A new and improved confidence interval for the Mantel-Haenszel risk difference

Area of Science:

• Biostatistics
• Clinical Trials Methodology
• Epidemiology

Background:

• The Mantel-Haenszel estimator is widely used for analyzing stratified 2×2 tables.
• Existing confidence intervals for the common risk difference can be suboptimal in various common scenarios.
• There is a need for improved confidence intervals that perform well across diverse data characteristics.

Purpose of the Study:

• To develop and evaluate an improved confidence interval for the common risk difference in stratified 2×2 tables.
• To compare the performance of the new interval against existing methods.
• To introduce a score-type interval incorporating strata weights.

Main Methods:

• Derivation of a new confidence interval by inverting a test based on the Mantel-Haenszel variance under homogeneity.
• Evaluation of the proposed interval's performance across various scenarios, including small/large strata, unbalanced allocation, and rare events.
• Development of a score-type confidence interval for weighted analyses.

Main Results:

• The proposed confidence interval demonstrates superior performance compared to existing intervals.
• The new interval is robust across a wide range of common scenarios in stratified trials and meta-analyses.
• The interval is available in a simple closed-form formula and applicable to matched pairs data.

Conclusions:

• The new confidence interval offers a significant improvement for estimating common risk differences in stratified data.
• The interval's simplicity, wide applicability, and strong performance make it a valuable tool for researchers.
• The study provides practical methods and reproducible code for enhanced statistical analysis in clinical research.