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Median Effective Dose

  1. Jen-pei Liu1,
  2. Shein-chung Chow2

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a06017

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Liu, J.-p. and Chow, S.-c. 2005. Median Effective Dose. Encyclopedia of Biostatistics. 5.

Author Information

  1. 1

    National Cheng-kung University, Taiwan, Republic of China

  2. 2

    Millennium Pharmaceuticals Inc., Cambridge, MA, USA

Publication History

  1. Published Online: 15 JUL 2005


The median effective dose (MED) is the median of the tolerance distribution of the dose levels for a stimulus that generates, on average, predefined responses in 50% of experimental units. The median effective dose is usually denoted as ED50. An overview of the design and analysis for inference about ED50 is provided. First, two commonly employed tolerance distributions—normal and logistic distributions—are introduced to characterize the relationship between the dose and response. Under a location/scale model for the tolerance distribution, estimation procedures for ED50 are reviewed. Interval estimation methods include delta method, the Fieller's theorem, likelihood approach, and Bayesian procedures. The difficulties associated with interval estimation by the Fieller's theorem and likelihood method are addressed. Inference procedures for ED50 are also summarized for the situations where (a) the underlying population consists of a mixture of homogeneous subpopulation, (b) the responses of individual experimental units are dependent, and (c) responses are observed at some prespecified time points. Nonparametric methods such as Spearman–Kärber estimators as well as other robust procedures are reviewed. An account of different nonsequential designs for MED under various optimality conditions is given. Finally, a brief summary of sequential procedures and designs is provided.


  • median effective dose;
  • tolerance distribution;
  • quantal responses;
  • interval estimation;
  • robust methods;
  • study design;
  • sequential procedures