The Odds, the Risk & the Hazard: Meaning and Interpretation

The relative risk (RR) is not the hazard ratio (HR). If the outcome is cure and follow-up is for 5 years; a RR of 2 means that after 5 years, twice as much of patients in the treatment group are expected to be cured, compared to the control group; i.e., the RR is cumulative, which is why it is the outcome of choice in RCT. A HR of 2 means that any time during the 5 years, twice as much of patients in the treatment group are expected to be cured, compared to the control; the HR is instantaneous, which is why it is the outcome of choice in time-to-event analysis.

Workshop items:

• Risk and odds 

• Two relative risks and one Odds ratio 

• The adjusted relative risk 

• The odds in logistic regression 

• HR versus RR 

• The exponential hazard 

• Hazard ratio in Cox regression 

• OR, RR and HR: calculation of their 95 confidence interval and testing statistical significance

• OR, RR and HR: interpretation in different models