An extension of the mantel-haenszel procedure to k 2×C contingency tables and the relation to the logit model

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Abstract
Suppose that we have series of 2×c contingency tables for different age groups and that each 2×c table consists of c bino-mial observations, which for later use, may be regarded as the number of deaths from leukemia during some period for c radiation dose groups among atomic bomb survivors. After adjusting the age constitution in each dose group, we wish to test the homogeneity of c binomial populations. The test statistic is based on the sum of the binomial observations through age for each dose group, the distribution of which is computed by the conditional distributions for given marginals in each contingency table. Because of the singularity of the covariance matrix, we have several ways, includ ing Amtitage (1966), to make X2 -statistic with c-1 degrees of freedom. We can show, however, that all of these are the same, which may be regarded as an extension of Cochran (1954) and Mantel- Haenszel procedure (1959). As Birch (1964) and Zelen (1971) noted, this test procedure is supported by the logit model, under which we can make simultaneous confidence intervals for the dose effect after eliminating the age effect, based on the limiting distribution. An numerical example is provided by the leukemia death observation at ABCC.

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