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


From   "Austin Nichols" <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: nl -choice between alternative parametrisations of sigmoid models
Date   Thu, 25 Oct 2007 12:03:26 -0400

Rosy--
I haven't used -nl- in a while, but it seems to me that a model like
y= b0 + b1/(1 + exp(-b2*(x-b3))) +error
where b2>0 can be written
y= b0 + b1/(1 + exp(-b^2*(x-b3))) +error
with new parameter b, and b2=b^2 has to be positive.

On 10/25/07, Rosy Reynolds <rr@dandr.demon.co.uk> wrote:
> Hello,
> I am fitting 4-parameter logistic (sigmoid Emax) dose-response models using
> the built-in -log4- feature of -nl-.
>
> The model is  y= b0 + b1/(1 + exp(-b2*(x-b3))) + error
> and the coefficients can be interpreted as
> b0 = baseline outcome
> b1 = Emax i.e. largest change from baseline
> b2 = Hill or slope coefficient
> b3 = ED50 i.e. value of x (dose) required to produce half-maximal effect,
>
> The same curve can actually be produced with two different sets of these
> parameters.
> In one set, the Hill slope b2 is positive and the other parameters
> intuitively have the interpretations above.
> 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.
> For ease of interpretation, I would prefer the set with positive b2.
> I can push -nl- into doing that by supplying carefully chosen starting
> values close to the desired coefficients. I could even run -nl- , manipulate
> the coefficients it obtains, and use those as starting values. That would
> always work, I suppose, but it seems long-winded.
>
> Please could you tell me an easier way to make -nl- parametrise the model in
> the preferred way, if you know of one? I haven't found anything about it in
> the manual.
> Thanks for thinking about this.
>
> best wishes
> Rosy Reynolds
> BSAC Resistance Surveillance Co-ordinator
> www.bsacsurv.org
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