# How to calculate OR and confidence interval for two binary explanatory variables with interaction

I have a logistic regression model with several categorical explanatory variables and one interaction term (between two binary variables, named A and B). I know how to calculate the odds ratios for the different levels of A and B (for A=1, e.g., I need to add the coeff for A and coeff for A*B, then exponentiate), but how do I get a confidence interval for this OR? I need to do this in R please, this is the only statistical package I have access to.

You can get confidence intervals for the parameters in a logistic regression with confint(). E.g.

set.seed(938838210)
x1 <- rnorm(1000)
x2 <- rnorm(1000)
ylat <- 3*x1 + 2*x2 + x1*x2 + rnorm(1000, 0, 5)
y <- ylat > 0
m1 <- glm(y ~ x1 + x2 + x1*x2, family = "binomial")
summary(m1)
confint(m1)


However, the odds ratios and their confidence intervals are not unique; they depend on the values of the ivs. I wrote about this (using SAS, but the ideas are the same) in this paper (see "Gotcha 5"). In SAS 9.2 they've implemented a simple solution, but I don't know of an easy one in R.