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From |
"Rosy Reynolds" <rr@dandr.demon.co.uk> |

To |
"statalist" <statalist@hsphsun2.harvard.edu> |

Subject |
st: nl -choice between alternative parametrisations of sigmoid models |

Date |
Thu, 25 Oct 2007 16:41:04 +0100 |

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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**Follow-Ups**:**Re: st: nl -choice between alternative parametrisations of sigmoid models***From:*"Austin Nichols" <austinnichols@gmail.com>

**Re: st: nl -choice between alternative parametrisations of sigmoid models***From:*Steven Joel Hirsch Samuels <sjhsamuels@earthlink.net>

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