inverse prediction and Poisson regression
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