Score confidence intervals and sample sizes for stratified comparisons of binomial proportions

Area of Science:

• Biostatistics
• Epidemiology
• Clinical Trials

Background:

• Gart and Nam developed efficient score tests for stratified binomial proportion comparisons.
• Understanding of stratified score methods and their properties remains limited.

Purpose of the Study:

• To rederive efficient score tests and elucidate their relationship with contrast-based score tests.
• To adapt score methods using alternative weighting schemes and provide guidance for rare event analysis.
• To propose a framework for calculating power and sample size in various clinical trial designs.

Main Methods:

• Re-derivation of efficient score tests to reveal theoretical relationships.
• Exploration of score approach behavior with extreme outcomes.
• Development of a general framework for asymptotic power and sample size calculations.
• Description of a nearly exact power calculation procedure.

Main Results:

• The inverse variance weight is optimal for common treatment effects in large samples.
• Guidance is provided for choosing weights in rare event analysis.
• The score method is recommended for studies with a small number of moderate to large strata.
• A framework for power and sample size calculations in superiority, noninferiority, and equivalence trials is proposed.

Conclusions:

• The re-derivation provides a basis for adapting score methods with different weighting schemes.
• The proposed methods offer practical guidance for statistical analysis in stratified comparisons and clinical trials.
• The score method is a valuable tool for researchers analyzing stratified binomial proportions, especially in rare event scenarios.