Testing hypotheses in case-control studies--equivalence of Mantel-Haenszel statistics and logit score tests

The two approaches in common use for the analysis of case-control studies are cross-classification by confounding variables, and modeling the logarithm of the odds ratio as a function of exposure and confounding variables. We show here that score statistics derived from the likelihood function in the latter approach are identical to the Mantel-Haenszel test statistics appropriate for the former approach. This identity holds in the most general situation considered, testing for marginal homogeneity in mK tables. This equivalence is demonstrated by a permutational argument which leads to a general likelihood expression in which the exposure variable may be a vector of discrete and/or continuous variables and in which more than two comparison groups may be considered. This likelihood can be used in analyzing studies in which there are multiple controls for each case or in which several disease categories are being compared. The possibility of including continuous variables makes this likelihood useful in situations that cannot be treated using the Mantel-Haenszel cross-classification approach.