RE: [NMusers] OMEGA priors using modes of inverse Wishart matrix

[Joachim Grevel]

Many thanks to all of you who responded so quickly and comprehensively.

For those looking into this exchange in the future through the NMuser
archive: Look at Mats’ and Tim’s response first then at all the others.
There is not a single answer. I for my part will employ several techniques
with sensitivity analysis, before I chose a model that gives me the most
useful individual parameters for my new small data set of interest.

 

Joachim

 

From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On
Behalf Of Mats Karlsson
Sent: 23 February 2012 05:55
To: nmusers@globomaxnm.com
Subject: FW: [NMusers] OMEGA priors using modes of inverse Wishart matrix

 

Hi again,

 

We use a formula to come up with a suitable number of subjects (N) for
degrees of freedom (df) for IW distribution. It is based on the assumption
that you know the SE of the variance estimate that you want to use as a
prior. 

 

•  How to choose N?

•  We know 0 < N < Nsubj

•  Guesstimate N

•  Closer to 0 if sparse info per subject

•  Closer to Nsubj if rich info per subject

•  If we know SE of omega, we can do better!

•  Calculate how many subjects with perfect information our SE
corresponds to and then use that N for calculation of df

•  For a variance (omega^2): SE=omega^2*SQRT(2/(N-1))

•  Rearrange to: N=2*omega^4/SE^2+1

•  N   = Estimate of N

•  Omega^2  = Variance estimate (from output of previous model)

•  SE = Standard error of Omega^2 (from output f
previous)

 

Best regards,

Mats

 

 

 

Mats Karlsson, PhD

Professor of Pharmacometrics

Dept of Pharmaceutical Biosciences

Faculty of Pharmacy

Uppsala University

Box 591

75124 Uppsala

 

Phone: +46 18 4714105

Fax + 46 18 4714003

 

From: Bauer, Robert [mailto:robert.ba...@iconplc.com] 
Sent: 23 February 2012 00:10
To: Mats Karlsson
Cc: chee ng
Subject: FW: [NMusers] OMEGA priors using modes of inverse Wishart matrix

 

Mats:

I think the general formula you gave me in your slides for degrees of
freedom for a prior OMEGA is quite useful to others, as noted below.  Is
this something you could share with nmusers?

 

 

Robert J. Bauer, Ph.D.

Vice President, Pharmacometrics, R&D

ICON Development Solutions

7740 Milestone Parkway

Suite 150

Hanover, MD 21076

Tel: (215) 616-6428

Mob: (925) 286-0769

Email: robert.ba...@iconplc.com

Web: www.iconplc.com  

 

 

  _  

From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On
Behalf Of Stephen Duffull
Sent: Wednesday, February 22, 2012 1:09 PM
To: Mats Karlsson; 'Joachim Grevel'; 'Coen van Hasselt'; 'nmusers'
Subject: RE: [NMusers] OMEGA priors using modes of inverse Wishart matrix

Hi

 

An appropriate value for dof of the IW is difficult to determine.  While it
can be set at n-1 from a prior this is somewhat arbitrary.  It is not in
this sense like a t-distn where we calculate dof in this manner.

 

You would have to get a feeling for the degree of spread in your deviates
given your guess at OMEGA(0) and dof.  This can be done by simulation or in
special circumstances by direct calculation.

 

Steve

--

 

 

From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On
Behalf Of Mats Karlsson
Sent: Thursday, 23 February 2012 3:58 a.m.
To: 'Joachim Grevel'; 'Coen van Hasselt'; 'nmusers'
Subject: RE: [NMusers] OMEGA priors using modes of inverse Wishart matrix

 

Dear Joachim,

 

The IW distribution is not something you get from NONMEM, you have to give
the degrees of freedom of the IW prior distribution. Normally this is at or
below the number of subjects in you previous study depending the information
about the parameter per subject.

 

In addition to User’s Guides, you may find useful info in Gisleskog et al J
Pharmacokinet Pharmacodyn. 2002 Dec;29(5-6):473-505.

 

Best regards,

Mats 

 

Mats Karlsson, PhD

Professor of Pharmacometrics

Dept of Pharmaceutical Biosciences

Faculty of Pharmacy

Uppsala University

Box 591

75124 Uppsala

 

Phone: +46 18 4714105

Fax + 46 18 4714003

 

From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On
Behalf Of Joachim Grevel
Sent: 22 February 2012 15:24
To: 'Coen van Hasselt'; nmusers
Subject: RE: [NMusers] OMEGA priors using modes of inverse Wishart matrix

 

Dear Coen,

 

There I do have the answer: with MCMC Bayesian in NONMEM 7.1 you have to use
NWPRI according to the guide.

 

Dear Nidal,

 

What I try to do is that: use an existing very well defined popPK model
(2500 conc in 200 patients) to obtain individual PK parameters in only 20
additional patients that have sparse sampling (2 to 4 conc per patient). I
was planning to use informative priors rather than add 80 conc  to a bulk of
2500 conc. What do you think?

 

Thanks to all, specifically Tim!

 

Joachim

 

From: Coen van Hasselt [mailto:coen.vanhass...@slz.nl]

[NMusers] Coding delayed covariate effects

[Elisabet Størset]

Dear nonmemusers


In my PK modeling project, a drug (elimination: 100 % hepatic metabolism)
is given orally twice daily over a period of 10 weeks. 100 subjects
contribute daily trough concentrations. During this period, covariates vary
within subjects. Two covariates that are difficult to handle are changes in
corticosteroid regime and changes in cytokine concentrations, which both
are expected to alter metabolism (CYP enzymes) at a transcriptional level.
This means that a covariate effect on CL is expected to be delayed and/or
last for some time (unknown for how long).


My first strategy is to code this in the normal way:

TVCL=THETA(1) + THETA(2) *(cytokine concentration) or (corticosteroid dose)


However, when coding the covariate as continuous with this method, it will
not take into account that an effect does still have an impact on the
parameter after the covariate value has returned to normal in the data set.


Example 1 - Low dose steroids are typically administered daily. Then, high
dose methylprednisolone is given I.V. for 3 days, before going back to the
low dose. The inductive effect on CYP enzymes from the high dose could be
delayed and then last for 1-2 weeks even though the high dose is not
maintained.

Example 2 - Cytokines marks an inflammation, which could have temporary
impact on CL/F. Cytokine concentration returns to normal, but the impact on
the parameter could be lasting for some days.


Does anyone have experience of a strategy to code these kinds of covariate
relationships in NONMEM? Could NONMEM estimate for how long time CL/F might
be affected, or is this too much to ask for? :)



Additional question: Is there any way to make the visual predictive check
an appropriate validation method when only trough concentrations are known
over a long period of time, when doses are frequently changing within and
between subjects during the period?


Thank you all in advance for your kind help :)


Elisabet, pharmacy student, University of Bergen

Re: [NMusers] Coding delayed covariate effects

[Sebastian Ueckert]

Dear Elisabet,

The most complete way to handle your problem would be to treat the
covariates as observations and build a separate model for them. Your
data set would change from wide to long format. So instead of having

ID TIME DV CYTC
1  0X1  Y1
1  1X2  Y2

you would have

ID TIME DV TYPE
1  0   X1  1
1  0   Y1  2
1  1   X2  1
1  1   Y2  2

where TYPE is a flag specifying the type of measurement.

In your model file you use the TYPE flag to return the prediction
corresponding to the current row i.e.,

IF(TYPE.EQ.1) Y=.;model prediction for concentration
IF(TYPE.EQ.2) Y=; model prediction for covariate

This would increase the modeling effort considerably but has the
advantage that you can now use any model to link your covariates and
clearance. One option for a delay between change in covariate and
clearance would be an indirect response model. Another advantage of
this approach, is that you acknowledge the uncertainty in the
covariate (since it is just another type of measurement).

Concerning your second question, you could have a look at prediction
corrected VPCs as described by Bergstrand et al.:

Bergstrand, Martin, Andrew C Hooker, Johan E Wallin, and Mats O Karlsson.
“Prediction-corrected Visual Predictive Checks for Diagnosing
Nonlinear Mixed-effects Models.”
The AAPS Journal 13, no. 2 (June 2011): 143–151.


I hope that helps!

Best regards,
Sebastian


Sebastian Ueckert, MSc, PhD student
---
Pharmacometrics Research Group,
Department of Pharmaceutical Biosciences,
Uppsala University
---
P.O. Box 591
SE-751 24 Uppsala
Sweden
---
sebastian.ueck...@farmbio.uu.se
---
Work:   +46-(0)18-471 4437



On Thu, Feb 23, 2012 at 2:50 PM, Elisabet Størset
 wrote:
> Dear nonmemusers
>
>
> In my PK modeling project, a drug (elimination: 100 % hepatic metabolism) is
> given orally twice daily over a period of 10 weeks. 100 subjects contribute
> daily trough concentrations. During this period, covariates vary within
> subjects. Two covariates that are difficult to handle are changes in
> corticosteroid regime and changes in cytokine concentrations, which both are
> expected to alter metabolism (CYP enzymes) at a transcriptional level. This
> means that a covariate effect on CL is expected to be delayed and/or last
> for some time (unknown for how long).
>
>
> My first strategy is to code this in the normal way:
>
> TVCL=THETA(1) + THETA(2) *(cytokine concentration) or (corticosteroid dose)
>
>
> However, when coding the covariate as continuous with this method, it will
> not take into account that an effect does still have an impact on the
> parameter after the covariate value has returned to normal in the data set.
>
>
> Example 1 - Low dose steroids are typically administered daily. Then, high
> dose methylprednisolone is given I.V. for 3 days, before going back to the
> low dose. The inductive effect on CYP enzymes from the high dose could be
> delayed and then last for 1-2 weeks even though the high dose is not
> maintained.
>
> Example 2 - Cytokines marks an inflammation, which could have temporary
> impact on CL/F. Cytokine concentration returns to normal, but the impact on
> the parameter could be lasting for some days.
>
>
> Does anyone have experience of a strategy to code these kinds of covariate
> relationships in NONMEM? Could NONMEM estimate for how long time CL/F might
> be affected, or is this too much to ask for? :)
>
>
>
> Additional question: Is there any way to make the visual predictive check an
> appropriate validation method when only trough concentrations are known over
> a long period of time, when doses are frequently changing within and between
> subjects during the period?
>
>
> Thank you all in advance for your kind help :)
>
>
> Elisabet, pharmacy student, University of Bergen

RE: [NMusers] Coding delayed covariate effects

[Mats Karlsson]

Dear Elisabet,

In addition to Sebastian's answer, the indirect response model he mentions
is a model for the turn-over of the (induced) enzyme. Thus the half-life of
the enzyme you may be able to get info in literature on a reasonable value
(probably 1-3 days). This type of model was used in:

A mechanism-based pharmacokinetic-enzyme model for cyclophosphamide
autoinduction in breast cancer patients.
Hassan et al, 
Br J Clin Pharmacol. 1999 Nov;48(5):669-77. 2. 

The associated model file looked like this:
$PROBLEM   Cyklofosfamid induktion
$INPUT NUMB  ID TIME DV NEWA AMT RATE CMT FLAG DURA
$DATA   /users/mats/Cancer/Musse/Data/cp11.dta  IGNORE=#
$SUBROUTINES ADVAN9 TOL=4
$MODEL COMP=CENTRAL
   COMP=PERI
   COMP=4OH
   COMP=ENZ
$PK
CLUI = THETA(1)*EXP(ETA(1))
CLI  = THETA(2)*EXP(ETA(2))
V1   = THETA(3)*EXP(ETA(3))
Q= THETA(4)*EXP(ETA(4))
V2   = THETA(5)*EXP(ETA(5))
CLOH = THETA(6)*EXP(ETA(6))
VOH  = THETA(7)*EXP(ETA(7))
EMAX = THETA(8)*EXP(ETA(8))
EC50 = THETA(9)*EXP(ETA(9))
KENZ = THETA(10)*EXP(ETA(10))
S1   = V1
S3   = VOH
K10  = CLUI /V1
K12  = Q/V1 
K13  = CLI  /V1
K21  = Q/V2
K30  = CLOH /VOH
$DES
CP = A(1)/V1
DADT(1)=-A(1)*(K10+K12+K13*A(4)) + K21*A(2)
DADT(2)= A(1)* K12   - K21*A(2)
DADT(3)= A(1)*A(4)*K13   - K30*A(3)
DADT(4)= KENZ*(1+EMAX*CP/(CP+EC50)-A(4))
$THETA   
 (0,.26)  ;CLUI
 (0,2.2)  ;CLI
 (0,9.75)  ;V1
 (0,12.6)  ;Q
 (0,21.5)  ;V2
 (0,387)  ;CLOH
 (7,253)  ;VOH
 (0,351)  ;EMAX
 (5540 FIX)  ;EC50
 (0,.0365)  ;KENZ
 (0,1.38)  ;ADD ERROR
 (0.04,.0642)  ;PROP ERROR
 (0,.026) ;ADD ERROR
 (0.04,.07)  ;PROP ERROR
$OMEGA 0.01 .2673 .267 .41 .219 .0274 2.48 .194 0 FIX .11 

$ERROR
 W   = 1
 IF(F.GT.0) W=  SQRT(THETA(11)**2+THETA(12)**2*F**2) 
 IF(F.GT.0.AND.CMT.EQ.3) W= SQRT(THETA(13)**2+THETA(14)**2*F**2) 
 IPRED   = F
 IRES= DV-IPRED
 IWRES   = IRES / W
 Y   = IPRED+EPS(1)*W

$SIGMA  1 FIX;RESIDUAL ERROR 
$ESTIMATION   MAXEVALS=9990 POSTHOC PRINT=1 MSFO=msfb31 NOABORT
$TABLE ID TIME IPRED IWRES  ONEHEADER NOPRINT FILE=sdtab31
$TABLE ID FLAG TIME IPRED IWRES ONEHEADER NOPRINT FILE=mutab31
$TABLE ID CLUI CLI V1 Q V2 CLOH VOH EMAX KENZ ETA1 ETA2 
   ETA3 ETA4 ETA5 ETA6 ETA7 ETA8 ETA10
ONEHEADER NOPRINT FILE=patab31

Mats Karlsson, PhD
Professor of Pharmacometrics
Dept of Pharmaceutical Biosciences
Faculty of Pharmacy
Uppsala University
Box 591
75124 Uppsala

Phone: +46 18 4714105
Fax + 46 18 4714003


-Original Message-
From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On
Behalf Of Sebastian Ueckert
Sent: 23 February 2012 22:43
To: Elisabet Størset
Cc: nmusers@globomaxnm.com
Subject: Re: [NMusers] Coding delayed covariate effects

Dear Elisabet,

The most complete way to handle your problem would be to treat the
covariates as observations and build a separate model for them. Your data
set would change from wide to long format. So instead of having

ID TIME DV CYTC
1  0X1  Y1
1  1X2  Y2

you would have

ID TIME DV TYPE
1  0   X1  1
1  0   Y1  2
1  1   X2  1
1  1   Y2  2

where TYPE is a flag specifying the type of measurement.

In your model file you use the TYPE flag to return the prediction
corresponding to the current row i.e.,

IF(TYPE.EQ.1) Y=.;model prediction for concentration
IF(TYPE.EQ.2) Y=; model prediction for covariate

This would increase the modeling effort considerably but has the advantage
that you can now use any model to link your covariates and clearance. One
option for a delay between change in covariate and clearance would be an
indirect response model. Another advantage of this approach, is that you
acknowledge the uncertainty in the covariate (since it is just another type
of measurement).

Concerning your second question, you could have a look at prediction
corrected VPCs as described by Bergstrand et al.:

Bergstrand, Martin, Andrew C Hooker, Johan E Wallin, and Mats O Karlsson.
“Prediction-corrected Visual Predictive Checks for Diagnosing Nonlinear
Mixed-effects Models.”
The AAPS Journal 13, no. 2 (June 2011): 143–151.


I hope that helps!

Best regards,
Sebastian


Sebastian Ueckert, MSc, PhD student
---
Pharmacometrics Research Group,
Department of Pharmaceutical Biosciences, Uppsala University
---
P.O. Box 591
SE-751 24 Uppsala
Sweden
---
sebastian.ueck...@farmbio.uu.se
---
Work:   +46-(0)18-471 4437



On Thu, Feb 23, 2012 at 2:50 PM, Elisabet Størset
 wrote:
> Dear nonmemusers
>
>
> In my PK modeling project, a drug (elimination: 100 % hepatic 
> metabolism) is given orally twice daily over a period of 10 weeks. 100 
> subjec