Augmented mixed models for clustered proportion data.

Area of Science:

• Biostatistics
• Biomedical Data Analysis
• Statistical Modeling

Background:

• Biomedical research frequently encounters clustered proportion data (0-1) for disease status.
• Standard regression models like beta regression are unsuitable for data with exact zeros or ones.
• Existing methods struggle to adequately model the full range of proportion responses in clustered populations.

Purpose of the Study:

• To develop a flexible statistical framework for analyzing clustered proportion data with values in the [0, 1] interval.
• To address the limitations of existing parametric models when dealing with boundary values (0 and 1).
• To provide a computationally convenient Bayesian approach for disease status analysis.

Main Methods:

• Introduction of a general proportion density augmented with probabilities for zero and one.
• Bayesian framework for regression analysis, incorporating clustering effects.
• Development of Bayesian case-deletion influence diagnostics using q-divergence measures from Markov chain Monte Carlo output.

Main Results:

• The proposed method effectively models clustered proportion data, including boundary values.
• The Bayesian approach provides a computationally convenient and flexible analysis framework.
• Influence diagnostics are readily obtainable from the MCMC output, aiding model assessment.

Conclusions:

• The novel Bayesian regression model offers a robust solution for analyzing clustered proportion data in biomedical research.
• The methodology accommodates the full range of proportion values, including zeros and ones, which are common in disease status studies.
• The approach is practical due to its computational convenience and integration with freeware, supported by effective influence diagnostics.