PROC PROBIT, correcting for control mortality, what is difference between optc and Abbott's formula?

[Perlid]

In the analysis of dose-response bioassay data (such as testing the effectiveness of an insecticide) it is usually necessary to adjust the response values to compensate for control mortality (aka natural mortality). One way this is done is by using Abbott's formula. 

In PROC PROBIT the optc option can be used to estimate and control for(?) the natural mortality.

However, it is unclear to me how optc differs from using Abbott's formula, which one is better to use, and if there are scenarios when one should be used over the other. (Using my own insecticide data, LC50 estimates are different when I use optc or Abbott's formula).

Furthermore, some published sources imply that they should be the same. 

In the textbook "Techniques in Aquatic Toxicology, Volume 1"
(edited by Gary K. Ostrander) it is stated that "...a continuous dose-response curve and 95% fiducial limits are generated using a probit procedure and SAS. The probit procedure corrects for control mortality (option c, optc) analogous to using Abbott's formula."

Can anyone provide a clear explanation (in layman's terms) how optc and Abbott's formula differ in adjusting for control mortality?

Any help would be appreciated.

thank you!

(Note: I am currently using SAS Studio, OnDemand for Academics)

[StatDave · Accepted solution]

They are the same thing in the sense that they both model Abbott's correction, probit[ (y-c)/(1-c) ], as a linear function of the predictors, where c is the natural threshold rate. See the Overview section of the PROBIT documentation. Details on the method are in the Finney reference in the PROBIT documentation. I am not sure if what you consider Abbott's formula estimates c in a particular way, but PROBIT estimates is along with the model parameters by maximum likelihood estimation. If what you are looking at estimates in some other way, then that would explain the difference you see. Note that if you estimate c by some other means, or have a prior estimate, you can specify it in PROBIT using the C= option. In that case, omit the OPTC option to avoid modifying the specified value.