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

Abstract

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 treatments. For this, consider the model: in the two treatment groups. If the odds-ratio 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 version of the Mantel Haenszel estimator of the odds-ratio is constructed, which is shown to be a consistent estimator of the treatment main effect and normally distributed in large samples.

Keywords:

• Covariate
• binary response
• treatment effect
• interaction
• Mantel Haenszel estimator

1980 AMS Subject Classzjications:

• 62F10
• 62F12
• 62502