Generalized Mantel-Haenszel estimators for K 2 x J tables

Area of Science:

• Biostatistics
• Statistical Modeling
• Categorical Data Analysis

Background:

• The Mantel-Haenszel method is a standard for estimating odds ratios in stratified tables.
• Extending Mantel-Haenszel to log-linear models for multi-dimensional tables (2 x J x K) presents statistical challenges.
• Existing generalizations of the Mantel-Haenszel estimator for K tables require robust variance estimation.

Purpose of the Study:

• To develop and present variance and covariance estimators for generalized Mantel-Haenszel estimators in K 2 x J tables.
• To ensure these new estimators are dually consistent, meaning they are reliable under both large strata and sparse data conditions.
• To compare the statistical efficiency of these generalized Mantel-Haenszel estimators.

Main Methods:

• Building upon the extension of Mantel-Haenszel estimation to log-linear models by Mickey and Elashoff (1985).
• Derivation of novel variance and covariance estimators for two generalized Mantel-Haenszel odds ratio estimators.
• Assessment of dual consistency (large strata and sparse data) and comparative efficiency analysis.

Main Results:

• The paper successfully provides variance and covariance estimators for generalized Mantel-Haenszel estimators.
• These estimators are demonstrated to be dually consistent, enhancing their applicability.
• Efficiency comparisons highlight the performance characteristics of the generalized estimators.

Conclusions:

• The developed estimators offer a statistically sound method for analyzing odds ratios in complex, multi-dimensional contingency tables.
• Dual consistency ensures the reliability of these estimators across various data scenarios, including sparse data.
• The findings contribute to more robust statistical inference in categorical data analysis.