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I wish to get a better understanding of the development and relationship
of sigmoid emax modeling of quantal responses to the standard form
logistic CDF. Can anyone suggest a paper in a statistics journal?
Thanks,
Nathan Pace
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For quantal responses, logistic regression (using generalized linear
models) clearly has theoretical advantage. The standard reference on
generalized linear models is
McCullagh, P. and Nelder, J.A., Generalized linear models, 2nd ed.,
Chapman & Hall, New York, 1989.
I heard that some people may find it difficult to read, but I do not know
of anything easier.
Chuanpu
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My question to the list asked "I wish to get a better understanding of the
development
and relationship of sigmoid emax modeling of quantal responses to the
standard form
logistic CDF. Can anyone suggest a paper in a statistics journal?"
******
Chuanpu HuFor quantal responses, logistic regression (using generalized linear
models) clearly has theoretical advantage. The standard reference on
generalized linear models is
McCullagh, P. and Nelder, J.A., Generalized linear models, 2nd ed.,
Chapman & Hall, New York, 1989.
I heard that some people may find it difficult to read, but I do not know
of anything easier.
******
I have perused McCullagh and Nelder, ANALYSIS OF QUANTAL RESPONSE DATA by
BJT Morgan
(Chapman & Hall, New York, 1992), and CONTINUOUS UNIVARIATE DISTRIBUTIONS,
Vol 2, 2nd
edition by Johnson, Kotz, & Balakrishnan (John Wiley & Sons, New York 1995)
and can find
no mention of sigmoid emax models or any related CDFs.
In the new monograph NONLINEAR MODELS FOR REPEATED MEASUREMENT DATA by
Davidian &
Giltinan (Chapman & Hall, New York, 1995) it is mentioned on page 241 in a
chapter about
PK and PD analysis: "Derivation of a suitable PD model: unlike PK
modeling, this is
usually done in a somewhat empirical fashion. By far the most commonly
used model is
the so-called 'Emax' model, or some variation thereof..."
In my specialty (Anesthesiology) most PD papers report use of sigmoid emax
models.
With the extensive developments in logistic regression, why do PD
researchers continue
to use the sigmoid emax model - a technique which appears to not have the
same rigorous
theoretical foundation as logistic models?
Nathan Pace
University of Utah
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> With the extensive developments in logistic regression, why do PD
> researchers continue
> to use the sigmoid emax model - a technique which appears to not have the
> same rigorous
> theoretical foundation as logistic models?
FOr the usual purposes of pharmacodynamic models the logistic function
and the sigmoid emax model are simply different parameterisations of the
same model. IMHO the parameterisation of the sigmoid emax model (esp.
EC50) is more helpful in understanding what is being described.
I understand logistic regression to mean the use of the logistic
function aka the sigmoid emax model to predict the probabilility of an
event what e.g. as a function of conc or dose.
There is no reason to prefer the sigmoid emax model over the logistic
function because they are the same. Logistic regression is statistical
shorthand for a particular applicaton of these models.
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, Private Bag 92019, Auckland, New Zealand
email:n.holford.at.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html
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There may be theoretical advantages of logistic function over a
sigmoid Emax model, however, from the practical point of view no
significant difference can be seen, since, after elementary
transformations the sigmoid Emax equation
E=Emax.C**n/(C50**n+C**n)
is converted into:
ln(E/(Emax-E))=n.ln(C) - n.ln(C50)
PharmPK Discussion List Archive Index page
Copyright 1995-2005 David W. A. Bourne (david@boomer.org)