A mixed Bell regression model for overdispersed medical count data.

Area of Science:

• Statistics
• Biostatistics
• Health Data Analysis

Background:

• Traditional mixed-effects models are widely used for count response variables.
• Existing models may have limitations in capturing specific data characteristics.
• The discrete Bell distribution presents an opportunity for developing novel regression approaches.

Purpose of the Study:

• Introduce a novel mixed-effects regression model based on the discrete Bell distribution.
• Evaluate the performance of frequentist and Bayesian inference approaches for this new model.
• Compare the proposed model with existing alternatives like Poisson and Poisson inverse Gaussian mixed-effects models.

Main Methods:

• Development of a mixed-effects regression model utilizing the discrete Bell distribution.
• Application of both frequentist and Bayesian statistical frameworks for parameter estimation.
• Monte Carlo simulation studies to assess parameter estimation accuracy and model comparison criteria performance.
• Empirical analysis using two real-world health datasets.

Main Results:

• Simulation experiments demonstrated the effectiveness of both frequentist and Bayesian approaches in parameter estimation.
• Model comparison criteria showed reliable performance in simulations.
• Real data applications indicated the proposed mixed-effects Bell regression model is a competitive alternative.
• The new model showed potential advantages over Poisson and Poisson inverse Gaussian mixed-effects models in specific applications.

Conclusions:

• The discrete Bell mixed-effects regression model is a viable and potentially advantageous alternative for count data analysis.
• Frequentist and Bayesian inference methods are suitable for this new class of models.
• The model shows promise for applications in health data and other fields dealing with count variables.