The Talk Contains a Short Presentation of the Task Arising from The

Abstract:

The talk contains a short presentation of the task arising from the

project requirements for a customer from the chemical industry, a

description of the theoretical statistical solution, a description of

the SAS software development and a short showcase of the application via

a Java interface.

The concerned task is to estimate the effective dose at 50% response

(ED50) and other corresponding measures (slope, confidence intervals

etc.) given measured S-shaped dose-response samples from chemical and

biological data. Real data dose-response curves do not always fulfill

the requirements for a successful typical sigmoidal curve fit. The

problems appear when measuring an improper dose range, when not having

enough measurements or when the response is not sigmoidal at all. These

problems get even higher when wishing to automatically fit the

estimation process for huge database amounts of different dose-response

curves. Therefore, we establish a package of representative sigmoidal

models used usually in the chemical, biological and medical research:

The two, three and four parametric logistic function, the GLM with

normal link, the Gompertz function and the Brain-Cousens five parametric

logistic function. The parameters of the three and four logistic

functions represent the ED50, the slope of the curve at ED50, the

asymptotic maximum and/or minimum of the fit. The fifth parameter of the

Brain-Cousens function expresses a linear shift on the dose scale and is

used in the research of some special types of dose-response curves. Here

it can happen that for small doses the compound of interest has the

adverse effect resulting in response values above the level of the

control group. The parameters of the two parametric logistic, GLM with

normal link and Gompertz models cannot be directly interpreted in terms

of ED50 or slope. We fit for a dose-response sample these models and

setup a filter for deciding upon the best of fit: First we drop the fits

for which the algorithm did not converge. Secondly, for the remaining

fits, we calculate the Akaike measure and the slightly for small samples

adapted Akaike measure and decide for the best-of-fit by using the

Akaike criterion. If the result consists of two fits with the same

Akaike measure, we decide for the fit giving the smaller confidence

intervals for the ED50. Using this best-of-fit model we deliver the

estimators for the desired ED50, slope, confidence intervals and other

doses determined by the inverse of the fit at certain responses.