Estimation of the odds-ratio in an observational study using bandwidth-matching

In many practical situations, such as incidence of a disease in two groups, a binary response variate Y depends on the effect of one of two treatments as well as a covariate X having different distributions under the two trea tments. For this, consider the model: P(Y-i = 1\x) = p(i)(x). P(Y-i = 0\x) = q(i)(x), i = 1,2 in the two treatment groups. If the odds-ratio theta(x) = (p(1)(x)q(2)(x))/(q(1),(x)p(2)(x)) is a constant, then it represents the treatment effect; otherwise, one can only think of a treatment main effect in the presence of a treatment-covariate interaction. A bandwidth-matched v ersion of the Mantel-Haenszel estimator of the odds-ratio is constructed, w hich is shown to be a consistent estimator of the treatment main effect and normally distributed in large samples.