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Tree-structured logistic models for over-dispersed binomial data with application to modeling developmental effects

H Ahn1, J J Chen

  • 1Department of Applied Mathematics and Statistics, State University of New York at Stony Brook 11794-3600, USA.

Biometrics
|June 1, 1997
PubMed
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This study introduces tree-structured logistic regression for over-dispersed binomial data, offering a novel method to analyze relationships between binomial responses and explanatory variables like malformation incidence and dose.

Area of Science:

  • Biostatistics
  • Statistical modeling
  • Toxicology

Background:

  • Over-dispersed binomial data present challenges for standard logistic regression.
  • Understanding dose-response relationships is crucial in toxicological studies.

Purpose of the Study:

  • To propose and evaluate a tree-structured logistic regression model for over-dispersed binomial data.
  • To explore the relationship between malformation incidence, dose, and fetal weight in developmental toxicology.

Main Methods:

  • Recursive partitioning using statistical tests and residual analysis.
  • Cross-validation with a deviance function as the splitting criterion.
  • A nested grid algorithm for estimating bootstrap parameters.
  • Conditional Gaussian chain model to account for covariates.

Related Experiment Videos

Main Results:

  • The proposed regression tree procedure effectively models complex relationships in binomial data.
  • The method was successfully applied to analyze malformation incidence in a developmental toxicology experiment.
  • The conditional Gaussian chain model appropriately handled the influence of fetal weight on dose-response.

Conclusions:

  • Tree-structured logistic regression offers a powerful new approach for analyzing over-dispersed binomial data.
  • This methodology enhances the exploration of biological and toxicological relationships.
  • The study demonstrates the utility of the proposed model in real-world toxicological research.