st: nl -choice between alternative parametrisations of sigmoid models

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

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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