Bayesian Analysis of Tweedie Compound Poisson Partial Linear Mixed Models with Nonignorable Missing Response and...

Area of Science:

• Statistics
• Biostatistics
• Longitudinal Data Analysis

Background:

• Longitudinal semicontinuous data present unique challenges, especially with nonignorable missing covariates and responses.
• Existing statistical models may not adequately address the complexities of such data structures.
• Bayesian methods offer a flexible framework for handling uncertainty and complex models.

Purpose of the Study:

• To propose a novel Bayesian Tweedie compound Poisson partial linear mixed model for longitudinal semicontinuous data.
• To develop a methodology that accounts for nonignorable missingness in both covariates and responses.
• To provide a robust framework for analyzing complex longitudinal data using P-spline approximations.

Main Methods:

• Utilizing a Bayesian P-spline approximation for nonparametric function estimation.
• Employing a logistic regression model to specify the missing response and covariate mechanisms.
• Implementing a hybrid algorithm combining Gibbs and Metropolis-Hastings samplers for parameter estimation.

Main Results:

• The proposed model successfully estimates unknown parameters, random effects, and nonparametric functions.
• Simulation studies demonstrate the effectiveness of the methodology in various scenarios.
• The approach is validated using real-world data from the Osteoarthritis Initiative.

Conclusions:

• The developed Bayesian Tweedie compound Poisson partial linear mixed model is a powerful tool for analyzing longitudinal semicontinuous data with complex missingness.
• The hybrid estimation algorithm provides reliable joint Bayesian estimates.
• The methodology offers significant advancements in statistical modeling for health-related longitudinal studies.