Researchers use statistical measures like the Odds Ratio (OR) and the Relative Risk (RR) to describe the association between an exposure and a health outcome. Although both are ratios, they are based on fundamentally different mathematical concepts: probability versus odds. Choosing the correct measure depends entirely on the study design, which dictates whether a true probability can be calculated or if an estimate must be used. Misunderstanding this distinction can lead to incorrect conclusions about the actual magnitude of a health risk.
Defining Relative Risk and Its Context
Relative Risk (RR), also known as the risk ratio, directly compares the probability of an event occurring in an exposed group versus an unexposed group. The calculation involves incidence, which is the number of new cases of an outcome over a specific period divided by the total population at risk. The RR is simply the ratio of these two probabilities.
An RR of 2.0 means the exposed group is twice as likely to experience the outcome as the unexposed group. Because RR requires knowing the total population at risk and observing the outcome over time, it can only be calculated directly in prospective studies. These include Cohort Studies, where researchers follow a group of people over time, and Randomized Controlled Trials (RCTs), where participants are assigned to different exposure groups.
Defining Odds Ratio and Its Context
The Odds Ratio (OR) is a measure that quantifies the association between an exposure and an outcome by comparing the odds of the outcome occurring in one group to the odds in another group. Odds are distinct from probability, representing the likelihood of an event happening divided by the likelihood of it not happening. The OR becomes necessary when researchers cannot directly measure the true risk or probability of an outcome.
This situation arises in retrospective studies, particularly Case-Control Studies. Investigators begin by identifying individuals who already have the outcome (cases) and compare them to a group without the outcome (controls). Since the study selects pre-existing cases, the total population at risk is unknown, making it impossible to calculate the true incidence or Relative Risk. In this design, the Odds Ratio serves as the appropriate and valid measure of association.
Key Differences in Interpretation
Although both measures describe an association, their numerical interpretation can diverge significantly, especially when the outcome is common. The Odds Ratio tends to overestimate the Relative Risk when the association is greater than 1, meaning the OR value will be numerically larger than the corresponding RR. This overestimation occurs because the OR’s denominator (the odds of not having the outcome) shrinks as the outcome becomes more frequent, causing the ratio to inflate.
The “rare disease assumption” addresses this discrepancy. When the outcome is uncommon, generally defined as having an incidence or prevalence of 10% or less, the OR and the RR will be very similar in value. In these instances, the OR closely approximates the RR. However, if the prevalence is above 10%, the OR increasingly exaggerates the strength of the association compared to the true risk. For example, an OR of 3.0 might suggest a much larger increase in risk than the actual RR.
Practical Guide to Recognizing the Right Measure
The most direct way to gauge the appropriateness of the reported measure is to identify the study’s design. If a study started with healthy participants and followed them forward in time (prospective design) to track new cases, researchers should report the Relative Risk. This structure allows for the direct calculation of incidence.
Conversely, if the study identified people who already have a condition and then looked backward to determine past exposure (retrospective design), the Odds Ratio should be reported. This retrospective approach is the fundamental design of case-control studies, where the OR is the statistically valid measure of association. Understanding the study type is the primary step in correctly interpreting the reported number.