odds ratio relative risk

Daniel Parker

3 min read

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16-03-2025

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Understanding the difference between odds ratio and relative risk is crucial for interpreting epidemiological studies and medical research. While both measures assess the association between an exposure (like smoking) and an outcome (like lung cancer), they do so in different ways, leading to potentially different interpretations. This article clarifies the distinction and explains when each measure is most appropriate.

What is Relative Risk (RR)?

Relative risk, also known as the risk ratio, directly compares the probability of an outcome occurring in an exposed group versus an unexposed group. It's calculated as:

RR = (Risk in exposed group) / (Risk in unexposed group)

Where "risk" is the probability of developing the outcome. For example, if 10% of smokers develop lung cancer and 1% of non-smokers develop lung cancer, the relative risk of lung cancer for smokers is 10 (10%/1%). This means smokers are 10 times more likely to develop lung cancer than non-smokers. A relative risk of 1 indicates no association between exposure and outcome. RR greater than 1 suggests increased risk, and less than 1 suggests a reduced risk.

Calculating Relative Risk: Relative risk is typically calculated from cohort studies, where a group of individuals is followed over time to observe the incidence of an outcome.

When to Use Relative Risk

Relative risk is generally preferred when studying the incidence of a disease or outcome in a prospective cohort study. It provides an intuitive measure of the increased or decreased risk associated with exposure.

What is Odds Ratio (OR)?

The odds ratio compares the odds of an outcome occurring in an exposed group versus an unexposed group. "Odds" are different from "probability." Odds are calculated as the ratio of the probability of an event occurring to the probability of it not occurring.

Odds of event = Probability of event / Probability of no event

The odds ratio is calculated as:

OR = (Odds of outcome in exposed group) / (Odds of outcome in unexposed group)

For example, let's say in a case-control study, 80 out of 100 lung cancer patients (cases) were smokers, while 20 out of 100 control subjects (non-lung cancer patients) were smokers. The odds of being a smoker among lung cancer patients is 80/20 = 4. The odds of being a smoker among controls is 20/80 = 0.25. The odds ratio is therefore 4/0.25 = 16. This indicates that the odds of being a smoker are 16 times higher among lung cancer patients than among the control group.

When to Use Odds Ratio

Odds ratios are commonly used in case-control studies, where individuals with the outcome (cases) and without the outcome (controls) are selected, and their past exposure is assessed. They are also useful in retrospective cohort studies and logistic regression models.

Key Differences Summarized

When OR Approximates RR

Importantly, when the outcome being studied is relatively rare (meaning the probability of the outcome is low in both exposed and unexposed groups), the odds ratio provides a good approximation of the relative risk. However, as the outcome becomes more common, the difference between the OR and RR becomes more pronounced.

Conclusion: Choosing the Right Measure

The choice between relative risk and odds ratio depends largely on the study design and the prevalence of the outcome. Relative risk provides a more intuitive measure of risk and is generally preferred for cohort studies, particularly when the outcome is common. Odds ratios are commonly used in case-control studies and often provide a reasonable approximation of relative risk when the outcome is rare. Understanding the nuances of each measure is vital for accurately interpreting research findings and making informed decisions based on epidemiological data.