A note on effective sample size for constructing confidence intervals for the difference of two proportions

Area of Science:

• Biostatistics
• Clinical Trials
• Longitudinal Data Analysis

Background:

• Proportion differences are key for binary outcome clinical trials.
• Logit-based models (logistic regression, GEE, GLMM) analyze adjusted effects but yield log-odds ratios, not proportion differences.
• Existing two-step methods for proportion difference confidence intervals lack performance evaluation.

Purpose of the Study:

• To investigate the performance of a two-step method for proportion difference confidence intervals.
• To propose an adjusted effective sample size formula for improved interval accuracy.
• To evaluate the modified method's coverage properties via simulations.

Main Methods:

• Examined properties of the existing two-step method for confidence interval calculation.
• Developed an adjusted effective sample size formula using Bayesian information theory.
• Conducted simulation studies to assess the performance of the modified method.

Main Results:

• The two-step method's performance was evaluated.
• A modified effective sample size formula was proposed and tested.
• Simulations demonstrated that the adjusted effective sample size improves confidence interval coverage.

Conclusions:

• The proposed adjustment to the effective sample size formula enhances the accuracy of confidence intervals for proportion differences.
• This modified approach offers improved treatment effect estimation in clinical trials with binary outcomes.
• The findings support the use of the adjusted method for more reliable statistical inference.