PharmPK Discussion - Sigmoid emax and the logistic CDF

• On 18 Mar 1996 at 09:50:24, "Nathan Leon Pace, M.D." (nlpace.-a-.bigpace.med.utah.edu) sent the message
  

  
  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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• On 19 Mar 1996 at 09:32:08, Chuanpu Hu (hu.aaa.or.Stanford.EDU) sent the message
  

  
  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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• On 22 Mar 1996 at 11:32:44, "Nathan Leon Pace, M.D." (nlpace.aaa.bigpace.med.utah.edu) sent the message
  

  
  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 Hu 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.
  ******
  
  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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• On 25 Mar 1996 at 09:44:46, Nick Holford (n.holford.-a-.auckland.ac.nz) sent the message
  

  
  > 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.-a-.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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• On 25 Mar 1996 at 09:44:52, "Vladimir Piotrovskij" (VPIOTROV.at.JANBELC1.SSW.JNJ.COM) sent the message
  

  
       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)
  
  

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