A note on posterior predictive checks to assess model fit for incomplete data.

Area of Science:

• Statistics
• Biostatistics
• Longitudinal Data Analysis

Background:

• Assessing model fit is crucial for incomplete longitudinal data.
• Existing methods may not fully address the complexities of missing data.
• Bayesian approaches offer flexible frameworks for longitudinal data analysis.

Purpose of the Study:

• To evaluate two posterior predictive distribution-based methods for model fit assessment in incomplete longitudinal data.
• To compare approaches using replicated complete data versus replicated observed data.
• To provide practical guidance for implementing these checks in statistical software.

Main Methods:

• Utilizing posterior predictive distributions for model fit assessment.
• Comparing a method based on replicated complete data (Gelman et al., 2005) with one based on replicated observed data.
• Applying analytic examples and real-world data from a longitudinal clinical trial.

Main Results:

• Demonstrated differences between the two posterior predictive approaches.
• Illustrated the application of both methods using a longitudinal clinical trial dataset.
• Confirmed the feasibility of implementation in standard Bayesian software (WinBUGS/JAGS/Stan).

Conclusions:

• Both posterior predictive distribution-based methods offer valuable tools for assessing model fit with incomplete longitudinal data.
• The choice between methods may depend on specific data characteristics and research questions.
• The proposed checks are readily implementable, enhancing their practical utility in research.