From: Quyen.Ho-Nguyen@serono.com

Subject: Bayesian estimation

Date: Fri, 29 Sep 2000 11:25:11 +0100

Dear NONMEM users,

We would like to obtain Bayesian estimation of PK parameters for each subject. In fact, I have a population 1 on which I performed population PK analysis and using the POSTHOC option I obtained the individual PK parameters for this Pop1. I have a Pop2 (concentration of the drug). Based on the fact that the PK of the drug is similar between Pop1 and Pop2, I would like to obtain the individual PK parameters (CL, V, etc...) for the Pop2, using information obtained in Pop1.

Has anybody already used this methodology using NONMEM (or another tool?).

thanks in advance for your help

Quyen Ho-Nguyen, Pharm D.

Serono International S.A

*****

From: "Jogarao Gobburu 301-594-5354 FAX 301-480-3212" <GOBBURUJ@cder.fda.gov>

Subject: Re: Bayesian estimation

Date: Fri, 29 Sep 2000 08:02:21 -0400 (EDT)

Hello,

Please find below a sample code that Dr.Diane Mould (major contributor), Dr.Holford and I have been using in our research. Essentially you need the population parameters from the pop1 and their respective posterior distributions (uncertainty). Typically the standard error estimates (from pop1) are employed to reflect uncertainty. For prior OMEGA you need to provide the degrees of freedom (see "dfCL", etc..)(according to inverse wishart distribution). Comments before each block of code should be helpful.

Diane/Nick: Please feel free to add to the comments.

Regards,

Joga Gobburu

Pharmacometrics,

CDER, FDA.

============================= BEGIN CTL ======

$PROBLEM Bayesian Estimation

$INPUT ID TIME AMT DV

$DATA ..\mydata.dat IGNORE=#

$SUB ADVAN2 TRANS2 PRIOR=..\prior.for

;Intial estimates for current data

$THETA (0,.976) ; CL

$THETA (0,10.4) ; V

$THETA (0,0.571) ; KA

$OMEGA 0.0663 ;cvcl

$OMEGA 0.0959 ;cvv

$OMEGA 0.2 ;cvka

$SIGMA (.11) ; cvcp

$SIGMA (.499) ; sdcp

;Prior normal mode for THETA

$THETA 0.976 FIX ; pcl

$THETA 10.4 FIX ;pv

$THETA 0.571 FIX ; pKA

$THETA 0.11 FIX ; pcvcp

$THETA 0.499 FIX ; psdcp

;Prior uncertainty on normal mode for THETA

;Covariance matrix after standard errors

$OMEGA BLOCK(8) FIX

.000838

.00165 .12

.000152 .000362 .00107

.0000583 -.00143 .000169 .00122

-.000003 -.0025 -.000001 .000131 .000478

;prior OMEGA

$OMEGA 0.0663 FIX ;pcvcl

$OMEGA 0.0959 FIX ;pcvv

$OMEGA 0.200 FIX ;pcvka

$THETA 99 FIX ; dfCL

$THETA 99 FIX ; dfV

$THETA 99 FIX ; dfKA

$PK

CL = THETA(1)*EXP(ETA(1))

V = THETA(2)*EXP(ETA(2))

KA = THETA(3)*EXP(ETA(3)))

S2 = V

$ERROR

Y = F*EXP(ERR(1))+ERR(2)

$EST METH=COND NOABORT POSTHOC

$TABLE ID TIME DV NOPRINT NOHEADER FILE=tsn.fit

======= END OF CTL =======

*****

From: "Gibiansky, Leonid" <gibianskyl@globomax.com>

Subject: RE: Bayesian estimation

Date: Fri, 29 Sep 2000 08:16:41 -0400

I think, a much simpler question was asked (Bayesian was the reference on the POSTHOC step). Definitely, the way described below is correct, but in the particular situation it may be sufficient to either

1. Fix population parameters to the values obtained for Pop1, and do POSTHOC for P2.

or

2. Combine Pop1 and Pop2, and re-estimate population and individual parameters.

If populations differ (and it can be observed if residuals or individual estimates differ between POP1 and Pop2), one can add STUDY covariate and try to account for the difference by allowing some population parameters differ between populations.

Leonid

*****

From: =?ISO-2022-JP?B?GyRCSj8yLCEhQDs8eRsoQg==?=<GCA02464@nifty.ne.jp>

Subject: RE:Bayesian estimation

Date: Fri, 29 Sep 2000 23:00:25 +0900

Quyen,

I asked similar question previously. The answer from Alison is in the NONMEM UsersNet Archive. (http://www.cognigencorp.com/nonmem/nm/99mar131997.html)

Masaki Hiraoka

*****

From: "Piotrovskij, Vladimir [JanBe]" <VPIOTROV@janbe.jnj.com>

Subject: RE: Bayesian estimation

Date: Fri, 29 Sep 2000 16:04:23 +0200

PRIOR is a nondocumented feature of NONMEM. Perhaps, someone from NONMEM project group or from Globomax could shed some light on it?

Best regards,

Vladimir

----------------------------------------------------------------------

Vladimir Piotrovsky, Ph.D.

Janssen Research Foundation

Human Pharmacokinetics (ext. 5463)

B-2340 Beerse

Belgium

Email: vpiotrov@janbe.jnj.com

*****

From: Lewis B Sheiner <lewis@c255.ucsf.edu>

Subject: Re: Bayesian estimation

Date: Fri, 29 Sep 2000 09:43:40 -0700

Joga is addressing a more subtle issue than I believe Dr. Ho-Nguyen intended. An adequate answer to the original question is the one Alison previously provided: put the "initial estimates" of all parameters to the estimates from pop1, and then run pop2 data with

$EST MAXEVAL=0 POSTHOC

This produces a Bayes estimate for each individual in pop2 CONDITIONAL on the model estimated from pop1 (i.e., as though pop1 was infinite and so the fitted model is the "true" model).

Joga's code, which involves an unsupported feature of NONMEM, and hence will not work with NONMEM V, attempts to find a Bayes estimate for the pop2 individuals that is unconditional; that is one which recognizes that the best fitting model to pop1 is not necessarily the "true" model.

Note that the usual posthoc estimates, for example those for pop1 obtained as part of the run that fit the model to pop1, are of the conditional type, not of the unconditional type. For consistency, then, it might be preferable to use the simpler approach, or to use the more complex approach on both pop1 and pop2 ...

As I said at the outset, this is a subtle issue, and if all that is rerquired is a reasonable set of estimates of the individual parameters in pop2, the simpler approach of conditioning on the model should suffice.

LBS.

--

_/ _/ _/_/ _/_/_/ _/_/_/ Lewis B Sheiner, MD (lewis@c255.ucsf.edu)

_/ _/ _/ _/_ _/_/ Professor: Lab. Med., Biophmct. Sci., Med.

_/ _/ _/ _/ _/ Box 0626, UCSF, SF, CA, 94143-0626

_/_/ _/_/ _/_/_/ _/ 415-476-1965 (v), 415-476-2796 (fax)

*****

From: Nick Holford <n.holford@auckland.ac.nz>

Subject: Re: Bayesian estimation

Date: Sat, 30 Sep 2000 10:43:17 +1200

Lewis,

Lewis Sheiner wrote:

>

> Joga's code, which involves an unsupported feature of NONMEM, and

> hence will not work with NONMEM V

I do not think this is correct. I am using a standard distribution of NONMEM V and the PRIOR feature appears to work but I have no direct way of checking on the correctness of the implementation. I understood from Stuart Beal that this is an implemented but undocumented and unsupported feature of NONMEM V. He is aware that I have used this feature in NONMEM V but has not told me that it does not work.

If you have reason to believe that the PRIOR feature as distributed in NONMEM V does not actually work then please let me know.

--

Nick Holford, Dept Pharmacology & Clinical Pharmacology

University of Auckland, Private Bag 92019, Auckland, New Zealand

email:n.holford@auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556

http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm

*****

From: Lewis B Sheiner <lewis@c255.ucsf.edu>

Subject: Re: Bayesian estimation

Date: Sat, 30 Sep 2000 08:47:05 -0700

My mistake, it is an unsupported feature of NONMEM V. Which means it is still experimental. As far as I know it works. Stu, I think, plans to elaborate on what an "unsupported feature" is in a note to nmusers.

L.

--

_/ _/ _/_/ _/_/_/ _/_/_/ Lewis B Sheiner, MD (lewis@c255.ucsf.edu)

_/ _/ _/ _/_ _/_/ Professor: Lab. Med., Biophmct. Sci., Med.

_/ _/ _/ _/ _/ Box 0626, UCSF, SF, CA, 94143-0626

_/_/ _/_/ _/_/_/ _/ 415-476-1965 (v), 415-476-2796 (fax)

*****

From: "S.Beal" <stuart@c255.ucsf.edu>

Date: Sat, 30 Sep 2000 09:33:25 -0700 (PDT)

Dear NM-Users:

I want, please, to briefly respond to a recent series of messages over the NM-Users Net, stemming from a question by Dr. Quyen Ho-Ngugen.

As has been pointed out already by Dr. Gibiansky and Dr. Sheiner, Dr. Gobburu seemed to have misunderstood the question. Also, Dr. Hiraoka has pointed to some useful earlier information (to be found on the NM-Users Archive) provided by Mrs. Boeckmann.

Dr. Gobburu's response, concerning the use of a user-routine called PRIOR (which is in fact not very relevant to Dr. Ho-Ngugen's question), prompted others to make comments concerning this routine. This in turn has prompted me to attempt to communicate the following policy statement.

The PRIOR routine is an unsupported feature of NONMEM Version V Level 1.1. No information concerning this feature or any other unsupported feature is available to the greater NONMEM user community from the NONMEM Project Group or from the NONMEM consult group at GloboMax. If you have heard about some feature, but it is not documented (a good place to look is in the Help Guide), the chances are that it is unsupported.

NONMEM contains some unsupported and undocumented features. This is done in part to allow us at the NPG to experiment with these features and learn about their use. As our understanding of a feature increases, we usually realize that the feature needs modification. Eventually we may come to feel that it should be made available to everyone in a future release, in some final, supported, and documented form. With other software, this type of "temporary feature" is found only in a beta version of the software. With NONMEM, on occasion we have embedded a temporary feature into our distributed version (currently NONMEM Version V Level 1.1). Perhaps this has not been a good idea, as it can lead to confusion. You may find someone using one of the temporary features in NONMEM Version V Level 1.1 (e.g. PRIOR). This person is either (a) someone working directly with Lewis Sheiner or myself and is helping us test the feature or (b) someone with whom we are not working but who has been able to obtain the help of a person of type (a). Anyone using a temporary feature is obviously running the risk that there is some problem with it, which will be readily discovered with further testing, or that the feature will not "look" or behave the same in a future release.

There are also beta versions of future releases. (The distribution of these is handled in a very restricted way; please do not inquire about them.) For those of you who might be using such a release, the chances are quite good that any temporary feature in NONMEM Version 5 Level 1.1 behaves differently with a beta version.

Stuart Beal

*****

From: "Stephen Duffull" <sduffull@pharmacy.uq.edu.au>

Subject: RE: Bayesian estimation

Date: Mon, 2 Oct 2000 09:02:41 +1000

Quyen,

> between Pop1 and Pop2, I

> would like to obtain the individual PK parameters

> (CL, V, etc...) for the

> Pop2, using information obtained in Pop1.

>

> Has anybody already used this methodology using

> NONMEM (or another tool?).

Another possibility is to use a program designed to perform Bayesian analysis such as WinBUGS or for a specific PK problem PKBUGS. These programs are currently free and are well documented.

Regards

Steve

=================

Stephen Duffull

School of Pharmacy

University of Queensland

Brisbane, QLD 4072

Australia

Ph +61 7 3365 8808

Fax +61 7 3365 1688

http://www.uq.edu.au/pharmacy/duffull.htm

*****

From: "Jogarao Gobburu 301-594-5354 FAX 301-480-3212" <GOBBURUJ@cder.fda.gov>

Subject: Bayesian Estimation

Date: Mon, 02 Oct 2000 09:27:12 -0400 (EDT)

Hello,

1. Thanks for the clarifications to the messages regarding the Bayesian estimation question.

2. I might have read too much into the question. There is no doubt that (as noted by Dr. Gibiansky and Dr. Sheiner) (1) Fixing the population estimates from pop1 to generate individual empirical bayesian parameter estimates of pop2 and (2) combining the 2 data sets (with probable inclusion of 'study' effect) to estimate the population parameters are simpler solutions to the question posed.

Regards,

Joga Gobburu

Pharmacometrics,

CDER, FDA.

*****

From: Quyen.Ho-Nguyen@serono.com

Subject: Bayesian estimation: a specific case

Date: Wed, 4 Oct 2000 13:58:25 +0100

Dear NONMEM users,

Thank you very much to all of you who took time to respond to my message. I understand better now... However, I am wondering if the solution suggested by most of you ("use the initial estimates of all parameters to the estimates from pop1 and then run pop2 data with $EST MAXEVAL=0 POSTHOC) is fully applicable in my case.

I need to better explain the circumstances of my problem. Pop1: 12 healthy subjects, 6 extravascular administrations, rich data including 10 blood samples (until 48 h post-dose) following the first administration, 10 blood samples following the last administration, and through concentrations (1 sample before each administration).The PK model is complicated (complicated input model) with 7 parameters in total to be estimated.

Pop2: 12 patients, 6 extravascular administrations, sparse data including 5 blood samples following the first administration, 5 blood samples following the 4th administration and through concentrations (1 sample before each administration). The PK developed in pop1 can not describe data of the study 2 (due to a low number of samples per subject in pop2).

By non compartmental approach, it "seems" that the PK between Pop1 and Pop2 are comparable (in terms of Cmax, AUC during the administration interval, Cthrough). The aim is to evaluate the total exposure (total AUC) of the patients in pop2. The question is: can I use the model of pop1to calculate the Posthoc PK (CL, V, etc...) of pop2? Is it relevant to apply the PK model found in Pop1 to the Pop2, even if data of Pop2 can not describe this model, due to a low number of samples per patient in Pop2 and to the complicated PK model ?

thank you for your feed back

best regards,

Quyen

*****

From: "Jogarao Gobburu 301-594-5354 FAX 301-480-3212" <GOBBURUJ@cder.fda.gov>

Subject: Re: Bayesian estimation: a specific case

Date: Wed, 04 Oct 2000 09:09:31 -0400 (EDT)

Hello,

1. I believe the suggestions offered earlier are valid ONLY if you do not have a priori expectations that PK-wise pop1 and pop2 are different. If you 'expect' that pop1,2 are different, your model is not complete.

2. Why not simply combine the 2 data sets and get the population parameters? Use a dummy variable to differentiate the two populations to start with, followed by a more mechanistic approach to explore 'relevant' prognostic factors (eg: variables reflecting renal/hepatic function etc..)

Regards,

Joga Gobburu

Pharmacometrics,

CDER, FDA.

*****

From: Pierre Maitre <maitre@cdg.ch>

Subject: Re: Bayesian estimation: a specific case

Date: Wed, 04 Oct 2000 21:29:05 +0200

Quyen.Ho-Nguyen@serono.com wrote:

>

> The question is: can I use the model of pop1 to calculate the Posthoc PK

> (CL, V, etc...) of pop2?

Sure, if

1) you believe that pop1 and pop2 are subgroups of the same population

2) the conditions and admistration scheme used in pop2 are not too different from thoses used in pop1

> Is it relevant to apply the PK model found in Pop1 to the Pop2,

> even if data of Pop2 can not describe this model, due to a low

> number of samples per patient in Pop2 and to the complicated PK model?

Yes, that's exactly the purpose of Bayesian regression.

Best regards

Pierre Maitre

*****

From: Mats Karlsson <Mats.Karlsson@biof.uu.se>

Subject: Re: Bayesian estimation: a specific case

Date: Thu, 05 Oct 2000 08:55:28 +0200

Dear Quyen,

I agree with what both Joga and Pierre writes. If you do use your model from Pop1 to obtain individual Bayes estimates of Pop2, then you should use a comparison of the individual estimates of Pop2 with the population parameters of pop1 as a diagnostic. If the individual estimates of a parameter in pop2 are not unbiased compared to the typical value of the parameter in the pop1 model, that is a sign that the two populations have different pharmacokinetics (and you can definately gain more information from doing what Joga suggests in 2 below). If the individual estimates of pop2 are not biased compared to parameters of the pop1 model, that is a sign of similarity between the two populations and/or lack of information in Pop2 about the parameter in question. If such lack of bias is true for all parameters, less is to be gained by combining the data sets.

Best regards,

Mats

--

Mats Karlsson, PhD

Professor of Biopharmaceutics and Pharmacokinetics

Div. of Biopharmaceutics and Pharmacokinetics

Dept of Pharmacy

Faculty of Pharmacy

Uppsala University

Box 580

SE-751 23 Uppsala

Sweden

phone +46 18 471 4105

fax +46 18 471 4003

mats.karlsson@biof.uu.se

*****

From: "Piotrovskij, Vladimir [JanBe]" <VPIOTROV@janbe.jnj.com>

Subject: RE: Bayesian estimation: a specific case

Date: Thu, 5 Oct 2000 10:03:18 +0200

Quyen,

I wonder how did you estimate interindividual variability in 7 parameters of your model having only 12 individuals?

Best regards,

Vladimir

----------------------------------------------------------------------

Vladimir Piotrovsky, Ph.D.

Janssen Research Foundation

Human Pharmacokinetics (ext. 5463)

B-2340 Beerse

Belgium

Email: vpiotrov@janbe.jnj.com

*****

From: Quyen.Ho-Nguyen@serono.com

Subject: RE: Bayesian estimation: a specific case

Date: Thu, 5 Oct 2000 10:46:36 +0100

In fact, I could estimate the inter-individual variability in only 3 parameters (CL, V and KA). It should be noted that we have a high number of parameters compared to the number of observations.

thanks for your question and kind regards,

Quyen