# Multivariable regression interaction with categorical covariates

I am interested in the interaction between two categorical variables that each have four states in a survival experiment.

My model: Surv(time, death) ~ size * state

My very basic question, is do I look at the individual interactions between the levels? For example, size2:state:2 or size2:state3, etc? Or do I use an anova that will combine individual effects into a single pvalue, size:state?

I realize this is very basic, so if someone can give me a simple explanation or point me to an answer I would appreciate it. I am finding with my own data that one can be significant and the other is not, so I am having a hard time interpreting.

A test for interaction can be obtained by a likelihood-ratio test between the model with main effect + interactions (size*state) and the model with only main effects size + state. To obtain the p-value of this test, see ?anova.coxph.