# 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?

This doesn't actually contain the denominator which was the number of people at risk. 22, 12, 11, and 11 are numbers dead in either treatment group comparing men(OR=1) and women(OR=2) respectively. The test of interaction comes from the 95% Wald test for the interaction parameter in a logistic regression model, something of this form:

fit <- glm(dead ~ sex * exposure, family=binomial)
coef(summary(fit))['sex:exposure', ]

• Thank you - I was specifically looking for what they meant in reference to a test comparing odds ratios. If I understand you, there isn't a test for interaction that only uses odds ratios, and that most likely the authors performed some sort of logistic regression? Jun 7, 2013 at 18:18
• Right. Intuitively, you could post-test for interaction with odds ratios using separately estimated models and the standard error of those estimates. That would be a consistent test, but it's of low power. Still, calculating the CIs for those ORs (2 and 1) requires you to know how many people were at risk in that sample... which I didn't bother to look up in the paper. That said, logistic regression models with interaction parameters are the de facto way of doing this. Jun 7, 2013 at 18:23
• I did see, while trying to research an answer to this question, a method in which the difference between risk ratios was divided by the standard error, but I wasn't sure what the standard method was. Jun 7, 2013 at 18:28