  In observational studies with dichotomous outcome of a population,
researchers need to present the effects of exposures and interaction between
the exposures jointly in order to learn the relationship between the exposure
effects and the interaction. In this article we study point and interval
estimation of exposure effects and the interaction based on logistic model,
where the exposure effects are measured by risk differences while the
interaction is measured by difference between risk differences. Using
approximate normal distribution of the maximum-likelihood (ML) estimate of the
model parameters, we obtain approximate non-normal distribution of the ML
estimate of the exposure effects and the interaction. Using the obtained
distribution, we obtain point estimate and confidence region of (exposure
effect, interaction) as well as point estimate and confidence interval of the
interaction when the ML estimate of an exposure effect falls into specified
range. Our maximum-likelihood-based approach provides a simple but reliable
method of interval estimation of exposure effects and the interaction.
