Mantel-Haenszel estimators of odds ratios for stratified dependent binomial data

A standard approach to analyzing n binary matched pairs usually represented in n 2x2 tables is to apply a subject-specific model; for the simplest situation it is the so-called Rasch model. An alternative population-averaged approach is to apply a marginal model to the single 2x2 table formed by n subjects. For the situation of having an additional stratification variable with K levels forming K 2x2 tables, standard fitting approaches, such as generalized estimating equations and maximum likelihood, or, alternatively, the standard Mantel-Haenszel (MH) estimator, can be applied. However, while all these standard approaches are consistent under a large-stratum limiting model, they are not consistent under a sparse-data limiting model. In this paper, we propose a new MH estimator and a variance estimator that are both dually consistent: consistent under both large-stratum and sparse-data limiting situations. In a simulation study, the properties of the proposed estimators are confirmed, and the estimator is compared with standard marginal methods. The simulation study also considers the case when the homogeneity assumption of the odds ratios does not hold, and the asymptotic limit of the proposed MH estimator under this situation is derived. The results show that the proposed MH estimator is generally better than the standard estimator, and the same can be said about the associated Wald-type confidence intervals.