# Interpreting Cox regression

My regression results are as follows.

Variable    B          exp(B)
age        0.004575    1.004586
capital    0.2250      1.2524
year      -0.1026      0.9024


Can someone please help me to interpret these? (eg: one year increase in age would increase/decrease the hazard by Xx%)

For two covariates ($x_1$ and $x_2$), the Cox model is written as (with standard notations) $$h(t; x_1, x_2) = h_0(t) \exp(x_1 \beta_1 + x_2 \beta_2).$$ To interpret $\beta_1$, note that $$\frac{h(t; x_1 + 1, x_2)}{h(t; x_1, x_2)} = \exp(\beta_1).$$ In words, the previous equation tells us that whenever $x_1$ increases by 1 unit ($x_2$ being held fixed), the hazard rate is multiplied by $\exp(\beta_1)$.
On the log-scale, we have $$\log(h(t; x_1 + 1, x_2)) - \log(h(t; x_1, x_2)) = \beta_1.$$