MantelHaenszel

Mantel and Haenszel developed a statistical method for analyzing stratified categorical data. This approach, often referred to as the Mantel-Haenszel test or Mantel-Haenszel odds ratio, is particularly useful when researchers want to examine the association between an exposure and an outcome while controlling for one or more confounding variables. These confounding variables are typically categorical and are used to create strata or subgroups within the data.

The core idea is to compute a common odds ratio across these strata, assuming that the association between the exposure and outcome is homogeneous across the strata. If the assumption of homogeneity holds, the Mantel-Haenszel odds ratio provides an efficient estimate of the overall association, adjusted for the stratification variable. The method calculates a weighted average of the odds ratios from each stratum, with weights determined by the precision of each stratum's estimate.

A key feature of the Mantel-Haenszel method is its robustness. It does not require a specific distribution for the data and is effective even with small sample sizes within strata. The test can also be used to assess the statistical significance of the observed association, typically by comparing the Mantel-Haenszel odds ratio to a null value of 1. This method has found widespread application in fields such as epidemiology, medicine, and social sciences for its ability to provide adjusted estimates of association.