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Equivalency Between the Generalized Bivariate Bernoulli Model Dependency Test and a Logistic Regression Model With

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Statistics in Medicine
|September 8, 2025
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Summary
This summary is machine-generated.

A standard logistic regression model with an interaction term is equivalent to the Generalized Bivariate Bernoulli Model (GBBM) dependency test. This accessible alternative enhances the analysis of bivariate binary data in biomedical research.

Keywords:
dependency testlongitudinal binary endpoints generalized linear modelsrepeated measures

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Area of Science:

  • Biostatistics
  • Epidemiology
  • Health Services Research

Background:

  • Bivariate binary data, common in health research, are analyzed using the Generalized Bivariate Bernoulli Model (GBBM).
  • The GBBM allows for covariate-dependent association tests conditional on baseline outcomes but is underutilized due to lack of software implementation.
  • Previous comparisons of GBBM with regressive logistic regression have limitations.

Purpose of the Study:

  • To propose a standard logistic regression model with an interaction term as a practical alternative to the GBBM dependency test.
  • To demonstrate the equivalence of this logistic regression model to the GBBM approach.
  • To compare the power of the GBBM dependency test with alternative methods.

Main Methods:

  • A standard logistic regression model with an interaction term was proposed and validated conceptually, theoretically, and empirically.
  • Simulations compared the power and Type 1-error rates of the GBBM dependency test against: regressive logistic model, logistic regression with interaction, and Pearson Chi-square test.
  • The methods were applied to infant mortality data from the Bangladesh Demographic and Health Survey.

Main Results:

  • The logistic regression model with interaction demonstrates equivalent power and Type 1-error rates to the GBBM dependency test across various effect and sample sizes.
  • This equivalence contrasts with the performance of the regressive logistic regression model used in prior GBBM comparisons.
  • The proposed logistic regression model provides a more accessible and flexible approach for analyzing bivariate binary data.

Conclusions:

  • A standard logistic regression model with an interaction term serves as a practical and accessible alternative to the GBBM dependency test.
  • This finding enhances the utility of dependency analyses for bivariate binary outcomes in biomedical research.
  • The approach facilitates extensions to more complex longitudinal binary data structures.