Relative Risk and Risk Difference
Comparing risk as a ratio and as a difference
Relative risk (risk ratio) divides the probability of an outcome in an exposed group by that in an unexposed group, expressing how many times more likely the outcome is. The risk difference (absolute risk reduction) subtracts the two probabilities, showing the absolute size of the change. Relative measures can look dramatic while the absolute change is tiny, so both should be reported together for a complete and honest interpretation.
Concept and Formula
Both measures compare the risk in two groups, but do so in different ways. Relative risk (RR) gives the ratio of the risk in the exposed group R1 to the risk in the unexposed group R0: RR = R1 / R0. RR = 1 signals no difference, RR > 1 signals increased risk, and RR < 1 signals decreased risk. The risk difference (RD) subtracts the two probabilities: RD = R1 - R0. RD = 0 means no difference, positive values indicate a harmful exposure, and negative values indicate a protective effect. Both formulas rest on a basic probability or proportion estimate.
How to Compute and Read Them
Consider a 2x2 table where a is exposed cases, b is exposed non-cases, c is unexposed cases, and d is unexposed non-cases. Then R1 = a / (a + b) and R0 = c / (c + d); apply the formulas above to get RR and RD. Confidence intervals should be reported for both: a log-transform-based interval is standard for RR, while a normal approximation is common for RD. In practical terms, RR = 2 means the outcome occurs twice as often, whereas RD = 0.05 means 5 additional people per 100 in the exposed group are affected.
Common Misuses and Misconceptions
The most common error is interpreting relative risk as if it were an absolute risk. When the baseline risk is very low, even a high RR such as 3 can correspond to a tiny absolute difference; for example the gap between R0 = 0.001 and R1 = 0.003 is only 2 per 1000. Conversely, RD can mislead when taken out of context: the same absolute gap looks far less impressive relative to a high baseline risk. Another frequent confusion is treating odds ratio as equivalent to risk ratio; for common outcomes the odds ratio substantially overstates RR. Correct reporting always includes both relative and absolute measures.
Why It Matters and How to Report It
Relative and absolute measures answer different questions: relative risk is suited to understanding biological effect size and mechanism, while risk difference is essential for estimating how many people are actually affected in clinical or policy decisions. Reporting both together is standard epidemiological practice. Reporting guidelines such as STROBE and CONSORT require that both measures be presented with their confidence intervals. Researchers should always address both dimensions when interpreting results, and must not highlight only dramatic ratios while obscuring the size of the absolute change.
Sources
- Rothman, K. J., Greenland, S., & Lash, T. L. (2008). Modern Epidemiology (3rd ed.). Lippincott Williams & Wilkins. ISBN: 978-0-7817-5564-1