A note on the covariance of the Mantel-Haenszel log-odds-ratio estimator and the sample marginal rates

A simple technique, developed in Phillips (unpublished Ph.D. dissertation, University of Windsor, Windsor, Ontario, 1987), is used to approximate cov(theta MH, pi), i = 1, 2, where theta MH is the Mantel-Haenszel log-odds-ratio estimator for a 2 x 2 x K table and the pi are the sample marginal proportions. These results are then applied to obtain an approximate variance estimate of an adjusted risk difference based on the Mantel-Haenszel odds-ratio estimator.