Maximum-likelihood estimation and presentation for the interaction between treatments in observational studies with a dichotomous outcome

ABSTRACTIn observational studies for the interaction between treatments, one needs to estimate and present both the treatment effects and the interaction to learn the significance of the interaction to the treatment effects. In this article, we estimate the treatment effects and the interaction jointly by using only one logistic model and based on maximum-likelihood. We present the interaction by (1) point estimate and confidence interval of the interaction, (2) point estimate and confidence region of (treatment effect, interaction), and (3) point estimate and confidence interval of the interaction when the maximum-likelihood estimate of one treatment effect falls into specified range.