Risk Ratio (Relative Risk)
Situation: You have two populations (or groups) for whom you have calculated their risk of a particular outcome. A typical scenario is one group has been exposed to something that might cause a disease and the other one hasn’t. Or one group has received treatment A and another treatment B, and you want to see if one of the treatments has a better chance of cure.
You could calculate the absolute risk difference (ARD). You could also calculate the risk ratio (also called relative risk). The risk ratio (RR) is the estimate of the strength of an association between an exposure (or treatment) and an outcome. The risk ratio places this estimated strength of the association between exposure (treatment) and outcome on a standard or universal scale. This is helpful when examining associations among various exposures/treatments and the outcome. The risk ratio allows each exposure or treatment to operate on the “same playing field,” so to speak.
The risk ratio (RR) is the risk calculated for one group divided by the risk calculated for the other group. Typically, the risk for the group exposed (or given a new treatment) is in the numerator and the risk for the unexposed (or standard, placebo, or no treatment) group is in the denominator.
RR = Riskexposed / Riskunexposed
- A risk ratio of 1.0 indicates that there is no discernible association between exposure (or treatment) and the outcome. A risk ratio of >1.0 suggests that the exposure (or treatment) makes the outcome more likely, and a risk ratio of <1.0 suggests the exposure (or treatment) makes the outcome less likely.
- Theoretically, the risk ratio can vary from 0 to +∞.
Example. For absolute risk difference we used the example of comparing the 30-day readmission risk in patients discharged from hospital after receiving treatment for sepsis with the 30-day readmission risk for all (other) patients. The readmission risk for patients with sepsis was 0.197 (19.7%) and it was 0.117 (11.7%) for all (other) patients. The calculation of the risk ratio for sepsis patients vs. other patients is as follows:
RR = RiskSepsis / RiskOther = 0.197 / 0.117 = 1.68
The absolute risk difference in 30-day readmissions between sepsis and other patients is 8%, which on a scale of 0-100% seems fairly small. However, because readmission itself is fairly uncommon, that 8% means that having sepsis increases the readmission risk by two-thirds. When considering the many patients who are hospitalized for sepsis, that suggests a larger impact than might otherwise be gleaned from an individual’s increased risk of 8%. About 1.7 million patients in the United States each year are hospitalized with sepsis [1]. If 19.7% are readmitted within 30 days, that’s 334,900. If an intervention could be developed to reduce that risk down to 11.7%, that would prevent 136,000 30-day readmissions every year. [Note: this is assuming that the 19.7% from the paper could be applied to all patients in the United States, which we are doing for the sake of this example. I also assumed all patients are discharged alive, which unfortunately is not the case.]
Risk ratios and absolute risk differences give distinct and important perspectives on the nature of a potential association between an exposure or treatment and an outcome.