A generalized right truncated bivariate Poisson regression model with applications to health data

Area of Science:

• Biostatistics
• Health Economics
• Statistical Modeling

Background:

• Bivariate Poisson regression models are essential for analyzing count data with two variables.
• Existing models may not adequately capture the complexities of health-related count data, such as the number of health conditions and healthcare services utilized.
• Truncation in statistical models is crucial when dealing with data that has inherent limits.

Purpose of the Study:

• To propose a generalized right truncated bivariate Poisson regression model.
• To develop and illustrate estimation and goodness-of-fit tests for both truncated and untruncated bivariate Poisson regression models.
• To compare the performance of the truncated model against the untruncated model using real-world health data.

Main Methods:

• Development of a generalized right truncated bivariate Poisson regression model.
• Application of a marginal-conditional approach for estimation and hypothesis testing.
• Utilizing data from the Health and Retirement Study, focusing on health conditions and healthcare services.
• Implementing tests for goodness of fit, overdispersion, and underdispersion.
• Employing non-nested model comparison tests.

Main Results:

• The proposed test statistics are computationally straightforward.
• Both untruncated and right truncated bivariate Poisson regression models demonstrate a good fit to the Health and Retirement Study data.
• The right truncated bivariate Poisson regression model significantly outperforms the untruncated model in fitting the analyzed health data.

Conclusions:

• The generalized right truncated bivariate Poisson regression model provides a superior fit for analyzing bivariate count data, particularly in health-related studies.
• The developed estimation and testing procedures are practical and effective.
• The findings highlight the importance of considering truncation in statistical modeling for health economics and biostatistics applications.