Relative Risk

The relative risk, or risk ratio, is the probability of an outcome in an exposed group divided by the probability of the same outcome in an unexposed group. It is the natural relative measure of association for cohort studies and randomised trials, summarising in a single number how many times more (or less) likely the outcome is among the exposed.

Definition

The relative risk (risk ratio) is the ratio of the probability (risk) of an outcome in an exposed group to the probability of that outcome in an unexposed group.

Scope

This entry covers the definition and interpretation of the relative risk, the data it requires, how a value above, below, or equal to one is read, its dependence on directly observed risks, and how it differs from the odds ratio. It treats the relative risk as a methodological measure, not as clinical guidance.

Key concepts

• Risk (cumulative incidence)
• Exposed and unexposed groups
• Null value of one
• Direction and strength of association
• Distinction from the odds ratio
• Need for directly estimable risks

Mechanisms

The relative risk is computed by estimating the risk of the outcome in the exposed group and dividing it by the risk in the unexposed group. A value of 1 indicates no association, a value above 1 indicates a higher risk among the exposed, and a value below 1 indicates a lower risk. Because it is built from risks (cumulative incidences), it can be estimated directly only from designs that observe the population at risk over time, such as cohort studies and randomised trials; case-control studies, which sample on outcome, cannot estimate risk directly and instead yield the odds ratio. When the outcome is common, the relative risk and odds ratio diverge, and the odds ratio overstates the relative effect; methods such as the Zhang-Yu correction or modified Poisson regression are used to recover a relative risk in those settings.

Clinical relevance

The relative risk is one of the most frequently reported summaries of how strongly an exposure or treatment is associated with an outcome, and reading it correctly is part of appraising cohort and trial evidence. It conveys the strength of an association but, on its own, says nothing about the absolute number of events; it is a measure for interpreting evidence, not a directive for individual care.

Epidemiology

Relative risk is the standard relative measure in cohort studies and randomised controlled trials, where the underlying risks are observable. It travels relatively well across populations with different baseline risks, which is why it is often the measure pooled in meta-analyses, though it must be paired with an absolute measure to convey real-world impact.

History

The notion of comparing disease rates between exposed and unexposed groups is foundational to modern epidemiology and was formalised as the risk ratio in twentieth-century cohort research. As logistic and case-control methods spread, the relationship between the odds ratio and the relative risk became a recurring concern, prompting the late-1990s and 2000s work of Zhang and Yu and of Zou on recovering relative risks when outcomes are common.

Debates

Reporting odds ratios as if they were relative risks

For common outcomes the odds ratio numerically exaggerates the relative risk; presenting an odds ratio as though it estimated the risk ratio can mislead readers, motivating correction methods and direct relative-risk regression.

Key figures

• Kenneth Rothman
• Sander Greenland
• Jun Zhang
• Guangyong Zou

Seminal works

• rothman-2008
• zhang-yu-1998
• zou-2004

Frequently asked questions

What does a relative risk of 1 mean?

A relative risk of 1 means the outcome is equally likely in the exposed and unexposed groups, so the exposure shows no association with the outcome; values above 1 indicate higher risk among the exposed and values below 1 indicate lower risk.

Why can a relative risk not be estimated directly from a case-control study?

Because a case-control study samples participants by outcome status rather than following a population at risk, it cannot observe the underlying risks needed to form a risk ratio, so it estimates the odds ratio instead.