Relative Risk (RR) and Odds Ratio (OR) are measures in statistics and epidemiology used to quantify the association between an exposure and an outcome. While both assess how an exposure might influence an outcome, their calculation and application differ significantly. The choice between using RR or OR depends on the research study design. Understanding these distinctions is important for accurate interpretation of study findings.
Relative Risk for Prospective Studies
Relative Risk, also known as the risk ratio, quantifies how much more likely an outcome is to occur in an exposed group compared to an unexposed group. This measure directly reflects the probability of an event happening within a defined population over a specific period. Calculating Relative Risk requires knowing the incidence, which is the rate of new cases of an outcome in a population at risk during a specified time frame.
Relative Risk is best suited for prospective study designs, such as cohort studies and randomized controlled trials (RCTs). In these studies, researchers follow groups of individuals forward in time. For example, in a cohort study investigating smoking and lung cancer, researchers would enroll smokers and non-smokers and track them to observe who develops lung cancer. Using a 2×2 table where ‘a’ is exposed with outcome, ‘b’ exposed without outcome, ‘c’ unexposed with outcome, and ‘d’ unexposed without outcome, Relative Risk is calculated as [a/(a+b)] / [c/(c+d)].
Odds Ratio for Retrospective Studies
The Odds Ratio represents the ratio of the odds of an outcome occurring in an exposed group compared to the odds of the outcome occurring in an unexposed group. Odds are defined as the probability of an event happening divided by the probability of it not happening. This measure is useful when it is not possible to directly calculate the incidence of an outcome within the population.
Odds Ratio is the appropriate measure for retrospective study designs, most notably case-control studies. In these studies, researchers identify individuals who already have the outcome (cases) and a comparable group without the outcome (controls). They then look backward to determine past exposure status for both groups. Since the study design selects individuals based on their outcome status, true incidence rates cannot be determined, making Relative Risk incalculable. Using the 2×2 table notation, the Odds Ratio is calculated as (a/c) / (b/d), which simplifies to the cross-product ratio (ad/bc). For example, in a case-control study examining a food poisoning outbreak, researchers compare the odds of prior exposure to a specific food among those who got sick (cases) versus those who did not (controls).
When Odds Ratio Approximates Relative Risk
Under specific conditions, the Odds Ratio can provide a reasonable approximation of the Relative Risk. This phenomenon is known as the “rare disease assumption.” When the outcome or disease being studied is uncommon in the population (generally defined as having an incidence of less than 10%), the numerical values of the Odds Ratio and Relative Risk are similar.
This approximation occurs because when the number of individuals with the outcome in both exposed (‘a’) and unexposed (‘c’) groups is very small compared to those without the outcome (‘b’ and ‘d’ respectively), the denominators in the Relative Risk calculation, (a+b) and (c+d), become numerically very close to ‘b’ and ‘d’. Consequently, the Relative Risk formula [a/(a+b)] / [c/(c+d)] approaches the Odds Ratio formula [a/b] / [c/d]. This explains why an Odds Ratio from a case-control study might sometimes be discussed as if it represents a risk ratio, particularly in studies of rare diseases. However, this approximation diminishes as the outcome becomes more prevalent in the population.
Interpreting the Measures Correctly
Accurate interpretation of Relative Risk and Odds Ratio is important to avoid misrepresenting study findings. A Relative Risk of 2.0 means the exposed group is twice as likely to develop the outcome as the unexposed group. Conversely, a Relative Risk of 0.5 indicates the exposed group is half as likely to develop the outcome, suggesting a protective effect.
Interpreting an Odds Ratio requires different phrasing to maintain precision. An Odds Ratio of 2.0 means the odds of having the outcome are two times higher for the exposed group compared to the unexposed group. A common pitfall involves interpreting an Odds Ratio as if it were a Relative Risk, especially when the rare disease assumption does not hold. When the outcome is not rare, the Odds Ratio will always overestimate the true Relative Risk, meaning it will be further from 1.0. This exaggeration becomes more pronounced as the incidence of the outcome increases, potentially leading to an inflated perception of the strength of the association between the exposure and the outcome.