# How to interpret hazard ratios of Cox output?

I'm really struggling to understand how to interpret my R outputs in terms of hazards ratios. I have ran a Cox proportional hazard regression to compare survival between 2 treatment groups (neutron and photon therapy) and I have adjusted for the biological site of cancer:

neutron$$site <- factor(neutron$$site, levels = c("Cervix", "Rectum", "Bladder", "Prostate")).


Regression:

cox2 <- coxph(Surv(stime, death)~treatment + site, data = neutron)


and finally the output:

exp(coef) exp(-coef) lower .95 upper .95
treatmentPhotons    0.7051     1.4183    0.4712     1.055
siteRectum          1.9813     0.5047    1.0837     3.622
siteProstate        0.8243     1.2132    0.2690     2.525


How would these values be interpreted relative to the baseline?

• By baseline, do you mean reference category? or baseline hazard? Nov 29, 2018 at 18:44
• Sorry, i guess i mean the baseline hazard? I just included the code for the reference so you could get an idea of what I was trying to do. Nov 29, 2018 at 18:46
• oh in that case I'm not really sure. I assumed you wanted to interpret the hazard ratio between your levels and the reference category. Nov 29, 2018 at 18:48
• Okay so how would I do that? Nov 29, 2018 at 18:49
• ok I'm typing that up now. I hope it's what you mean. well, we'll see. Nov 29, 2018 at 18:49

A hazard rate is the chances of the event happening, and the hazard ratio is simply the ratio of the two rates between two levels of a predictor. Or between a unit increase if its a continuous predictor. It lets us compare what happens to the chances of the event happening when you move between one level and another level.

Your baseline is the label that is not there. So, treatment photons is being compared to treatment neutrons. Your 4 levels of cancer location are all being (individually) compared to cervix.

The first column exp(coef) is literally the hazard ratio comparing the level listed to the reference(baseline) level. So having photon treatment reduces the hazard ratio by 30% compared to having neutron treatment. i.e. the chances of the event happening is 30% less when having photon treatments compared to neutron treatments.

Having cancer in the rectum increases the hazard ratio by 98% compared to having it in your cervix. i.e. It basically doubles the chances of the event happening (compared to the other group). Having it in the bladder increases it by 90% compared to having it in your cervix, and so on for the other levels of location.

These percentages is literally just the difference between the number and 1, because 1 is when a ratio is perfectly balanced; there is no difference between the two parts being compared. If the hazard ratio is, for example, 0.6 then i say 1-0.6=0.4, so the hazard ratio decreased by 40%, if it's 1.6 then i say 1.6-1=0.6, so the hazard ratio increased by 60%.

The column exp(-coef) is just the hazard ratio going the other way. Having cancer in your cervix decreases the hazard ratio by 50% compared to having it in your rectum. This might sound confusing but they're just mirror opposites of each other, you've just swapped the numerator on the ratio. i.e. 1/1.98=0.5, 1.98/1=1.98.

The last two columns are the upper and lower confidence intervals for your estimate.

I hope this is what you're after and I haven't completely missed the point. Sorry if i have.