Conditional and Unconditional Tests (and Sample Size) Based on Multiple Comparisons for Stratified 2 × 2 Tables

Area of Science:

• Biostatistics
• Statistical Methods
• Epidemiology

Background:

• The Mantel-Haenszel test is a common asymptotic test for stratified 2x2 tables.
• Existing tests like Mantel-Haenszel and Birch's exact test can yield results incompatible with stratum-specific tests.
• This incompatibility poses a challenge in the analysis of stratified categorical data.

Purpose of the Study:

• To introduce novel multiple comparisons (MC) methods for analyzing stratified 2x2 tables.
• To provide an alternative to the Mantel-Haenszel and Birch tests that avoids result incompatibility.
• To develop unconditional statistical approaches for stratified data analysis and propose sample size calculations.

Main Methods:

• Development and application of a multiple comparisons (MC) method for global tests on stratified 2x2 tables.
• Refinement of the MC method into the MCB method to create an alternative to existing tests.
• Exploration of unconditional statistical viewpoints for stratified data analysis.

Main Results:

• The proposed MC and MCB methods ensure compatibility between global and stratum-specific test results.
• These new methods can be applied from an unconditional perspective, a novel approach for this problem.
• Sample size calculation methods are also proposed for the new MC and MCB procedures.

Conclusions:

• The MC and MCB methods provide a statistically compatible and unconditional alternative for analyzing stratified 2x2 tables.
• These methods overcome the limitations of traditional Mantel-Haenszel and Birch tests.
• The developed approaches enhance the reliability of statistical inference in stratified analyses.