Standard Article

Quantal Response Models

  1. Byron J.T. Morgan

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a10050

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Morgan, B. J. 2005. Quantal Response Models. Encyclopedia of Biostatistics. 6.

Author Information

  1. University of Kent, Canterbury, UK

Publication History

  1. Published Online: 15 JUL 2005


In a quantal response experiment, a particular organism is selected and exposed in groups to different concentrations of a drug for a fixed time, and a discrete response is observed (such as death or survival). In the binary response case, a tolerance or threshold assumption yields a model for the probability of response at a particular dose that has the form of the cumulative distribution function of the tolerances. The median effective dose (ED50) is the dose level that results in an expected 50% response under certain model assumptions. The Spearman–Karber estimate is a nonparametric estimate of the ED50. This article also surveys parametric estimates, which can have improved precision. Parametric models are discussed, including extensions for polytomous responses and multivariate responses. Also discussed are the effect of overdispersion, and design issues such as sequential methods for finding the point at which a certain probability of response occurs.


  • beta-binomial distribution;
  • binary data;
  • logistic regression;
  • median effective dose;
  • ordered categorical data;
  • overdispersion;
  • probit analysis;
  • sequential methods;
  • Spearman–Karber estimate;
  • Weibull model