What is the Mantel Haenszel method?

The Mantel-Haenszel method is a statistical technique used to analyze stratified data and assess the association between two categorical variables while controlling for a third confounding variable. It is particularly useful in epidemiological studies where researchers are interested in the relationship between an exposure and an outcome, but there are concerns about the potential influence of confounding factors.

The method was developed independently by Nathan Mantel and William Haenszel in the 1950s. It has since become a fundamental tool in the analysis of stratified case-control and cohort studies.

### Key Features of the Mantel-Haenszel Method


1. Stratification: The data is divided into strata based on the confounding variable. This allows for the analysis of the association between exposure and outcome within each stratum, which can help to control for the confounding effect.


2. Dichotomous Variables: The method is typically applied when both the outcome and the exposure are binary (e.g., present/absent, yes/no).


3. Common Odds Ratio: The Mantel-Haenszel method estimates a common odds ratio across strata, which represents the association between exposure and outcome, adjusted for the confounder.


4. Mantel-Haenszel Chi-Square Test: This test is used to determine if the odds ratio is significantly different from 1, indicating a significant association between exposure and outcome.


5. Breslow-Day Test: An extension of the Mantel-Haenszel method, the Breslow-Day test assesses whether the odds ratios are homogeneous across strata, which would suggest that a common odds ratio is appropriate.

### Steps in Applying the Mantel-Haenszel Method


1. Stratify the Data: Organize the data into groups based on the confounding variable.


2. Calculate the Odds Ratios: For each stratum, calculate the odds ratio of the exposure given the outcome.


3. Estimate the Common Odds Ratio: Using the odds ratios from each stratum, estimate the overall common odds ratio.

4. **Perform the Mantel-Haenszel Chi-Square Test**: This will test the null hypothesis that the common odds ratio is equal to 1.


5. Assess Homogeneity: Optionally, use the Breslow-Day test to check for homogeneity of odds ratios across strata.

### Example

Suppose we are studying the relationship between smoking (exposure) and lung cancer (outcome), with a focus on different age groups (strata). We might find that within each age group, smokers have a higher odds of developing lung cancer. The Mantel-Haenszel method would allow us to estimate the overall effect of smoking on lung cancer risk, taking into account the different age distributions across the groups.

### Limitations

While the Mantel-Haenszel method is powerful, it does have limitations. It assumes that the confounding effect is the same across strata, which may not always be the case. Additionally, the method may be less reliable with small sample sizes or when there is a high degree of stratification.

### Conclusion

The Mantel-Haenszel method is a valuable tool for epidemiologists and statisticians when analyzing the relationship between exposure and outcome in the presence of confounding variables. It provides a way to estimate the effect of exposure on outcome while accounting for the influence of confounders, leading to more accurate and reliable conclusions in health research.

The Cochran-Mantel-Haenszel method is a technique that generates an estimate of an association between an exposure and an outcome after adjusting for or taking into account confounding. The method is used with a dichotomous outcome variable and a dichotomous risk factor.Jun 3, 2016