A simple technique, developed in Phillips (unpublished Ph.D. dissertation, University of Windsor, Windsor, Ontario, 1987), is used to approximate cov($\hat\theta_{MH}, \hat p_i$), i = 1, 2, where ...

Suppose the number of 2 x 2 tables is large relative to the average table size, and the observations within a given table are dependent, as occurs in longitudinal or family-based case-control studies.