The Mantel-Haenszel procedure revisited: models and generalizations

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Traditional methods for adjusting odds ratios, like binary logistic regression, lack symmetry in handling dichotomous variables (X and Y).
• The standard Mantel-Haenszel method is limited to discrete confounders and lacks a clear statistical model basis.
• Existing methods struggle with continuous or vector-valued confounders (Z).

Purpose of the Study:

• To propose an extension of the Mantel-Haenszel method applicable to continuous and vector-valued confounders (Z).
• To develop a symmetrical statistical approach for odds ratio adjustment.
• To introduce a method with a basis in statistical models, specifically the multinomial logistic model.

Main Methods:

• Revisiting the Mantel-Haenszel method and extending it by replacing observed cell entries with subject-specific classification probabilities.
• Utilizing the multinomial logistic model for situations requiring symmetrical treatment of variables X and Y.
• Proposing methods to test the homogeneity hypothesis, where the odds ratio is independent of confounder Z.

Main Results:

• The extended Mantel-Haenszel method provides a symmetrical adjustment for odds ratios with continuous confounders.
• Under the homogeneity hypothesis, the logarithm of the odds ratio estimator is a linear combination of multinomial logistic model parameters.
• The proposed method demonstrates a clear relationship with binary logistic regression.

Conclusions:

• The extended Mantel-Haenszel method offers a statistically grounded and symmetrical alternative for odds ratio adjustment, especially with continuous confounders.
• The multinomial logistic model provides a framework for symmetrical analysis and hypothesis testing.
• This approach enhances the utility of the Mantel-Haenszel method in complex epidemiological and statistical analyses.