# Cox model stratification

I am confused about stratifying on a variable in Cox models. I think $$e^{\beta_1}$$ still represents the hazard ratio for somebody with $$x=2$$ vs $$x=1$$, but I don't quite understand how it's still a proportional hazards model. What if two people being compared are in a different stratum? Then how is $$e^{\beta_1}$$ valid? Shouldn't it be $$\frac{h_1(t)}{h_2(t)} e^{\beta_1}$$? But then $$e^{\beta_1}$$ no longer represents a hazard ratio, unless the two are in the same stratum. Is this right?

• The "hazard ratio" is constrained to be consistent across the multiple strata. Jun 2, 2022 at 18:44

• Thanks for the answer. I'm still a bit confused though, it doesn't seem obvious how you compare somebody from stratum 1 to somebody from stratum 2. It's clear now that $e^{\beta}$ is the same regardless of which stratum somebody is in. But I don't understand how the math works with $\frac{h_1(t)}{h_2(t)} e^{\beta_1}$...the hazards do not cancel? Jun 2, 2022 at 19:22