Equal-tailed confidence intervals for comparison of rates

Area of Science:

• Biostatistics
• Statistical Inference
• Epidemiology

Background:

• Existing methods for confidence intervals of rate differences, rate ratios, and odds ratios often exhibit systematic bias.
• This bias affects one-sided coverage and can lead to inflated Type I error rates in hypothesis testing for binomial and Poisson rates.
• Skewness-corrected asymptotic score methods show promise for binomial proportions but require extension to other scenarios.

Purpose of the Study:

• To introduce novel skewness corrections for Poisson incidence rates and odds ratios, including stratified analyses.
• To evaluate the performance of these new methods against existing alternatives using graphical comparisons.
• To provide robust statistical methods for the analysis of rates, particularly in challenging situations like small sample sizes or rare events.

Main Methods:

• Development of skewness-corrected asymptotic score methods for Poisson rates and odds ratios.
• Introduction of a novel stratified score method based on the t-distribution for fixed and random effects meta-analysis.
• Utilized a novel weighting scheme for improved meta-analysis performance compared to methods relying on crude stratum variance estimation.
• Graphical methods were employed to compare the performance of proposed intervals against selected alternatives.

Main Results:

• Skewness-corrected methods demonstrate superior equal-tailed coverage properties for binomial and Poisson cases.
• The proposed methods perform favorably across various situations, including small sample sizes and rare events.
• The stratified method shows excellent coverage properties for fixed-effects analysis.
• The new t-distribution-based stratified score method improves upon conventional meta-analysis techniques.

Conclusions:

• Skewness correction is essential for accurate analysis of rate ratios.
• The developed methods are robust and suitable for a wide range of applications in rate analysis.
• The novel stratified score method offers an improved approach for meta-analysis of rates.