Likelihood methods for binary responses of present components in a cluster.

Area of Science:

• Biostatistics
• Epidemiology
• Biomedical Data Analysis

Background:

• Clustered binary responses are common in biomedical studies, such as disease status.
• Varying cluster sizes occur due to absent components within clusters.
• Analyzing both component presence and disease status requires specialized statistical approaches.

Purpose of the Study:

• To propose a novel two-stage random effects logistic regression framework for clustered binary responses with varying cluster sizes.
• To ensure interpretable regression effects for both component presence/absence and disease status.
• To provide a robust and efficient statistical methodology for complex biomedical data.

Main Methods:

• Developed a two-stage random effects logistic regression model.
• Utilized maximum likelihood estimation, implementable with standard statistical software.
• Conducted simulation studies to assess robustness and compare finite-sample performance with existing methods.
• Applied the methodology to analyze periodontal health in a diabetic Gullah population.

Main Results:

• The proposed framework maintains approximate logistic regression forms for marginal and conditional probabilities, enhancing interpretability.
• Simulation studies demonstrated the procedure's robustness to misspecification of random effects distributions.
• The method showed competitive finite-sample performance compared to existing techniques.

Conclusions:

• The novel two-stage random effects logistic regression framework offers a flexible and interpretable approach for analyzing clustered binary data with variable cluster sizes.
• The methodology is well-suited for complex biomedical research, as demonstrated by its application to periodontal health in a specific population.
• The statistical approach provides a valuable tool for researchers dealing with similar data structures in public health and clinical studies.