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inverse prediction and Poisson regression

Vincent Philion 
Hello to all, I'm a biologist trying to tackle a "fish" (Poisson Regression) which is just too big for my modest understanding of stats!!!

Here goes...

I want to find good literature or proper mathematical procedure to calculate a confidence interval for an inverse prediction of a Poisson regression using R. 

I'm currently trying to analyse a "dose-response" experiment. 

I want to calculate the dose (X) for 50% inhibition of a biological response (Y). My "response" is a "count" data that fits a Poisson distribution perfectly. 

I could make my life easy and calculate: "dose response/control response" = % of total response... and then use logistic regression, but somehow, that doesn't sound right.
 
Should I just stick to logistic regression and go on with my life? Can I be cured of this paranoia?
;-)

I thought a Poisson regression would be more appropriate, but I don't know how to "properly" calculate the dose equivalent to 50% inhibition. i/e confidence intervals, etc on the "X" = dose. Basically an "inverse" prediction problem.

By the way, my data is "graphically" linear for Log(Y) = log(X) where Y is counts and X is dose.

I use a Poisson regression to fit my dose-response experiment by EXCLUDING the response for dose = 0, because of log(0)

Under "R" =
(that's why you see the "dose[-1]" term. The "first" dose in the dose vector is 0. 

This is really a nice fit. I can obtain a nice slope (B) and intercept (A):

log(Y) = B log(x) + A

I do have a biological value for dose = 0 from my "control". i/e Ymax = some number with a Poisson error again

So, what I want is EC50x :

Y/Ymax = 0.5 = exp(B log(EC50x) + A) / Ymax

exp((log(0.5) + Log(Ymax)) - A)/B) = EC50x

That's all fine, except I don't have a clue on how to calculate the confidence intervals of EC50x or even if I can model this inverse prediction with a Poisson regression. In OLS linear regression, fitting X based on Y is not a good idea because of the way OLS calculates the slope and intercept. Is the same problem found in GLM/Poisson regression? Moreover, I also have a Poisson error on Ymax that I would have to consider, right?

Help!!!!

Thread (13 messages)

Vincent Philion inverse prediction and Poisson regression Jul 24 Spencer Graves inverse prediction and Poisson regression Jul 24 Vincent Philion inverse prediction and Poisson regression Jul 24 Brian Ripley inverse prediction and Poisson regression Jul 24 Spencer Graves inverse prediction and Poisson regression Jul 25 Peter Dalgaard inverse prediction and Poisson regression Jul 25 Vincent Philion inverse prediction and Poisson regression Jul 25 Vincent Philion inverse prediction and Poisson regression Jul 25 Brian Ripley inverse prediction and Poisson regression Jul 25 Spencer Graves inverse prediction and Poisson regression Jul 25 Vincent Philion inverse prediction and Poisson regression Jul 25 Vincent Philion inverse prediction and Poisson regression Jul 25 Spencer Graves inverse prediction and Poisson regression Jul 25