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

Binary endpoints measured at two timepoints-such as pre- and post-treatment-are common in biomedical and healthcare research. The Generalized Bivariate Bernoulli Model (GBBM) provides a specialized framework for analyzing such bivariate binary data, allowing for formal tests of covariate-dependent associations conditional on baseline outcomes. Despite its potential utility, the GBBM remains underutilized due to the lack of direct implementation in standard statistical software. Moreover, we contend that the comparison made in the original publication between the GBBM dependency test and the regressive logistic regression model has shortcomings and does not provide an ideal basis for evaluating the model's performance.

In this paper, we propose a standard logistic regression model with an interaction term and demonstrate that it yields an equivalent dependency test to the GBBM approach. This equivalence is established conceptually, theoretically, and empirically. Extensive simulations compared the power of the GBBM dependency test with: (a) dependency test from the regressive logistic model; (b) test derived from the logistic regression model with interaction; and (c) the Pearson Chi-square test. We also applied these methods to infant mortality data from the Bangladesh Demographic and Health Survey (BDHS).

The power of the GBBM dependency test differs from the regressive logistic regression model used as a benchmark in the original paper that introduced the GBBM methodology. In contrast, the power and type 1-error rate of the GBBM dependency test and the logistic regression model with interaction described herein are equivalent across varying effect sizes and sample sizes.

Our work reveals that a widely available and flexible logistic regression model can serve as a practical alternative to the GBBM dependency test, enhancing accessibility for researchers. Moreover, this approach provides a foundation for extending dependency analyses to more complex longitudinal binary data structures, broadening its applicability in biomedical research.