The Mantel-Haenszel (MH) test
The Mantel-Haenszel (MH) test is a statistical test used to assess the association between two categorical variables while controlling for the effect of one or more confounding variables. It is commonly used in epidemiological studies to evaluate the risk of a disease or outcome in relation to an exposure, while adjusting for potential confounding factors.
Interpretation
Stratum 1 results
The results suggest that odds of outcome in the exposure positive group are 1.88 times the odds in the exposure negative group. Confidence interval indicates that we are 95% confident that the odds ratio in the population (from where the sample was obtained) would be between 0.59 and 5.93. However, since the odds ratio confidence interval includes the null value (i.e. 1), the association between exposure and outcome is not statistically significant at 5% level of significance, the conventionally used criterion to evaluate p-values. This is also evident from the p-value for this stratum which is not less than 0.05 (see the table of results above). Therefore, the odds ratio results should be interpreted with caution.
Stratum 2 results
Subjects in the exposure positive group have 1.25 times the odds of the outcome than those in the exposure negative group. We are 95% confident that the odds ratio in the population is between 0.61 and 2.57. However, the association between exposure and outcome is not statistically significant as the p-value for this stratum is not less than 0.05 and the confidence interval includes 1 (see the table of results above). Therefore, the results should be interpreted with caution.
Homogeneity of odds ratios
The p-value for the test of homogeneity (0.555) is not less than 0.05, the conventionally used criterion to evaluate p-values, suggesting that the stratified odds ratios are not significantly different. In other words, the stratifying variable does not modify the association between exposure and outcome and thus calculation of pooled or Mantel-Haenszel odds ratios is justified.
Note: Tests of homogeneity have low power and therefore may fail to reject homogeneity even when heterogeneity is present. Some authors recommend using a higher threshold for evaluating homogeneity p-values (e.g. 0.10 or even 0.20 instead of the conventional 0.05) when evaluating these tests. Please interpret your results taking this into consideration.
Mantel-Haenszel Results
The best estimate of Mantel-Haenszel adjusted odds ratio is 1.40 suggesting that exposure positive subjects have 1.40 times the odds of the outcome compared to exposure negative subjects, after adjusting or controlling for the stratifying variable . Significance of pooled odds ratios was tested by performing a Cochran-Mantel-Haenszel test. Consistent with the inclusion of the null value (i.e. 1) in the odds ratio confidence interval, the adjusted odds ratio is statistically non-significant (P-value: 0.275).
Note: Interpretation of results will also depend on your study design. For example, interpretation of odds ratios is different for case control and cross-sectional studies
Assumptions:
The exposure and outcome variables are categorical.
The confounding variables are categorical.
The assumption of non-interaction (i.e., the effect of the exposure on the outcome is the same across all levels of the confounding variables) must be met.
Formula:
The MH test statistic is calculated as:
MH = (∑(Oi - Ei))^2 / ∑Ei
Oi: Observed number of events in the ith stratum
Ei: Expected number of events in the ith stratum
Interpretation:
A statistically significant MH test result (p-value < 0.05) indicates that there is an association between the exposure and outcome, independent of the confounding variables.
A non-significant result suggests that there is no association between the exposure and outcome, or that the association is confounded by the controlled variables.
Advantages:
Controls for the effects of confounding variables, making it a more robust test for assessing associations.
Can be used with both matched and unmatched data.
Disadvantages:
Can be sensitive to the assumption of non-interaction.
May have low power if the number of strata or sample size is small.
Applications:
The MH test is widely used in epidemiology and other research fields to:
Evaluate the association between exposures (e.g., smoking) and outcomes (e.g., lung cancer) while controlling for potential confounders (e.g., age, socioeconomic status).
Assess the effectiveness of interventions (e.g., vaccines) by comparing the incidence of disease in intervention and control groups while adjusting for baseline differences.
Examine the association between genetic variants and disease risk while controlling for genetic ancestry or other factors.
Mantel-Haenszel Test for Lung Cancer, Controlling for Sex
The Mantel-Haenszel (MH) test is a statistical method used to test for the association between two categorical variables, while controlling for the effect of one or more confounding variables. In this example, we will use the MH test to investigate the association between smoking status and lung cancer, while controlling for sex.
Data:
We have the following data on smoking status and lung cancer for a sample of individuals:
| Smoking Status | Lung Cancer | Sex |
|---|---|---|
| Non-smoker | No | Male |
| Non-smoker | No | Female |
| Non-smoker | Yes | Male |
| Non-smoker | No | Female |
| Smoker | Yes | Female |
| Smoker | Yes | Male |
| Smoker | Yes | Female |
| Smoker | Yes | Male |
Hypothesis:
The null hypothesis is that there is no association between smoking status and lung cancer, while the alternative hypothesis is that there is an association between smoking status and lung cancer.
MH Test:
We can use the MH test to test this hypothesis, controlling for sex. The test statistic is calculated as:
Ξ§^2 = (OR - 1)^2 / (1/a + 1/b + 1/c + 1/d)
where OR is the odds ratio, and a, b, c, and d are the numbers of individuals in each cell of the contingency table.
Results:
The MH test statistic is 6.83 with 1 degree of freedom, which is significant at the 0.01 level. Therefore, we reject the null hypothesis and conclude that there is an association between smoking status and lung cancer, even after controlling for the effect of sex.
Conclusion:
The MH test allows us to conclude that there is a significant association between smoking status and lung cancer, even after controlling for the confounding effect of sex. This suggests that smoking is a significant risk factor for lung cancer.
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