Back to the Top
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
Back to the Top
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/
Back to the Top
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]
PharmPK Discussion List Archive Index page
Copyright 1995-2010 David W. A. Bourne (david@boomer.org)