Confidence interval of the difference between two proportions with overdispersion

Area of Science:

• Biostatistics
• Statistical Inference
• Correlated Data Analysis

Background:

• Traditional confidence interval methods for comparing two proportions often fail under positive correlation, leading to undercoverage.
• Overdispersion due to positive correlations in sample data reduces the reliability of standard statistical inference.
• Accurate estimation is crucial for reliable conclusions in various scientific fields.

Purpose of the Study:

• To develop improved methods for confidence interval estimation of the difference between two proportions when data exhibit positive correlations.
• To address the undercoverage issue prevalent in existing methods for correlated data.
• To enhance the accuracy of statistical inference in the presence of overdispersion.

Main Methods:

• Proposed three novel asymptotic normality-based methods by incorporating the concept of effective sample size.
• Applied effective sample size adjustments to existing methods designed for independent data.
• Conducted an extensive Monte Carlo simulation study to evaluate method performance.

Main Results:

• The proposed methods demonstrated superior performance compared to the usual asymptotic normality-based method.
• Improved coverage rates were observed, particularly for moderate sample sizes.
• The new methods effectively mitigated the undercoverage problem caused by positive correlations.

Conclusions:

• The developed methods provide more reliable confidence intervals for the difference between two proportions in the presence of positive correlations.
• Effective sample size is a valuable concept for adapting independent data methods to correlated data scenarios.
• The findings offer practical improvements for statistical analysis in fields with correlated observational data.