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.