Confidence intervals for difference between two binomial proportions derived from logistic regression

Abstract

A common method of reporting the result of logistic regression is to provide an odds ratio and its corresponding confidence interval. The results of such statistical analyses cannot be further evaluated with respect to the consistency of confidence intervals between the odds ratio and the difference between proportions. In this paper, we propose a simple method to construct the confidence intervals for the difference between binomial proportions based on parameter estimates of logistic regression. Simulation results showed that the score-based confidence interval based on the sample marginal approach is a recommended method for sensitivity analysis in randomized clinical trials.

Keywords:

• Delta method
• Logistic model
• Population marginal approach
• Randomized clinical trials
• Risk difference
• Sample marginal approach

Acknowledgments

The authors thank the referees for their insightful comments.

Additional information

Funding

This research was partially supported by a Grant-in-Aid for Scientific Research (17K12649) from the Ministry of Education, Culture, Sports, Science and Technology of Japan.