# Interaction Test with Odds Ratio

Reading Pocock et. al on subgroup analysis, the authors describe calculating an interaction test given 2 odds ratios (and the count data used to get them). Specifically,

mat <- matrix(c(22,12, 11, 11), nrow=2, ncol=2, byrow=T)


Where 22, 12 correspond to deaths/not deaths in one group and 11, 11 are same for another group. They report ORs of 2 and 1 respectively, and then report that the interaction test comparing odds ratios has p = 0.21.

What is the interaction test they performed?

fit <- glm(dead ~ sex * exposure, family=binomial)