- On 24 Sep 2004 at 14:43:41, "Gordi, Toufigh" (Toufigh.Gordi.at.cvt.com) sent the message

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Dear all,

Many concentration-effect relations can be described by a Hill equation

(E = Emax*C/(EC50+C)) or various versions of it. The way I understand

it, one needs to have good data on all parts of the effect vs.

concentration data in order to get reliable estimates of the model.

This means that we need to get the system to true maximum effects,

where increasing concentrations does not change the magnitude of the

effect significantly. If I remember correctly, reaching anything but

over 90-95% of the maximum effect has a significant influence,

resulting in biased estimates.

My question is: what to do when it is physiologically impossible to get

to the maximum effect? If the effect is, let's say, increase in heart

rate, it cannot go beyond 170-180. Is there any "smart" way of applying

a Hill function to these type of data and get reliable estimates?

Reference to publications are highly appreciated.

Best regards,

Toufigh Gordi - On 25 Sep 2004 at 10:53:19, Nick Holford (n.holford.aaa.auckland.ac.nz) sent the message

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Toufigh,

A more robust parameterization of the sigmoid Emax model was described

by Bill Bachman and Bill Gillepie in a poster at the ASCPT meeting in

1998. Its probably in the Feb 1998 issue fo CPT but I don't have that

handy to check.

Bachmann WJ, Gillespie WR. =93TRUNCATED SIGMOID Emax MODELS=94: A

REPARAMETERIZATION OF THE

SIGMOID EMAX MODEL FOR USE WITH TRUNCATED PK/PD DATA. Clinical

Pharmacology & Therapeutics 1998.

EE0+(Beta^Hill+1)*(Estar - E0)*C^Hill/(Cstar^Hill + Beta^Hill*C^Hill)

The idea is to fix an effect, Estar, which is included in the actual

range of effect observations e.g. close to the maximum actually

observed, and then estimate two parameters, Beta and Cstar. Beta is

simply Cstar/EC50 while Cstar is a parameter defining the conc (C) that

produces the chosen effect, Estar.

The EC50 and Emax can be derived from the final estimates as follows:

Emax(1+Beta^Hill)/Beta^Hill*(Estar-E0)

EC50Cstar/Beta

They concluded "The sigmoid Beta parameterization improved parameter

estimation

characteristics only. It does not offer any advantages for predicting

values

outside the range of observations."

Nick

--

Nick Holford, Dept Pharmacology & Clinical Pharmacology

University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New

Zealand

email:n.holford.aaa.auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556

http://www.health.auckland.ac.nz/pharmacology/staff/nholford/ - On 27 Sep 2004 at 12:47:09, kim.travis.-a-.syngenta.com sent the message

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Re-parameterising a model to give stable parameter estimates is an

underused

technique, perhaps because it is seen as something of a black art.

Gavin

Ross's book "Nonlinear estimation" (Springer-Verlag, 1990) is unusual in

covering it in some detail. Gavin's advice to me was to choose

parameters

which you could see in your dataset, ie you should be able to estimate

the

parameters by eye from a plot of the data. The paper cited by Nick

effectively does this,

Regards,

Kim

[Sounds a little like ensuring identifiability - also

reparameterization should take into account incorporation of the error

structure in the original data - db]

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