# Questions regarding cox regression

#### perhexilline

##### New Member
Hi all, just some questions regarding interpretation of cox regression, thanks for any time or help you can spare.

If the variable under investigation has a negative co-efficient (i.e -0.5), how would you interpret a hazard ratio of <1 (i.e HR = 0.765)? would there be an increased or decreased association with the event? If increased, would the amount increased be 76.5% or 23.5%?

Second, if the variable under investigation was higher in the group with events (i.e 0.5 vs 0.3 in the group without events), how would you interpret a hazard ratio of 1.9? Would you say a 0.5 unit of the variable under investigation was associated with a 90% increased risk of the event? or would you say a 0.2 increment of the unit of the variable was associated with a 90% increased risk of the event?

Thanks all

#### hlsmith

##### Not a robit
You exponeniate your coefficient, so if after that it is below 1 along with its confidence interval, then it is protective. Like exercise and heart disease. If it is a categorical variable you can flip the reference group and it should be greater than 1 and you interpret the other categorical group.

#### perhexilline

##### New Member
Thanks @hlsmith, would that mean (using the example in qn 1), the increase in association would be 76.5%?

Apologies for being unclear. The question was meant to be, if the variable under investigation i.e systolic blood pressure, was 160 in the group with events vs 120 in the group without events, resulting in a HR of 1.9 for increased risk of stroke. How would you best report it?
Would it be a systolic blood pressure of 160mmHg was associated with a 90% increased risk of stroke? or a 40 mmHg increment of systolic BP was associated with a 90% increased risk of stroke? (please pardon the simplicity of the example in trying to illustrate my problem.)

Thanks alot once again