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When data analysts, researchers, and practitioners need to understand how certain phenomena impact the chances of an outcome, they resort to measures like relative risk (RR) and odds ratio (OR). The good news: they are not as daunting as they may sound. Here’s what they mean and how they differ.
In a nutshell:
- RR is used in cohort or prospective studies, requiring incidence or probability data.
- OR is defined as a ratio of odds and is commonly used in case-control or retrospective studies, where risk cannot be directly estimated.
Both measures are traditionally used on categorical variables with binary or dichotomous outcomes.
Understanding And Calculating Relative Risk
RR is a simple comparison between the probability of an outcome in two groups. Suppose we observe students who prepare for an exam with two different methods of study: A and B. RR can determine the likelihood of student group A passing the exam compared to group B. It is a ratio; thus, RR = 3.0 means group A is three times as likely as group B to pass. Conversely, RR = 0.5 means group A is half as likely to pass as group B.
If 60% of students using method A passed the exam and 40% of those using method B passed, RR is easily calculated by dividing both percentages: RR = 0.6 / 0.4 = 1.5.
Understanding And Calculating Odds Ratio
OR is a comparison between the odds of an outcome in two groups. Its use is particularly common when we need to observe past data.
Suppose we want to analyze whether having attended a past tutorial session before the exam affected exam success. Now the students are divided into two groups depending on whether they have attended the session or not.
| Passed exam | Did not pass exam | |
|---|---|---|
| Attended tutorial | 80 | 20 |
| Did not attend tutorial | 50 | 50 |
First, compute the odds of the outcome (pass) in each group. For the group that attended the tutorial, the odds are 80/20 = 4. For the group that did not attend, the odds are 50/50 = 1. Finally, take the ratio of the two odds: OR = 4/1 = 4.
The Key Difference Between RR And OR
OR and RR may look very similar or distinct depending on the actual data. When the target outcome (e.g., passing the exam) is rare, both OR and RR yield similar values. But when the outcome is common, their differences become more pronounced, and OR tends to inflate the strength of association — if it is interpreted as a relative risk.
In the last example, OR is higher because passing is a frequent outcome and not a rare event. Which one should we rely on the most, and when?
As a rule of thumb, since RR is more intuitive and interpretable, choose it when it is feasible to directly estimate probabilities or risks. In situations where risks cannot be directly obtained and odds arise naturally — such as in logistic regression analysis or case-control studies — OR is a good choice. Either way, a best practice is to accompany results with their confidence intervals to account for uncertainty and help ascertain the precision of the association studied.
