Keywords: Effective dose, Mixed models, Nonlinear regression, Self starter functions, Sigmoidal models


Dose-response analysis is used extensively in applied research in biology, ecology, environmental sciences, medicine, pharmacology, toxicology, in the pharmaceutical industry, and in regulatory contexts for risk assessment.

Therefore, this turorial on dose-response analysis may be of interest to many R users from very different disciplines.


The aim of the tutorial is twofold:


Various commercial software packages, both large systems and small stand-alone programs, offer limited flexibility in how dose-response data may be modelled.

In contrast the R package “drc” and its sister package “medrc” for mixed-effects dose-response models provide a wide range of options for analysis of dose-response data.

The tutorial provides an overview of the wide range of functions and tools available within “drc” for carrying out dose-response analysis.

Special emphasis is placed on hands-on application using R together with real data examples without use of complex mathematical/statistical formulae.


  • General concepts of dose-response modelling will be introduced: linear vs. nonlinear models, commonly used sigmoidal model functions (e.g., log-logistic/Hill-slope models, Weibull models, hormesis models), derived parameters such as effective doses and relative potencies (approx. 1 hour).

  • Analysis of binary/binomial, continuous, count, and possibly event-time dose-response data will be demonstrated in detail. Salient aspects of the estimation procedure will be discussed (e.g., distributional assumptions) (approx. 1 hour).

  • More advanced concepts for handling multiple dose-response curves, including the use of sandwich variance estimators and nonlinear mixed-effects models, will also be covered (approx. 1 hour).


An elementary understanding of statistical concepts and some familiarity with R is a prerequisite. It is recommended that participants bring their own laptop with R already installed.

About instructors