- On 26 Sep 2000 at 13:17:07, "Ronald Li" (RCLi.aaa.war.wyeth.com) sent the message

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The following equation represents the stimulation of output of

response (R) in the family of indirect response models proposed by

Jusko:

dR/dt=kin - kout * (1+((Emax*Cp)/(EC50 +Cp)))* R

where kin is defined as the zero order input rate constant, kout is

the first output rate constant, Emax is the maximal effect, EC50 is

the concentration producing 50% of maximal effect, and Cp is plasma

concentration.

Although this may sound silly, Emax should be unitless in order to

balance the equation. If so, what is the physiological meaning of

Emax and is there a constraint in its direction (+ or - ) and

magnitude? - On 27 Sep 2000 at 10:38:04, Thierry Buclin (Thierry.Buclin.-at-.chuv.hospvd.ch) sent the message

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Ronald,

In the parametrization proposed by Jusko :

dR/dt=kin - kout * (1+((Emax*Cp)/(EC50 +Cp)))* R

one plus the expression for Effect ((Emax*Cp)/(EC50 +Cp))is a

multiplicator of kout. This means that in the absence of any effect

(at Cp=0), kout is at its basal value (kout*1), and at maximal effect

(at Cp >> EC50), kout reaches the value kout*(1+Emax). So Emax is the

maximal percent increase attainable with the drug. Therefore it is

unitless : an Emax of 0.7 simply means that the drug is able, at very

high concentration, to increase the elimination of the Response

marker by 70%. A negative Emax is equivalent to the indirect model of

inhibition of the output response.

Hope this helps

Thierry BUCLIN, MD

Division of Clinical Pharmacology

University Hospital CHUV - Beaumont 633

CH 1011 Lausanne - SWITZERLAND

Tel: +41 21 314 42 61 - Fax: +41 21 314 42 66 - On 27 Sep 2000 at 10:38:45, "Jogarao Gobburu 301-594-5354 FAX 301-480-3212" (GOBBURUJ.aaa.cder.fda.gov) sent the message

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Hello,

1. You are right, Emax in the equation you specified is unitless. It

is define as the maximal 'FRACTION' stimulation in the bio-flux (kin or

kout). For eg: Emax=0.6 implies 60% increase in the kout from basal

value.

2. The constraint in the direction is imposed by the mechanistic basis

of the model. If you believe that insulin indeed stimulates glucose

metabolism then you would constrain the value of Emax to be greater than

zero. But for this particular model there is no upper bound. The

equation (or the modeler!) fails otherwise, in the sense that it means a

different mechanism (inhibition of kout).

3. To avoid confusion, some researchers prefer to use the terms Smax

and Imax for maximal stimulation and inhibition, respectively.

Regards,

Joga Gobburu

Pharmacometrics,

CDER, FDA. - On 27 Sep 2000 at 21:10:58, "David W Boulton" (boultond.at.musc.edu) sent the message

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This is a good question. I am currently working on something similar

and have struck the same problem.

Intuitively, you would think changing the ..... kout(1+ ... to

......kout(1-.... might account for negative changes from baseline,

but it doesn't solve the units problem.

Would the equation work if you convert your data to ratios - ie

Rt/Rt=0? This would also solve the units problem and as ratios the

data would be readily interpreted. You could also model responses

that fall below baseline which would be a fraction of Rt=0. The

problem comes with PD responses that start at 0.

I hope you get some useful responses

Best wishes

Dave

Dave Boulton, Ph.D. M.P.S.

Assistant Director

Laboratory of Drug Disposition and Pharmacogenetics

Department of Psychiatry and Behavioral Science

Medical University of South Carolina

67 President Street, P.O. Box 250861

Charleston, SC 29425

Ph: (843) 792 5589 Fax: (843) 792 7260

--F77C9A9.B4D5F55C-- - On 28 Sep 2000 at 10:22:28, "Jogarao Gobburu 301-594-5354 FAX 301-480-3212" (GOBBURUJ.-a-.cder.fda.gov) sent the message

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Hello,

1. Data transformation is not recommended. It confounds the

interpretation of the results and further, modeling all the data, as is,

is more efficient. Particularly data transformation affects aspects

related to understanding of disease progression, time course of drug

effects, and handling missing data (and others).

2. The physiologic interpretation power of the formation and

dissipation rates is lost if the response modeled is a ratio (unitless).

3. The fact that some individuals may have lower than baseline values

after drug treatment, even though mechanism dictates otherwise, has to

do with factors such as possible biorhythms and/or just variability! It

is case-specific. But this is not a unique problem with the indirect

response models. The way we should/handle the data is identical

irrespective of the PD model/mechanism.

Regards,

Joga Gobburu

Pharmacometrics,

CDER, FDA. - On 29 Sep 2000 at 11:56:46, ml11439.at.goodnet.com sent the message

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Ron,

I can see that this indirect pharmacologic response model

is completely different from the direct Emax model, as defined

in textbooks:

dR/dt=kin - kout * (1+((Emax*Cp)/(EC50 +Cp)))* R

The (1+E) term changes the mathematical meaning of the Emax

equation(E).

In the kinetics of direct pharmacologic response, the

Emax term is simply the maximum response when C approaches

infinity(1-4). So that in the Emax model, the response would

approach Emax as the concentration greatly exceeds EC50:

E= [EmaxC]/[EC50 +C]

The units of Emax would be determined by the nature

of the pharmacologic response. For example, in one study

regarding midazolam, the pharmacologic response was the

change over baseline in the EEG activity in the 13-30HZ

range. The Emax in this study was calculated to be a

21.2% change in baseline EEG activity(4). However, the Emax

could also be fraction in this case as well, if the

response is modeled as a measurable fraction of something.

Mike Leibold, PharmD, RPh

ML11439.aaa.goodnet.com

References

1) Gibaldi, M., Perrier, D., Pharmacokinetics, New York, Marcel Dekker

1975

2) Gibaldi, M., Perrier, D., Pharmacokinetics 2nd ed, New York, Marcel Dekker

1982

3) Wagner, J., Fundamentals of Clinical Pharmacokinetics, Hamilton, Drug

Intelligence Publications 1975

4) Wagner, J.G., Pharmacokinetics for the Pharmaceutical Scientist, Lancaster,

Technomic Publishing Co 1993 - On 30 Sep 2000 at 09:30:27, ml11439.aaa.goodnet.com sent the message

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Ron,

The indirect pharmacologic response model of Jusko

is similar to a Emax model with a baseline(5):

E= EmaxC/[EC50+ C] + Eo

The inhibitory version is:

E= Eo - EmaxC/[IC50+C]

Eo= baseline effect

The form of the above equation can be changed to:

E= Eo*[Emax'C/[EC50+C] +1]

Where Emax'= Emax/Eo

In this case, the Emax' term would be a multiple of Eo, the

basline response. This form is similar to the Jusko equation, and

might explain the units of Emax:

dR/dt=kin - kout * (1+((Emax*Cp)/(EC50 +Cp)))* R

The Emax baseline model could also be modeled as occurring in an

effect compartment, in which case the concentration term would

represent the concentration in the effect compartment(1-5). This

differential equation is:

dCe/dt= K1eCp - KeoCe

Mike Leibold, PharmD, RPh

ML11439.aaa.goodnet.com

References

1) Gibaldi, M., Perrier, D., Pharmacokinetics, New York, Marcel Dekker

1975

2) Gibaldi, M., Perrier, D., Pharmacokinetics 2nd ed, New York, Marcel Dekker

1982

3) Wagner, J., Fundamentals of Clinical Pharmacokinetics, Hamilton, Drug

Intelligence Publications 1975

4) Wagner, J.G., Pharmacokinetics for the Pharmaceutical Scientist, Lancaster,

Technomic Publishing Co 1993

5) Holford, H.G., Sheiner, L.B., Understanding the dose-effect relationship:

clinical application of pharmacokinetic-pharmacodynamic models, Clinical

Pharmcokinetics 1981;6:429-453 - On 2 Oct 2000 at 15:09:28, Janusz Byczkowski (janusz.byczkowski.-a-.usa.net) sent the message

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"David W Boulton"

Re: Indirect Response Model

Wrote:

>"...Would the equation work if you convert your data to ratios - ie

Rt/Rt=0? This would also solve the units problem and as ratios the

data would be readily interpreted...">

David:

As far as I know,

Rt/Rt=1

always!

Am I missing something?

Janusz Z. Byczkowski, Ph.D.,D.Sc.,D.A.B.T.

Consultant

212 N. Central Ave.

Fairborn, OH 45324

voice (937)878-5531

office (614)644-3070

confidential fax (603)590-1960

e-mail januszb.aaa.AOL.com

homepage: http://members.aol.com/JanuszB/index.html

JZB Consulting web site: http://members.delphi.com/januszb/

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