From: Eyas Abu-Raddad <RADDADE@mail.rx.uga.edu>

Subject: Unreasonable VSS estimate

Date: Mon, 07 May 2001 15:44:17 GMT

Dear NONMEM users,

I am trying to fit a 2-compartment model with first order absorption (ADVAN4 TRANS3) to IV and PO data (4-10 points from each of 10 rats in a cross over study). The IV data clearly show biphasic decline of the compound, but the first phase is usually very short, with only 1 to 3 points. PO data show flip flop kinetics (terminal half life after PO is longer than after IV).If I do not specify an upper bound, the estimate for Vss that I got is unreasonably high (about 30 times what I obtained from SHAM (noncompartmental) analysis). If I specify a reasonable upper bound, the estimate is always equal to the upper bound, no matter what the initial estimate is. The same problem persisted when only intravenous data were used for fitting.

Any suggestions are appreciated.

Eyas AbuRaddad

University of Georgia

From: Bachman, William <bachmanw@globomax.com>

Subject: RE: Unreasonable VSS estimate

Date: Mon, 7 May 2001 13:34:56 -0400

Try constraining your parameters (not the values of the parameters). This is probably easiest if you use TRANS5. Decide the order of the magnitudes of the exponentials (KA, ALPHA, BETA) that you think is correct and then define the parameters in terms of increments of the other parameters. e.g. if you think KA <ALPHA < BETA then.

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

ALPHA=KA+THETA(2)*EXP(ETA(2))

BETA=ALPHA+THETA(3)*EXP(ETA(3))

William J. Bachman, Ph.D.

GloboMax LLC

7250 Parkway Dr., Suite 430

Hanover, MD 21076

Voice (410) 782-2212

FAX (410) 712-0737

bachmanw@globomax.com

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

Subject: RE: Unreasonable VSS estimate

Date: Mon, 7 May 2001 13:52:23 -0400

If you follow Bill's suggestion, I would rather use

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

ALPHA=(THETA(1)+THETA(2) )*EXP(ETA(2))

BETA=(THETA(1)+THETA(2)+THETA(3))*EXP(ETA(3))

(and restrict THETAs from below by zeros).

Leonid Gibiansky

From: Bachman, William <bachmanw@globomax.com>

Subject: RE: Unreasonable VSS estimate

Date: Mon, 7 May 2001 14:07:29 -0400

Your parameterization would also have a more straight forward interpretation of the etas.

Bill

From: "HUTMACHER, MATTHEW [Non-Pharmacia/1825]" <matthew.hutmacher@pharmacia.com>

Subject: RE: Unreasonable VSS estimate

Date: Mon, 7 May 2001 13:31:40 -0500

Please note that Leonid's parameterization does not insure that an individual will have ka>alpha>beta, whereas Bill's does. Leonid's parameterization does insure that the typical individual will have ka>alpha>beta.

Matt

From: =?utf-8?B?R2liaWFuc2t5LCBMZW9uaWQ=?= <gibianskyl@globomax.com>

Subject: =?utf-8?B?UkU6IFVucmVhc29uYWJsZSBWU1MgZXN0aW1hdGU=?=

Date: Mon, 7 May 2001 14:59:27 -0400

Yes, that is true. But with the parameterization

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

ALPHA=KA+THETA(2)*EXP(ETA(2))

BETA=ALPHA+THETA(3)*EXP(ETA(3))

you may have strongly correlated ETAs, and this correlation will be an artifact of the parameterization. Moreover, if you rewrite it as

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

ALPHA=THETA(1)*EXP(ETA(1))+THETA(2)*EXP(ETA(2))

BETA=THETA(1)*EXP(ETA(1)) +THETA(2)*EXP(ETA(2))+THETA(3)*EXP(ETA(3))

you will see that it will be hard to interpret the meaning of ETA2 and ETA3. Also, absorption often is not well-defined, with large OMEGA. With the parameterization above, you will have all three ETAs poorly defined in this case.

As to the individual estimates, population inequality should "provide support" to the corresponding inequalities on the individual's level. Flip-flop kinetics results from the identifiability problem, when you do not have any means to distinguish between the exponent terms in the equation. Population inequality will most likely remove this problem.

Leonid

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

Subject: Re: Unreasonable VSS estimate

Date: Tue, 08 May 2001 08:02:21 +1200

The suggestions from Bill and Leonid seem to be focussing on a different question from the one that was asked. I personally prefer not to use the physiologically uninterpretable alpha, beta parameterization and the original question asked about VSS.

The original question was based on the assumption that if a SHAM estimate of Vss was different from a NONMEM estimate then the NONMEM estimate was unreasonable.

Estimation of VSS using SHAM requires an assumption about the input function i.e. the mean absorption time has to be assumed. How was this done for the oral data?

SHAM methods typically assume homoscedasticity (additive residual error model). What residual error model was used with NONMEM? If a constant CV (proportional error model was used then more emphasis would be given to the later observations when using NONMEM and it is these values that critically influence the estimate of VSS. A mixed additive and proportional error model in NONMEM may be appropriate although there is not really much data to obtain precise estimates.

Finally, and perhaps most importantly, what did the fits look like? Did you get good individual predictions? Did the typical value predicted curves scatter themselves more or less at random around the individual value predicted curves? If the predictions are good from NONMEM and the purpose of doing the modelling is to make concentration predictions in these rats then it really doesnt matter what the estimate of VSS happens to be.

Nick

--

Nick Holford, Divn Pharmacology & Clinical Pharmacology

University of Auckland, 85 Park Rd, 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: "Bachman, William" <bachmanw@globomax.com>

Subject: RE: Unreasonable VSS estimate

Date: Mon, 7 May 2001 17:01:57 -0400

Not being of the same philosophical bent that you are, Nick, Leonid and I just cut to the chase. :)

As I read it, the question was "are there any suggestions?". Because, the likely problem is the flip-flop business, we suggested solutions that circumvent this problem. Once one has a model that gives a reasonable answer, even if it uses a less than easy interpretation, you can reparameterize the model anyway you like (once you've determined the situation that was causing the problem). The ADVAN5 parameterization just makes the best mathematical sense in this case.

Your other points re: goodness of fit and value of Vss are well taken.

Bill

From: "Eyas Abu-Raddad" <raddade@mail.rx.uga.edu>

Subject: RE: Unreasonable VSS estimate

Date: Tue, 8 May 2001 01:59:54 -0400

All suggestions were valuable, some were more than what I asked for. Thanks for all.

The problem was, actually, NOT with the flip flop kinetics. I had a problem obtaining reasonable VSS estimates from intravenous (and oral) data. I mentioned flip-flop lest it had something to do with the poor estimate of VSS, which now I understand it could. The VSS estimates were drastically different from what I obtained from INTRAVENOUS data using the SHAM analysis. I agree with Nick that VSS estimation from oral data needs some assumption about absorption. Although fits with the drastically different VSS were good with regard to prediction of observation, this is not my ultimate goal of modeling. I am studying the pharmacokinetics of enantiomers of a compound after administration of pure enantiomers, and racemate. My basic question is whether there is a difference in PK parameters between the 2 enantiomers, and whether there is interaction between the enantiomers (by allowing enantiomers to have a different value of the parameters of interest, and so for enantiomer or racemate administration, and comparing fits and objective functions for those nested models). As a beginning, I wanted to fit each enantiomer's data alone.

For the records, it seems that according to Nick's suggestion, using a mixed residual error model (proportional and additive) stabilized the estimate of VSS to a reasonable value(yet a little different that SHAM value), with all other parameter estimates being acceptable and so were the scatters. :) Thanks, Nick! This was obtained using IV data only. Adding PO data complicated things, obviously because of the higher variability and seemingly erratic absorption. I had to fix disposition parameters to obtain good fits.

I would like to follow up with another question in my next email.

Regards,

Eyas