[R] inverse prediction and Poisson regression
Prof Brian Ripley
ripley at stats.ox.ac.uk
Fri Jul 25 08:56:17 CEST 2003
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, ripley at stats.ox.ac.uk
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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