From: Anna Chan Kwong <*anna.chankwong*>

Date: Fri, 17 May 2019 14:39:47 +0200

Dear Jakob and Mats,

Thank you very much for your kind answers.

My questions were general, for different applications. After reading the

article by Gisleskog at al. (in particular, the last part of the

discussion), I thought it was possible to build a “Model without co=

variate”

with $PRIOR and then to add covariates with SCM (with the 4 conditions I

listed in my first email). Moreover, the building of a model using SCM in

combination with a frequentist prior is sometimes reported in the

literature, without precision on its implementation.

Thus, I wanted to add a PRIOR on the theta of the parameter (not on the

theta of the covariate), that is : PAR = PARp * PARCOV

PARp = parameter with prior ($THETAP = parameter in the prior populatio=

n)

PARCOV estimated on the new dataset only, and centered around prior median

of the covariate, e.g. with the equation (PARCOV =

(COV/medianCOV)**THETA(COV), medianCOV is the median in the prior dataset).

I wrote ”"OBJECTIVE FUNCTION VALUE WITHOUT CONSTANT" (without PRIOR

penalty).” because this is what is reported in the output of NONMEM=

with

$PRIOR:

N*LOG(2PI) CONSTANT TO OBJECTIVE FUNCTION: 2152.15

OBJECTIVE FUNCTION VALUE WITHOUT CONSTANT: 3633.00

OBJECTIVE FUNCTION VALUE WITH CONSTANT: 5785.15

[...]

PRIOR CONSTANT TO OBJECTIVE FUNCTION: 1297.35

OBJECTIVE FUNCTION VALUE WITHOUT CONSTANT: 3633.00

OBJECTIVE FUNCTION VALUE WITH CONSTANT: 4930.35

REPORTED OBJECTIVE FUNCTION DOES NOT CONTAIN CONSTANT

The first block, with the N*LOG(2PI) constant, is common to all the outputs

(also without PRIOR).

I’m interested in the second block, which reports

- first the “PRIOR penalty” (PRIOR CONSTANT TO OBJECTIV=

E FUNCTION),

- second the objective function on the data (OBJECTIVE FUNCTION VALUE

WITHOUT CONSTANT),

- third the SUM of the “PRIOR penalty” and the objectiv=

e function on

the data (OBJECTIVE FUNCTION VALUE WITH CONSTANT)

From the article by Gisleskog et al, I understood that the third term (=

PRIOR

penalty” + objective function on the data (OBJECTIVE FUNCTION VALUE=

WITH

CONSTANT)) should be used to perform hypothesis tests. However, when I

tried to perform an automated SCM in PsN on a “Model without covari=

ate”

with $PRIOR NWPRI (which I thought was possible because of the $PRIOR NWPRI

mention in the SCM user guide), it was the second term (objective function

on the data (OBJECTIVE FUNCTION VALUE WITHOUT CONSTANT)) that was compared.

Jakob, if I understand correctly the beginning of your email, you use

$PRIOR NWPRI with SCM to test if a parameter is different in a new

population. That is, testing if DIFF is different from zero if we code the

parameter PARn = PARp * (1 + DIFF),

PARn = parameter in the new population

PARp = parameter with prior ($THETAP = parameter in the prior populatio=

n)

Then comparing two models, one with PARn = PARp (DIFF=0), one with PARn=

=

PARp * (1 + DIFF), with the Likelihood Ratio Test.

Is that what you meant? I was not aware of this method.

Again, thank you very much for your suggestions,

Best regards,

Anna

Le jeu. 16 mai 2019 à 14:22, Mats Karlsson <Mats.Karlsson

e> a

écrit :

*> Hi Anna,
*

*>
*

*>
*

*>
*

*> That you want to explore covariate relationships on a parameter suggests
*

*> that you believe your data contain plenty of information about the
*

*> parameter. Therefore do you really need to use a prior on the parameter(s=
*

)

*> in question? A little more info around what your “base” m=
*

odel is and why

*> you use a prior could help answering.
*

*>
*

*>
*

*>
*

*> You write “"OBJECTIVE FUNCTION VALUE WITHOUT CONSTANT" (without P=
*

RIOR

*> penalty). ”, but the CONSTANT mentioned is not related to the pri=
*

or, but

*> rather the term of the OFV that is related to the number of observations
*

*> only (Nobs*LN(2*PI)).
*

*>
*

*> For obtaining a reference distribution for the likelihood ratio test a
*

*> randomization (permutation) test is often useful as it uses the real data
*

*> as opposed to simulated data. PsN functionality for this is “rand=
*

test”.

*>
*

*>
*

*>
*

*> Best regards,
*

*>
*

*> Mats
*

*>
*

*> *From:* owner-nmusers *

*> Behalf Of *Anna Chan Kwong
*

*> *Sent:* den 16 maj 2019 10:46
*

*> *To:* nmusers *

*> *Subject:* [NMusers] inclusion of covariates with $PRIOR
*

*>
*

*>
*

*>
*

*> Dear NMusers
*

*>
*

*> I am wondering about the inclusion of covariates with the $PRIOR
*

*> subroutine.
*

*>
*

*> The article "Use of Prior Information to Stabilize a Population Data
*

*> Analysis" (Gisleskog, Karlsson, Beal 2002) states that Stepwise Covariat=
*

e

*> Modelling (SCM) is possible on a parameter estimated with prior
*

*> information, under conditions :
*

*>
*

*> 1) Population parameters have to be centered around the prior geometric
*

*> mean (often the median) of the covariate (for example, if the power
*

*> function is used: (COV/medianCOV)**THETA(COV), medianCOV is the median in
*

*> the prior dataset)
*

*> Is it correct to use functions like linear function
*

*> (1+THETA(COV)*(COV-medianCOV) or exponential function
*

*> (exp(THETA(COV)*(COV-medianCOV) ?
*

*>
*

*> 2) the SUM of the objective function and the PRIOR penalty should be used
*

*> to perform hypothesis tests.
*

*>
*

*> Could you confirm I have properly understood this condition??
*

*> I am in doubt because automated SCM with $PRIOR in PsN (
*

*> https://uupharmacometrics.github.io/PsN/docs.html
*

*> <https://urlproxy.sunet.se/canit/urlproxy.php?_q=aHR0cHM6Ly91dXBoYXJtYW=
*

NvbWV0cmljcy5naXRodWIuaW8vUHNOL2RvY3MuaHRtbA%3D%3D&_s=bWF0cy5rYXJsc3NvbkB=

mYXJtYmlvLnV1LnNl&_c=ef5b1054&_r=dXUtc2U%3D>)

*> compares the "OBJECTIVE FUNCTION VALUE WITHOUT CONSTANT" (without PRIOR
*

*> penalty).
*

*>
*

*>
*

*> 3) hypothesis tests such as the Likelihood Ratio Test needs to be
*

*> performed with the ACTUAL significance level
*

*>
*

*> Is there a way to determine the actual significance level faster than
*

*> Stochastic Simulation and Estimation?
*

*>
*

*> 4) the prior omega of the parameter on which the covariate impacts should
*

*> be decreased by the product of THETA(COV)² and the prior population
*

*> variance of log(COV).
*

*> Does that mean we should manually adjust the $OMEGAP value of a parameter
*

*> on which we test the covariate ? OMEGAP(adjusted) = OMEGAP -
*

*> (THETA(COV))²*var
*

*>
*

*> with OMEGAP = prior OMEGA estimate of the parameter on which the covari=
*

ate

*> is added ; var = prior population variance of log COV
*

*>
*

*> Thank you very much for your understanding,
*

*>
*

*> Sincerely yours,
*

*>
*

*> Anna Chan Kwong
*

*> PhD sudent in Pharmacometrics, Marseille University.
*

*>
*

*>
*

*>
*

*>
*

*>
*

*>
*

*>
*

*>
*

*> När du har kontakt med oss på Uppsala universitet med e-post s=
*

å innebär

*> det att vi behandlar dina personuppgifter. För att läsa mer om =
*

hur vi gör

*> det kan du läsa här: http://www.uu.se/om-uu/dataskydd-personupp=
*

gifter/

*>
*

*> E-mailing Uppsala University means that we will process your personal
*

*> data. For more information on how this is performed, please read here:
*

*> http://www.uu.se/en/about-uu/data-protection-policy
*

*>
*

Received on Fri May 17 2019 - 08:39:47 EDT

Date: Fri, 17 May 2019 14:39:47 +0200

Dear Jakob and Mats,

Thank you very much for your kind answers.

My questions were general, for different applications. After reading the

article by Gisleskog at al. (in particular, the last part of the

discussion), I thought it was possible to build a “Model without co=

variate”

with $PRIOR and then to add covariates with SCM (with the 4 conditions I

listed in my first email). Moreover, the building of a model using SCM in

combination with a frequentist prior is sometimes reported in the

literature, without precision on its implementation.

Thus, I wanted to add a PRIOR on the theta of the parameter (not on the

theta of the covariate), that is : PAR = PARp * PARCOV

PARp = parameter with prior ($THETAP = parameter in the prior populatio=

n)

PARCOV estimated on the new dataset only, and centered around prior median

of the covariate, e.g. with the equation (PARCOV =

(COV/medianCOV)**THETA(COV), medianCOV is the median in the prior dataset).

I wrote ”"OBJECTIVE FUNCTION VALUE WITHOUT CONSTANT" (without PRIOR

penalty).” because this is what is reported in the output of NONMEM=

with

$PRIOR:

N*LOG(2PI) CONSTANT TO OBJECTIVE FUNCTION: 2152.15

OBJECTIVE FUNCTION VALUE WITHOUT CONSTANT: 3633.00

OBJECTIVE FUNCTION VALUE WITH CONSTANT: 5785.15

[...]

PRIOR CONSTANT TO OBJECTIVE FUNCTION: 1297.35

OBJECTIVE FUNCTION VALUE WITHOUT CONSTANT: 3633.00

OBJECTIVE FUNCTION VALUE WITH CONSTANT: 4930.35

REPORTED OBJECTIVE FUNCTION DOES NOT CONTAIN CONSTANT

The first block, with the N*LOG(2PI) constant, is common to all the outputs

(also without PRIOR).

I’m interested in the second block, which reports

- first the “PRIOR penalty” (PRIOR CONSTANT TO OBJECTIV=

E FUNCTION),

- second the objective function on the data (OBJECTIVE FUNCTION VALUE

WITHOUT CONSTANT),

- third the SUM of the “PRIOR penalty” and the objectiv=

e function on

the data (OBJECTIVE FUNCTION VALUE WITH CONSTANT)

From the article by Gisleskog et al, I understood that the third term (=

PRIOR

penalty” + objective function on the data (OBJECTIVE FUNCTION VALUE=

WITH

CONSTANT)) should be used to perform hypothesis tests. However, when I

tried to perform an automated SCM in PsN on a “Model without covari=

ate”

with $PRIOR NWPRI (which I thought was possible because of the $PRIOR NWPRI

mention in the SCM user guide), it was the second term (objective function

on the data (OBJECTIVE FUNCTION VALUE WITHOUT CONSTANT)) that was compared.

Jakob, if I understand correctly the beginning of your email, you use

$PRIOR NWPRI with SCM to test if a parameter is different in a new

population. That is, testing if DIFF is different from zero if we code the

parameter PARn = PARp * (1 + DIFF),

PARn = parameter in the new population

PARp = parameter with prior ($THETAP = parameter in the prior populatio=

n)

Then comparing two models, one with PARn = PARp (DIFF=0), one with PARn=

=

PARp * (1 + DIFF), with the Likelihood Ratio Test.

Is that what you meant? I was not aware of this method.

Again, thank you very much for your suggestions,

Best regards,

Anna

Le jeu. 16 mai 2019 à 14:22, Mats Karlsson <Mats.Karlsson

e> a

écrit :

)

odel is and why

RIOR

or, but

test”.

e

NvbWV0cmljcy5naXRodWIuaW8vUHNOL2RvY3MuaHRtbA%3D%3D&_s=bWF0cy5rYXJsc3NvbkB=

mYXJtYmlvLnV1LnNl&_c=ef5b1054&_r=dXUtc2U%3D>)

ate

å innebär

hur vi gör

gifter/

Received on Fri May 17 2019 - 08:39:47 EDT