Absolute risk, relative risk, relative risk reduction & number needed to treat
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Absolute risk (AR)
Absolute risk is the probability (or incidence) of an individual in a specific group experiencing a particular event or outcome over a defined period of time.Note: Outcome event typically refers to the worst outcome, such as disease occurrence, death, or complication.
| Group | Outcome Event | No Outcome Event | Total |
|---|---|---|---|
| Treatment | a | b | a + b |
| Control | c | d | c + d |
| Total | a + c | b + d | n = a + b + c + d |
Calculation:
- ART (absolute risk in treatment group) = a / (a + b)
- ARC (absolute risk in control group) = c / (c + d)
Absolute risk reduction (ARR)
Absolute risk is often interpreted using absolute risk reduction (ARR). ARR is the difference in absolute risk between control and treatment groups.
Calculation:
ARR = ARC - ART
Interpretation: Shows how much the treatment reduces the risk of the outcome in absolute terms.
Note if the risk is increased in the treatment group the term absolute risk increase (ARI), also called absolute increase in risk, is used
ARI = ART - ARC
Terminology
- The absolute risk in control group (ARC) may also be referred to as the control event rate (CER)
- The absolute risk in treatment group (ART) may also be referred to as the experimental event rate (EER)
Relative risk (RR)
Relative risk is the ratio of the probability (risk) of an event occurring in an exposed or treatment group to the probability of the event occurring in a control or unexposed group.
The term relative risk ratio, or just risk ratio, is sometimes used instead of relative risk.
Calculation:
RR = ART ÷ ARC
Interpretation:
- RR = 1 → No difference in risk
- RR < 1 → Treatment reduces risk
- RR > 1 → Treatment increases risk
Relative Risk is defined as the incidence of outcome in intervention group DIVIDED by the Incidence of outcome in control group
Relative risk reduction (RRR)
Relative risk reduction describes the proportion by which the treatment reduces the risk relative to the control group.Calculation:
RRR = (ARC - ART) / ARC or
RRR = 1 - RR
Interpretation: Tells you how much the risk is reduced in proportional terms.
Relative risk reduction (RRR) or relative risk increase (RRI) is calculated by dividing the absolute risk change by the absolute risk in control group
Number needed to treat (NNT)
NNT describes the number of patients who need to be treated to prevent one additional adverse event.Calculation:
NNT = 1 / ARR
Interpretation:
- Lower NNT = more effective treatment
- NNT = 1 means every treated patient benefits
- Higher NNT means more people need to be treated for one to benefit
Number needed to harm (NNH)
NNH describes the number of patients who need to be treated for one additional person to experience an adverse or harmful outcome.
Calculation:
NNH = 1 / Absolute risk increase
Interpretation:
- Lower NNH = more harmful
- If treatment increases risk, NNT becomes negative and is interpreted as NNH
Comparing NNT and NNH
The NNT:NNH ratio helps assess benefit versus harm.
Must be interpreted in clinical context, a high NNT might still be acceptable for a rare but serious outcome.
Real world clinical example: statins in primary prevention
In a study of 1,000 patients without prior heart disease:
Control group (no statin): 20 heart attacks
→ ARC = 20 / 1000 = 0.02 (2%)
Treatment group (statin): 10 heart attacks
→ ART = 10 / 1000 = 0.01 (1%)
Calculations:
Interpretation: You need to treat 100 people with statins to prevent 1 heart attack over the study period. The relative risk is reduced by 50%, but the absolute benefit is only 1%.
In a study of 1,000 patients without prior heart disease:
Control group (no statin): 20 heart attacks
→ ARC = 20 / 1000 = 0.02 (2%)
Treatment group (statin): 10 heart attacks
→ ART = 10 / 1000 = 0.01 (1%)
Calculations:
- ARR = 0.02 - 0.01 = 0.01 (1%)
- RR = 0.01 / 0.02 = 0.5
- RRR = (0.02 - 0.01) / 0.02 = 0.5 (50%)
- NNT = 1 / 0.01 = 100
Interpretation: You need to treat 100 people with statins to prevent 1 heart attack over the study period. The relative risk is reduced by 50%, but the absolute benefit is only 1%.
Key Points
- Relative measures (RR, RRR) can exaggerate perceived benefits.
- Absolute measures (ARR, NNT) are more informative for clinical decision-making.
- Use both in context to weigh risks, benefits, and cost-effectiveness of treatments.