Re: st: nl -choice between alternative parametrisations of sigmoid models

["Rosy Reynolds" <rr@dandr.demon.co.uk>]

Perfect! That deals with everything, including where to find the code 
for -log4-.
Yes, our dose-response curves are descending, unlike my synthetic example 
data. It makes sense to me (as well as Nick Holford) to think of inhibitory 
curves as having negative Emax. That's why I wanted the model to give me the 
coefficient set with negative Emax and positive Hill coefficient, rather 
than the alternative set with positive Emax and negative Hill which was 
what -nl log4- naturally produced.
I have a choice of ways forward now. I'll compare fitting the sigmoid Emax 
directly, using a little substitutable expression program to pick starting 
values, with the 4-parameter logistic, and compare also with results from 
other software that colleagues have used previously.
Thanks again to you, and everyone else who has contributed.
best wishes
Rosy

----- Original Message ----- 
From: "Joseph Coveney" <jcoveney@bigplanet.com>
To: "Statalist" <statalist@hsphsun2.harvard.edu>
Sent: Saturday, October 27, 2007 8:18 AM
Subject: Re: st: nl -choice between alternative parametrisations of sigmoid 
models



> Rosy Reynolds wrote (excerpted):
>
> In the other set, b2 is negative, the sign of b1 is reversed, and b0 
> becomes
> the outcome at infinitely high dose instead of at the lowest doses. The
> lowest-dose outcome is now given by b0+b1.
>
> With our data, -nl- naturally produces the set of coefficients with 
> negative
> b2.
>
> --------------------------------------------------------------------------------
>
> I wonder if your dose-response curve is descending (e.g., growth rate of a
> bacterium in presence of increasing concentrations of an antibiotic drug 
> to
> which it's susceptible).  If that's the case, then it explains
> why -nllog4.ado- sets up initial values that lead to what you've been
> seeing.  If it's the case, then you can reparameterize your model to
> accommodate that the response is inhibitory in nature.  Take a look at:
> www.boomer.org/pkin/PK01/PK2001138.html .  Scroll down about halfway, 
> where
> Nick Holford posts a reply.  The pertinent text includes,
>
> "The inhibitory sigmoid Emax model simply has a negative value for
> Emax but can also be written like this (the inhibitory fractional
> sigmoid Emax model):
> E = E0*(1 - Emax * C^Hill / (EC50^Hill + C^Hill))
> where Emax is now a (non-negative) fraction between 0 and 1. If
> Emax=1 then the response will be 0 at infinite C i.e. the drug
> produces complete inhibition of the response."
>
> On the otherhand, if your dose-response curve is ascending with
> homoscedastic errors as in the example do-files that you've posted, and if
> you set up your initial values with Emax >> Emin, Hill >=1 and any
> reasonable estimate for log ED50, then I can't imagine why -nl- would 
> wander
> off toward negative values for Hill coefficients with any dataset where 
> it's
> going to attain convergence with nonmissing coefficient standard errors.
> About the only other thought that occurs (other than imposing nonlinear
> constraints, as others have already suggested) would be to automatically
> calculate initial values:
>
> summarize response, meanonly
> local Emax = r(max)
> local E0 = r(min)
> summarize log_dose, meanonly
> local log_ED50 = r(mean)
> nl log4: . . . , initial(b0 `E0' b1 `Emax' b2 1 b3 `log_ED50')
>
> If your dose-response is descending (inhibitory) and you're using Nick
> Holford's suggestion to parameterize as an inhibitory fraction sigmoid 
> Emax
> model, then you'd set E0 to be r(max), and set Emax to be 1 - r(min) /
> r(max).  If the middle dose is always the same in your designed 
> experiments,
> then there's no need to go through the motions of -summarize log_dose- 
> each
> replicate to get an initial value.  Likewise, if you some prior knowledge
> that the Hill coefficient should be in the neighborhood of, say, 3, then
> that will be a better fixed initial value than 1.
>
> You might be able to accommodate zero doses by modifying the 
> four-parameter
> logistic model in the manner that Daniel Waxman suggests, i.e., set up an
> indicator variable for zero-valued doses, create a modified 
> logarithmically
> transformed dose variable that has nonmissing value (pick one arbitrarily)
> for observations at zero dose, and fit:
>
> nl (response = {Emin} * dose_is_zero_dummy + ///
>  {Emax} * (1 - dose_is_zero_dummy) / (1 + ///
>  exp({Hill} * ({ED50} - log_dose))), initial(. . .)
>
> I'm not sure that that would be my first choice over just using the
> conventional parameterization of the sigmoid Emax model, but it might be
> worth a try if you insist upon the four-parameter logistic.
>
> In your reply to Austin Nichols, you indicated a reluctance to choose
> starting values.  With nonlinear regression, you're liable to encounter a
> few occasions where you'll need to choose starting values manually.
>
> Joseph Coveney
>
>
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