Mantel-Haenszel method

The null hypothesis tested by the Mantel-Haenszel method is as follows ... 

As an illustration of the Mantel-Haenszel method, we take the data from our example as detailed in Section 10.5.1 and separate them into data collected at each of three centers, which in this case represent the three strata. 

Several methods have been found adequate for low event count situations. For odds ratio summary measures, the Mantel-Haenszel, Peto, and exact methods appear to work well. The commonly used method in meta-analysis based on inverse variance weights does not perform well in low event count situations because the weights are not stable with low event counts. The Mantel-Haenszel risk difference appears to work well as well. This method has the added benefit in that unlike the methods for the odds ratio, this... 

The foundations of the method were laid by Cornfield, Dom, Mantel and Haenszel " in the 1950s, and it was rapidly adopted by epidemiologists as a major new technique. An interesting historical account of case-control studies has been given by Lilienfeld and Lilienfeld," who trace the method back to PCA Louis and his study of tuberculosis in 1844." Later developments have been reviewed by Cole, " who provides... 

One method applicable to the difference of two proportions, originally described by Mantel and Haenszel (1959) and well described by Fleiss et al. (2003), utilizes weights that are proportional to the size of each stratum (in this case, centers) to calculate a test statistic that follows approximately a distribution. 

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