Interpreting interaction terms in Cox Proportional Hazard model

Question

I am new to survival analysis, so forgive me if this questions is stupid - but I couldn't find the answer anywhere else. We are looking at readmission to a treatment program, which is defined as failure. I have two variables in my Cox regression/survival analysis. One is binary (v1, 0,1), the other is essentially discrete (v2, 1-200, with 1 being least severe and 200 being most severe). Interpreting their individual effects are simple, but their interaction makes no intuitive sense to me.

Here is the output of the coefficients (not hazard ratios just to be clear):

v1 (binary) Coef: 1.347 (p < 0.001) v2 (discrete) Coef: 0.162 (p <0.001). This makes sense, since intuitively these are expected risk factors for readmission. If v1 = 1 then there's an increased likelihood of readmission. If v2 = 200 then there's an increased likelihood of readmission. Right?

v.1 x v.2 (interaction) Coef: -0.750 (p < 0.001). Now this is where I'm lost. This makes no intuitive sense that the interaction between these variables would reduce the likelihood of readmission. If anything, you'd expect them to increase the likelihood of readmission.

My question is - am I interpreting this right? Or am I missing something? Is this saying that increasing v.1 + increasing v.2 leads to a reduced likelihood of readmission to treatment?

Anyway, thanks for tolerating my stupidity and for any replies.

Answer 1

Interactions are tricky. The short answer is: the effect of v2 is bigger if v1 is 0.

For calculation the following holds. The interaction terms suggests that having a zero for v1 and a high v2 score increases readmission. Having a 1 for v1 and a high v2 score also increases readmission, but the same score for v2 leads to a somewhat lower readmission than the first case.

Further interpretation is possible, but this is speculative. It might be that v1 is 1 is associated with a higher v2. Then the additional effect to v1 is less big. If v1 is 0 though, one could say that v2 is the sole contributing factor with a bigger impact.