Re: [R] inverse prediction and Poisson regression

[Spencer Graves]

	  1.  If you provide a toy data set with, e.g., 5 observations, to 
accompany your example, it would be much easier for people to try out 
ideas and then give you a more solid response.

	  2.  Have you tried something like log(dose+0.5) or I(log(dose+0.5)) 
in your model statement in conjunction with "predict" or "predict.glm" 
on the output from "glm"?

hope this helps.  spencer graves

Vincent Philion wrote:
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" = 


	glm.dose <- glm(response[-1] ~ log(dose[-1]),family=poisson())


(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!!!!


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