Negative binomial regression in dose-effect relationships

In many applied problems often there is a problem of constructing effective estimators of distribution function and the quantile function using both complete and incomplete samples. In the talk, we consider the problem of constructing estimators of the distribution function and studying their asymptotic behaviour using incomplete samples, namely, in the dose-effect relationships. The aim of our message is to both explain the general ideas behind some important parts of this estimation theory as well as actually construct usable optimal estimators for dose-response functions commonly applied in toxicology. Both binary and binomial regression models are used for this purpose (see [1-9]). Also we proposed to the negative binomial regression model.