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Markov counting models for correlated binary responses.

Forrest W Crawford1, Daniel Zelterman2

  • 1Yale School of Public Health, Biostatistics, PO Box 208034, New Haven, CT 06510, USA forrest.crawford@yale.edu.

Biostatistics (Oxford, England)
|March 21, 2015
PubMed
Summary
This summary is machine-generated.

We introduce continuous-time Markov counting processes for analyzing correlated binary data, generalizing existing models. This approach offers interpretable parameters and handles varying cluster sizes and ascertainment bias effectively.

Keywords:
Bernoulli trialsDevelopmental toxicityFamilial diseaseMarkov processTeratology

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Area of Science:

  • Statistics
  • Biostatistics
  • Epidemiology

Background:

  • Analyzing correlated binary data is crucial in various scientific fields.
  • Existing models for correlated outcomes have limitations in flexibility and interpretability.
  • There is a need for generalized models that accommodate diverse data structures and biases.

Purpose of the Study:

  • To propose a novel class of continuous-time Markov counting processes.
  • To establish a theoretical link between these processes and sums of exchangeable Bernoulli random variables.
  • To develop a flexible framework for analyzing correlated binary data with improved interpretability.

Main Methods:

  • Development of continuous-time Markov counting processes.
  • Establishing a correspondence with sums of exchangeable Bernoulli random variables.
  • Algorithms for computing maximum likelihood estimates.
  • Incorporation of cluster-specific covariates for regression analysis.

Main Results:

  • The proposed models generalize existing approaches for correlated outcomes.
  • The framework naturally incorporates ascertainment bias and allows for different cluster sizes.
  • New models for dependent outcomes were demonstrated.
  • Improved fits were observed on datasets from familial disease epidemiology and developmental toxicology.

Conclusions:

  • Continuous-time Markov counting processes provide a powerful and flexible tool for analyzing correlated binary data.
  • The developed methods offer enhanced interpretability and broader applicability compared to previous models.
  • The approach demonstrates practical utility in epidemiological and toxicological research.