# [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