hazard ratio interpretation

Imagine that when we compare treatment A to treatment B (the group A is a high expression and group B is a low expression of gene X) and the pooled hazard ratio (group A in comparison to group B) is 0.56 (95% CI: 0.36 to 0.87). Do I simply say that in group B the risk of cancer is higher? (I.e. instead of saying there is a lower risk of cancer in group A?)

Remember that high expression of gene X is associated with low risk of cancer and low expression of gene X is associated with a higher risk of cancer.

If it's OK, please give me a scientific reference.

• would u please help me? I've conducted a meta analysis the pooled HR is 0.56 which shows that high expression of gene "x" is associated with better survival could I report this result as below in my article? the low expression of gene "x" is associated with worse prognosis i mean that are these to phrase equal? if they are please give me a refrence thanks a lot – maya Oct 18 '18 at 10:14
• If A is lower than B, then B is higher than A. There's no reference for this, except maybe a book of elementary school arithmetic. Maybe you are asking something else, but, if so, please clarify it by editing your question. – Peter Flom - Reinstate Monica Oct 18 '18 at 11:04
• If $h_A < h_B$, then $\frac{h_A}{h_B} < 1$, and likewise if $\frac{h_A}{h_B} < 1$, then $h_A < h_B$. If what you care about is which group has a higher hazard, then you can instead report $\frac{h_B}{h_A} = \left(\frac{h_A}{h_B}\right)^{-1} = 1.8$ (i.e. group $B$ has almost twice the hazard of group $A$). – Alexis Oct 18 '18 at 15:09