A Comparison of Some Approximate Confidence Intervals for a Single Proportion for Clustered Binary Outcome Data

Area of Science:

• Biostatistics
• Medical Statistics
• Epidemiology

Background:

• Accurate interval estimation of proportion parameters is crucial for binary outcome data in cluster studies.
• Existing methods for complex survey data and extensions of standard techniques may have limitations.

Purpose of the Study:

• To propose and evaluate novel interval estimation methods for proportion parameters in cluster studies.
• To compare the performance of proposed methods against existing approaches using simulation and real-world data.

Main Methods:

• Development of two new interval estimation approaches: profile likelihood and Wilson score.
• Comparison with established methods including complex survey data techniques, generalized estimating equations, and Rao and Scott ratio estimators.
• Extensive simulation studies to assess coverage and expected lengths.

Main Results:

• The proposed profile likelihood and Wilson score methods demonstrate competitive or superior performance.
• Evaluation metrics include statistical coverage and expected interval lengths across various parameter combinations.
• Biomedical data applications illustrate the practical utility of the new methods.

Conclusions:

• The profile likelihood and Wilson score methods provide reliable interval estimation for cluster study proportions.
• These methods enhance the analysis of binary outcome data in biomedical research.
• The findings support the adoption of these improved techniques in biostatistical practice.