Is it possible to perform Abbott's correction before smooth the data using the PAVA algorithm?

[lijuanyanbasf]

Dear Brenton,

I got two questions here:

First of all, in tsk::tsk(), you smooth the data (of course only when the data do not show monotonically increasing trend) before doing the Abbott's correction of the control response (when control response is not 0). Shouldn't the Abbott's correction be done before smoothing?

In tsk::tsk(), smoothing using gpava() will sometimes result in a smoothed control p different from the original control p.

# Correct for the control dose.
  data.smoothed$p <- (data.smoothed$p-control)/(1-control)

Then you correct the smoothed data with the original control p based on Abbott's formula. It will not normalize the smoothed corrected control p to 0, likely leading to biases in the results.

Secondly, in the ecotoxicology::TSK(), after Abbott's correction, sample size (n) for all groups is also corrected to n_i_-r[1], where ni is the sample size of each test group, r[1] is the number of original control response. I am not sure if it is correct to do this sample size correction, but would like to hear your opinion. Thank you very much!

[brsr]

The results of this function match those published by Hamilton et al, and those of the DOS program published by the EPA. Hamilton et al didn't publish any test cases with fatalities at r[1]. I don't have that paper on hand to check which order they specify. The developer of the ecotoxicology package is a lot more active in R than I am, so I'd trust what he's doing.