
> 
> 

RE: [NMusers] Parameter uncertainty

[Max Taubert]

Dear Fanny,

I would use either bootstrapping or likelihood profiling, both of them are 
implemented in PsN ('bootstrap' and 'llp').

Kind regards
Max Taubert


Von: owner-nmus...@globomaxnm.com [owner-nmus...@globomaxnm.com]" im Auftrag 
von "Fanny Gallais [gallais.fa...@gmail.com]
Gesendet: Mittwoch, 15. Februar 2017 11:55
An: nmusers@globomaxnm.com
Betreff: [NMusers] Parameter uncertainty

Dear NM users,

I would like to perform a simulation (on R) incorporating parameter 
uncertainty. For now I'm working on a simple PK model. Parameters were 
estimated with NONMEM. I'm trying to figure out what is the best way to assess 
parameter uncertainty. I've read about using the standard errors reported by 
NONMEM and assume a normal distribution. The main problem is this can lead to 
negative values. Another approach would be a more computational non-parametric 
method like bootstrap. Do you know other methods to assess parameter 
uncertainty?


Best regards

F. Gallais

RE: [NMusers] Parameter uncertainty

[Eleveld-Ufkes, DJ]

Hi Fanny,
Likelihood profiles are very useful to asses parameter uncertainty.
I am sure you find a tutorial somewhere how they work.
A number of software packages automate the process quite a bit.
They are usually much more computationally efficient than bootstrap.
Warm regards,
Douglas Eleveld

From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On 
Behalf Of Fanny Gallais
Sent: woensdag 15 februari 2017 11:55
To: nmusers@globomaxnm.com
Subject: [NMusers] Parameter uncertainty

Dear NM users,

I would like to perform a simulation (on R) incorporating parameter 
uncertainty. For now I'm working on a simple PK model. Parameters were 
estimated with NONMEM. I'm trying to figure out what is the best way to assess 
parameter uncertainty. I've read about using the standard errors reported by 
NONMEM and assume a normal distribution. The main problem is this can lead to 
negative values. Another approach would be a more computational non-parametric 
method like bootstrap. Do you know other methods to assess parameter 
uncertainty?


Best regards

F. Gallais






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[NMusers] Parameter uncertainty

[Fanny Gallais]

Dear NM users,

I would like to perform a simulation (on R) incorporating parameter
uncertainty. For now I'm working on a simple PK model. Parameters were
estimated with NONMEM. I'm trying to figure out what is the best way to
assess parameter uncertainty. I've read about using the standard errors
reported by NONMEM and assume a normal distribution. The main problem is
this can lead to negative values. Another approach would be a more
computational non-parametric method like bootstrap. Do you know other
methods to assess parameter uncertainty?


Best regards

F. Gallais

Re: [NMusers] Parameter Uncertainty and Covariate effects

[Mats Karlsson]

Dear Sven

If you don't assume the covariance between THETA(1) and THETA(2) to be zero but 
use the estimated covariance value, you do let the data speak. A problem in 
this respect is that publications never give such values even if it of course 
is possible. With online access to model code and output (as with the DDMoRe 
repository (repository.ddmore.eu)) it will be more likely to find the 
information.

Best regards,
Mats

Skickat från min iPhone

> 11 jan 2016 kl. 14:28 skrev Stodtmann, Sven :
> 
> Dear All,
> 
> In order to account for uncertainty in estimated parameters when running a 
> simulation, a natural approach would be running multiple simulations for 
> different parameter vectors which are drawn from the (theoretical, 
> asymptotic) distribution of the estimator (i.e. normal with mean THETA and 
> covariance according to the NONMEMs $COR output for the THETAs).
> This approach may in some cases (particularly, when there are a lot of 
> covariate effects estimated) lead to very broad parameter distributions, even 
> assigning some quite high probability of unphysiological values if one didn’t 
> have good quality data, strong priors or a very careful parametrization of 
> the model (e.g. transforming/bounding parameters, which requires/introduces 
> prior knowledge as well).
> 
> Another problem connected with parameter uncertainty on covariate effects is 
> the following. Say we model
> TVCL = THETA(1)
> SEX_EFF = THETA(2)
> CL = TVCL * SEX_EFF**SEX,   (Eq. 
> 1)
> where male is coded as SEX=0, female as SEX=1.
> In this case, when using the above mentioned technique to account for 
> parameter uncertainty, the female population will have a more variable 
> (uncertain) PK, not just different one. If we phrase the problem differently, 
> using
> CL = TVCL * SEX_EFF**(1-SEX) ,(Eq. 2)
> The conclusion would be the other way around (i.e. male PK is more uncertain).
> 
> One approach to deal with the second problem could be this:
> In order to remove this (usually unjustified) assumption (the female 
> population having a less certain PK compared to the male), one could try to 
> model the same covariate effect as follows:
> TVCL = THETA(1)
> SQRT_SEX_EFF = THETA(2)
> CL = TVCL * SQRT_SEX_EFF**SEX / SQRT_SEX_EFF**(1-SEX)
> In this case TVCL would already include “half” of the effect (on the log 
> scale; the “new” TVCL would be TVCL*SQRT(SEX_EFF) in terms of the parameters 
> used in Eq.1).
> With this approach, both sub-populations, male and female get “some part” of 
> the uncertainty effect.
> Of course it would be even nicer to let the data decide which sub-population 
> gets how much uncertainty exactly instead of evenly splitting it.
> 
> How do you deal with uncertainty in the estimates of covariate effects when 
> it comes to simulations/predictions?
> 
> Kind Regards,
> 
> SVEN STODTMANN, PHD
> Pharmacometrician
> 
> AbbVie Deutschland GmbH & Co KG
> Clinical Pharmacology and Pharmacometrics
> Knollstrasse 50
> 67065 Ludwigshafen am Rhein, Germany
> OFFICE +49 621-589-1940
> EMAIL  sven.stodtm...@abbvie.com
> 
> abbvie.com
> 
> 
> 
> 
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> Persönlich haftende Gesellschafterin: AbbVie Komplementär GmbH
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> Geschäftsführer: Dr. Patrick Horber, Thomas Scheidmeir, Dr. Stefan Simianer, 
> William J. Chase
> Vorsitzende des Aufsichtsrats: Dr. Azita Saleki-Gerhardt
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[NMusers] Parameter Uncertainty and Covariate effects

[Stodtmann, Sven]

Dear All,

In order to account for uncertainty in estimated parameters when running a 
simulation, a natural approach would be running multiple simulations for 
different parameter vectors which are drawn from the (theoretical, asymptotic) 
distribution of the estimator (i.e. normal with mean THETA and covariance 
according to the NONMEMs $COR output for the THETAs).
This approach may in some cases (particularly, when there are a lot of 
covariate effects estimated) lead to very broad parameter distributions, even 
assigning some quite high probability of unphysiological values if one didn’t 
have good quality data, strong priors or a very careful parametrization of the 
model (e.g. transforming/bounding parameters, which requires/introduces prior 
knowledge as well).

Another problem connected with parameter uncertainty on covariate effects is 
the following. Say we model
TVCL = THETA(1)
SEX_EFF = THETA(2)
CL = TVCL * SEX_EFF**SEX,   (Eq. 1)
where male is coded as SEX=0, female as SEX=1.
In this case, when using the above mentioned technique to account for parameter 
uncertainty, the female population will have a more variable (uncertain) PK, 
not just different one. If we phrase the problem differently, using
CL = TVCL * SEX_EFF**(1-SEX) ,(Eq. 2)
The conclusion would be the other way around (i.e. male PK is more uncertain).

One approach to deal with the second problem could be this:
In order to remove this (usually unjustified) assumption (the female population 
having a less certain PK compared to the male), one could try to model the same 
covariate effect as follows:
TVCL = THETA(1)
SQRT_SEX_EFF = THETA(2)
CL = TVCL * SQRT_SEX_EFF**SEX / SQRT_SEX_EFF**(1-SEX)
In this case TVCL would already include “half” of the effect (on the log scale; 
the “new” TVCL would be TVCL*SQRT(SEX_EFF) in terms of the parameters used in 
Eq.1).
With this approach, both sub-populations, male and female get “some part” of 
the uncertainty effect.
Of course it would be even nicer to let the data decide which sub-population 
gets how much uncertainty exactly instead of evenly splitting it.

How do you deal with uncertainty in the estimates of covariate effects when it 
comes to simulations/predictions?

Kind Regards,

SVEN STODTMANN, PHD
Pharmacometrician

AbbVie Deutschland GmbH & Co KG
Clinical Pharmacology and Pharmacometrics
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67065 Ludwigshafen am Rhein, Germany
OFFICE +49 621-589-1940
EMAIL  sven.stodtm...@abbvie.com

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[NMusers] Parameter uncertainty in simulations

[Mendel_Jansen]

Dear all,

I would appreciate to learn your experience and tips on how to a) estimate
parameter uncertainty, and b) sample from such uncertainty in simulations.
References would also be much appreciated.

In the archives there is mention of parameter uncertainty, but I could not
find this subject discussed directly. Hopefully, we may start an
informative thread.

Methods I found mentioned for estimating parameter uncertainty are either
taking the covariance matrix from NONMEM, or obtaining the - not
necessarily normally distributed - covariance structure from a
non-parametric bootstrap. Estimation and simulation can be quick, but a
bootstrap of 1000 replicates or more often is not done that quickly.
It may be quicker to use the NONMEM covariance matrix. When should one not
do this, or how could one tell that actually there may be problems with
using the reported precision of parameters in NONMEM, and the true
uncertainty is much better estimated via the bootstrap?

When taking the parameter precision from NONMEM's covariance matrix, should
one log transform parameters and estimate random subject level and residual
error parameters as thetas, added to fixed etas and sigmas? (See also:
http://www.cognigencorp.com/nonmem/current/2008-July/1060.html)

I have seen an example for a PKPD model where the concentration effect
relationship is modelled as a linear relationship with estimation of slope
and inter-patient variability in slope. When parameters are not
transformed, NONMEM reports a precision of 48% in the population slope and
99% in the variance, however these both drop to  7% after the transforms.
Are these typical of the reductions in biased estimation of parameter
uncertainty we seek, or may such large changes prompt you to further
examine the model and / or trigger you to run the bootstrap?

Thank you for your thoughts and responses.

Kind regards,

Mendel

Mendel Jansen
Director Modeling and Simulation
Clinical Pharmacology and Translational Medicine
Eisai Limited
London
UK
e-mail mendel_jan...@eisai.net

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