Interpreting Cox regression

Question

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%)

Answer 1

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 $$ \log(h(t; x_1 + 1, x_2)) - \log(h(t; x_1, x_2)) = \beta_1. $$

Answer 2

For every unit increase in year, the hazard decreased by 9.8% assuming the other variables are held constant.