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An EM Algorithm for Fitting a 4-Parameter Logistic Model to Binary Dose-Response Data.

Gregg E Dinse1

  • 1Biostatistics Branch, National Institute of Environmental Health Sciences, Mail Drop A3-03, P.O. Box 12233, Research Triangle Park, NC 27709 USA dinse@niehs.nih.gov.

Journal of Agricultural, Biological, and Environmental Statistics
|July 20, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces an EM algorithm for fitting the 4-parameter logistic (Hill) model to binary dose-response data. This method simplifies analysis for biological and environmental scientists, offering computational advantages.

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Area of Science:

  • Biological Sciences
  • Environmental Sciences
  • Toxicology
  • Biostatistics

Background:

  • Binary dose-response data analysis is crucial in biological and environmental sciences.
  • The 4-parameter logistic (Hill) model offers a flexible nonlinear approach for such data.
  • Existing methods for fitting the Hill model can be computationally intensive.

Purpose of the Study:

  • To develop an efficient algorithm for maximum likelihood estimation (MLE) of the Hill model parameters.
  • To provide a computationally appealing and programmable method for analyzing binary dose-response data.
  • To illustrate the algorithm's utility with a toxicology study on selenium's effect on fly mortality.

Main Methods:

  • Development of an Expectation-Maximization (EM) algorithm for MLE under the Hill model.
  • Conceptualizing the Hill model as a mixture of subpopulations with varying response behaviors.
  • The EM algorithm decomposes the problem into two independent 2-parameter optimizations.

Main Results:

  • The EM algorithm provides a computationally efficient alternative to simultaneous four-parameter optimization.
  • This approach facilitates the estimation of covariances, incorporation of predictors, and imposition of constraints.
  • The algorithm is demonstrated effectively using toxicology data on insect mortality rates.

Conclusions:

  • The developed EM algorithm offers a practical and computationally advantageous method for fitting the Hill model to binary dose-response data.
  • This technique is broadly applicable across biological, environmental, medical, and agricultural research fields.
  • Computer code is available to facilitate implementation and further research.