[R] inverse prediction and Poisson regression

[Jim Rogers]

Vincent, 

As long as you are going to digest all those suggestions, let me offer
one more:

If you want to avoid making an assumption about the functional form of
the dose-response relationship (you don't even need to assume
monotonicity!), and also avoid having to trust the asymptotic
distributions of MLE's, a completely different approach is described in 

Stepwise Confidence Intervals without Mulitplicity Adjustment for Dose
Response and Toxicity Studies
Jason C. Hsu and Roger L. Berger 
June 99 issue of JASA

In your case, this approach would involve a pairwise test for each
positive dose population with the zero dose population (but without
multiplicity adjustment, even though you are doing multiple tests!). So
if you can pick a good test for comparing the means of two Poisson
distributions (I'm sure there are plenty, though I'm not sure what I
would recommend), then you can apply this method very easily. You lose
the power of "pooling" that comes with the assumption of a functional
relationship, but you may make up for this by getting more exact (not
asymptotic) confidence bounds (and it's always comforting to make fewer
assumptions). 

Just one more thing for you to stew on...

Happy thinking,
Jim Rogers 


> Hello to all: first and foremost: thank you for all this input. I only
discovered about "R" last week (!) and I think I will dump my SAS
license!!! 
> 
> 
> ;-) 
> 
> 
> This is a very dynamic listserve! 
> You "R" all great! Thank you! 
> 
> 
> I just hope some day I can help out a student the way you did today. 
> 
> 
> I will spend part of the weekend studying the different suggestions in
detail. Again, I'm not a stats person, so I will need some time and good
coffee to digest all this correctly. (I'm most worried about
understanding the nonlin suggestion.) Early next week, I will post a
"summary" of the suggestions and the path I chose to follow. (with
proper syntax Professor Ripley, I promise) 
> 
> 
> ;-) 
> 
> 
> Have a nice weekend 
> 
> 
> Best regards, 
> 
> 
> Vincent Philion 

James A. Rogers, Ph.D. <rogers at cantatapharm.com>
Statistical Scientist
Cantata Pharmaceuticals
300 Technology Square, 5th floor
Cambridge, MA  02139
617.225.9009 x312
Fax 617.225.9010