On Fri, 25 Jul 2003, Vincent Philion wrote:

> Hello and thank you for your interest in this problem. 
> 
> "real life data" would look like this:
> 
> x     y
> 0             28
> 0.03          21
> 0.1           11
> 0.3           15
> 1             5
> 3             4
> 10            1
> 30            0
> 100           0
> 
> x     y
> 0     30
> 0.0025        30
> 0.02  25
> 0.16  25
> 1.28  10
> 10.24 0
> 81.92 0
> 
> X     Y
> 0     35
> 0.00025       23
> 0.002 14
> 0.016 6
> 0.128 5
> 1.024 3
> 8.192 2 
> 
> X     Y
> 0  43
> 0.00025  35
> 0.002  20
> 0.016  16
> 0.128  11
> 1.024  6
> 8.192   0 
> 
> Where X is dose and Y is response. 
> the relation is linear for log(response) = b log(dose) + intercept

Is that log(*mean* response), that is a log link and exponential decay 
with dose?

> Response for dose 0 is a "control" = Ymax. So, What I want is the dose
> for 50% response. For instance, in example 1:
> 
> Ymax = 28 (this is also an observation with Poisson error)

Once you observe Ymax, Y is no longer Poisson.

> So I want dose for response = 14 = approx. 0.3

What exactly is Ymax?  Is it the response at dose 0?  The mean response at
dose 0?  The largest response?  About the only thing I can actually
interpret is that you want to fit a curve of mean response vs dose, and
find the dose at which the mean response is half of that at dose 0.
That one is easy.

I think you are confusing response with mean response, and we can't 
disentangle them for you.

-- 
Brian D. Ripley,                  [EMAIL PROTECTED]
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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