What Is the Relative Risk Equation and How Is It Calculated?

Relative risk (RR) is a statistical measure used in science and medicine to compare the likelihood of an event occurring between two distinct groups. This metric is a ratio that helps researchers understand how much an exposure, such as a treatment, a lifestyle factor, or a toxin, changes the probability of a specific outcome, like developing a disease or experiencing recovery. The resulting number indicates whether the exposure increases, decreases, or has no effect on the likelihood of the outcome.

Calculating Risk Comparison

The fundamental structure of the relative risk equation is a simple division of two probabilities. It is the ratio of the risk of the outcome in the exposed group divided by the risk of the outcome in the unexposed, or comparison, group.

To perform the calculation, researchers determine the risk of the outcome in the group that was exposed to the factor of interest; this figure forms the numerator. Next, they calculate the risk of the same outcome in the group that was not exposed to the factor, which becomes the denominator. For example, if 17% of smokers develop lung cancer and 1% of non-smokers develop lung cancer, the relative risk is calculated by dividing 17% by 1%, which yields a result of 17.

Decoding the Relative Risk Number

Interpreting the relative risk number is straightforward because the value of 1.0 serves as the reference point. A relative risk of exactly 1.0 indicates that the probability of the event occurring is identical in both the exposed and unexposed groups. This means the exposure had no discernible association with the outcome being measured.

When the relative risk is greater than 1.0, it signifies an increased risk of the outcome in the exposed group. For instance, a relative risk of 1.5 means the risk in the exposed group is 50% greater than the risk in the unexposed group, which is calculated as (1.5 – 1.0) multiplied by 100. A higher number, such as an RR of 3.0, suggests the exposed group is three times as likely to experience the outcome.

Conversely, a relative risk that is less than 1.0 suggests the exposure may have a protective effect, decreasing the risk of the outcome. If a study yields an RR of 0.57, it means the exposed group has a risk that is 43% lower than the unexposed group, calculated as (1.0 – 0.57) multiplied by 100. This protective effect is more pronounced as the relative risk approaches zero.

Relative Risk Versus Absolute Risk

Relative risk is often confused with absolute risk, but the two measures convey very different information about the magnitude of a health event. Absolute risk is the raw probability of an event happening in a single group, such as the chance of a person developing a certain condition over a specific period.

Relative risk, however, is a ratio that tells you nothing about the actual, underlying frequency of the event in the population. Understanding the absolute risk is necessary to put the relative risk into proper context. This distinction is important when the baseline risk of an event is very low, a concept sometimes known as the “rare event paradox.”

For example, a study might report a high relative risk of 8.0 for a condition due to a specific factor, meaning the risk is 800% higher in the exposed group. If the absolute risk in the unexposed group is only 1 in 100,000 people, an eight-fold increase still results in an absolute risk of only 8 in 100,000.

Why Researchers Rely on Relative Risk

Relative risk is used in epidemiological research because it allows for a standardized comparison of associations across different populations and studies. This measure is commonly used in prospective research designs, such as cohort studies and randomized controlled trials, where researchers follow groups over time to track event incidence.

The measure’s direct comparison between exposed and unexposed populations makes it valuable for public health decision-making and risk communication. By quantifying the effect of a specific exposure, such as a new medication or a change in dietary habits, relative risk helps policymakers and clinicians determine the potential public health impact of interventions. It is a tool for assessing treatment effectiveness and understanding how various factors influence health outcomes.