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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.

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    $\begingroup$ 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 $\endgroup$ – maya Oct 18 '18 at 10:14
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    $\begingroup$ 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. $\endgroup$ – Peter Flom - Reinstate Monica Oct 18 '18 at 11:04
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    $\begingroup$ 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 $A$). $\endgroup$ – Alexis Oct 18 '18 at 15:09
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The best way to proceed is simply to state the result that you found: "The hazard ratio for Group A versus Group B in terms of survival is 0.56 (95% CI: 0.36 to 0.87)." As comments have suggested, you certainly could choose to say that the hazard for Group B is higher than that for Group A.

This is not, however, the same as saying the the risk of cancer differs between the two groups, as you seem to wish to do. And unless you are looking specifically at death from cancer (data that are often hard to get in a meta-analysis), it's not even the same thing as saying that the risk of dying from cancer differs between the two groups.

Further complicating the matter is that moving from hazard ratios to relative risks is not straightforward. See this paper for an introduction to that issue.

So you do have to be careful in how you discuss your results.

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