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Related Experiment Videos

Estimation methods for the join distribution of repeated binary observations

S R Lipsitz1, G M Fitzmaurice, L Sleeper

  • 1Department of Biostatistics, Harvard School of Public Health, Boston, Massachusetts 02115, USA.

Biometrics
|June 1, 1995
PubMed
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This study introduces the Bahadur representation for analyzing repeated binary observations, linking marginal probabilities to covariates. It also addresses estimating the probability of an event occurring at least once across multiple measures.

Area of Science:

  • Statistics
  • Biostatistics
  • Longitudinal Data Analysis

Background:

  • Repeated binary observations follow a multinomial distribution.
  • The Bahadur representation (1961) and Cox's method (1972) model these joint distributions.
  • Interest lies in both marginal probabilities and the probability of an event occurring across repeated measures.

Purpose of the Study:

  • To utilize the Bahadur representation for modeling joint distributions of repeated binary data.
  • To relate marginal probabilities of success to covariates using logistic or other link functions.
  • To estimate the probability of an event occurring at least once in a series of observations.

Main Methods:

  • Employing the Bahadur representation to link marginal probabilities with covariates.

Related Experiment Videos

  • Utilizing logistic link functions for marginal regression models.
  • Estimating parameters of the Bahadur model, including those for union probabilities.

    • Main Results:

    • The Bahadur representation allows for the specification of joint distributions of repeated binary outcomes.
    • Marginal probabilities can be modeled using covariates and link functions.
    • Union probabilities can be derived from joint probabilities and higher-order correlations.

    Conclusions:

    • The Bahadur model provides a flexible framework for analyzing longitudinal binary data.
    • Methods for estimating model parameters are discussed, enabling insights into both individual and combined event probabilities.
    • This approach is applicable to various fields, such as public health studies like the Six Cities study.