odds ratio vs relative risk

Daniel Parker

3 min read

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13-03-2025

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Understanding the difference between odds ratios (OR) and relative risks (RR) is crucial for interpreting epidemiological studies and medical research. While both measures assess the association between an exposure and an outcome, they do so in different ways, leading to potentially different interpretations. This article will clarify the distinction, highlighting their strengths and limitations.

What is Relative Risk (RR)?

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

RR = [Risk in Exposed Group] / [Risk in Unexposed Group]

Where risk is calculated as:

Risk = [Number of events] / [Total number of individuals in the group]

Example: Let's say we're studying the risk of lung cancer (the event) in smokers (exposed) versus non-smokers (unexposed). If 100 out of 1000 smokers develop lung cancer and 10 out of 1000 non-smokers develop it, the RR would be (100/1000) / (10/1000) = 10. This means smokers are 10 times more likely to develop lung cancer than non-smokers.

Advantages of RR:

• Intuitively easy to understand: A RR of 2 means double the risk.
• Directly interpretable as a risk difference: It reflects the actual increase or decrease in the risk of the outcome.

Limitations of RR:

• Cannot be calculated from case-control studies: Case-control studies don't provide the necessary information on the total number of individuals in each group.
• Affected by prevalence of the outcome: The magnitude of the RR can vary depending on the prevalence of the outcome in the population.

What is Odds Ratio (OR)?

The odds ratio compares the odds of an event occurring in an exposed group to the odds of it occurring in an unexposed group. Odds are calculated as:

Odds = [Probability of event] / [Probability of no event]

The odds ratio is then calculated as:

OR = [Odds in Exposed Group] / [Odds in Unexposed Group]

Example: Using the same lung cancer example, the odds of lung cancer in smokers are 100/900 = 0.11, and the odds in non-smokers are 10/990 = 0.01. The OR is therefore 0.11/0.01 = 11.

Advantages of OR:

• Can be calculated from case-control studies: This is a major advantage as case-control studies are often more efficient and cost-effective.
• Less affected by prevalence bias compared to RR.

Limitations of OR:

• Less intuitive than RR: An OR of 2 doesn't necessarily mean double the risk.
• The magnitude of the OR can vary depending on the prevalence of the outcome, particularly when the outcome is common.
• Can overestimate the RR, especially when the outcome is common in the population. The higher the prevalence of the outcome in the population, the larger the discrepancy between OR and RR tends to be.

When to Use Which?

• Relative Risk (RR): Use RR when you have cohort study data (where you follow a group of individuals over time) and you want a direct measure of the risk difference. It provides a more intuitive measure of risk increase.

• Odds Ratio (OR): Use OR when you have case-control study data (where you compare individuals with and without the outcome). It's also useful when the outcome is rare.

Interpreting OR and RR: A Summary Table

Conclusion

Both odds ratios and relative risks are valuable tools in epidemiological research. Understanding their differences, strengths, and limitations is crucial for accurately interpreting study results and making informed decisions based on the data. Always consider the study design and the prevalence of the outcome when interpreting either measure. When the outcome is rare, the OR will approximate the RR closely. However, it's essential to remember that they are not interchangeable and should be interpreted appropriately within their respective contexts.