The Cochran-Mantel-Haenszel (CMH) test is used to test multiple 2 × 2 contingency tables across different values of a confounding variable. The test determines whether there is a significant difference between the odds ratios across the different values of the confounding variable.
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References
PennState (2017) Cochran-Mantel-Haenszel test
https://online.stat.psu.edu/stat504/lesson/5/5.3/5.3.5
SAS Help Center (2019) Cochran-Mantel-Haenszel statistics
https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.4/statug/statug_freq_details92.htm
Moral de la Rubia, J., Valle de la O, A. (2023) Everything you wanted to know but could never find from the Cochran-Mantel-Haenszel test
https://www.scirp.org/pdf/jdaip_2023082810224634.pdf