Relative Risk, Odds Ratios, Absolute Risk Reduction, and Attributable Risk

Relative Risk

Definition

RR compares the probability of an event occurring in the treatment group to the probability in the control group.¹

Formula

RR = Risk in Treatment Group/Risk in Control Group

Interpretation

• RR = 1: No difference between groups.
• RR > 1: Increased risk in the treatment group.
• RR < 1: Decreased risk in the treatment group.

Example

If 10% of patients receiving a new anesthetic agent experience postoperative nausea, compared to 20% with the standard agent, the RR is 0.5, indicating a 50% reduction in risk.

Calculation

Assumptions and Limitations

The validity of RR relies on key assumptions.

• RR requires that the exposures or interventions are independent and do not influence each other.²
• RR works best in studies that track participants over time.^1,2
  • Therefore, this measure is limited to cohort studies and randomized controlled trials (RCTs) because incidence data are necessary for calculations.^1,2
  • RR is unsuitable for case-control studies.^1,3
• In populations with low event rates, RR may overstate the clinical significance of findings.³
• A 95% confidence interval (CI) around RR reflects the precision of the estimate. If the CI is narrow, the estimate is considered reliable, while a CI crossing 1 indicates no statistically significant difference between groups.^1,2

Odds Ratio

Definition

OR compares the odds of an event occurring in the treatment group to those in the control group.¹

Formula

OR = Odds in Treatment Group/Odds in Control Group

Interpretation

• OR = 1: No difference between groups.
• OR > 1: Increased odds in the treatment group.
• OR < 1: Decreased odds in the treatment group.

Example

In a study, if 30 out of 300 patients in the intubation group experience laryngeal injury, compared to 10 out of 300 in the supraglottic airway group, the OR is approximately 3.22, indicating higher odds of injury with intubation.

Calculation

Assumptions and Limitations

• OR is most appropriate for case-control and retrospective studies where incidence rates are not directly available.^1,5
• OR can overestimate risk when the event is common.^1,3
• OR approximates RR accurately when the event is rare.^1,5
• CIs are crucial for interpreting OR, as a wide CI reflects uncertainty, often due to small sample sizes. If the CI does not cross 1, the OR suggests a statistically significant difference between groups.^1,5

Absolute Risk Reduction

Definition

ARR is the absolute difference in event rates between the control and treatment groups.¹

Formula

ARR = (Risk in Control Group) – (Risk in Treatment Group)

Interpretation

ARR quantifies the actual decrease in risk provided by the treatment.¹

One of the most critical applications of ARR is calculating the number needed to treat (NNT) and number needed to harm (NNH).

NNT indicates how many patients must receive the intervention to prevent one additional adverse event.¹ This measure offers a straightforward way to express treatment effectiveness in patient terms.¹

• Formula: 1/ARR
• Clinical Relevance: A lower NNT signifies a more effective treatment, while higher values suggest modest benefits.¹

NNH indicates how many patients need to be treated for one additional patient to experience an adverse effect.⁴

• Formula: 1/(Absolute Risk Increase)
• Clinical Relevance: A higher NNH signifies that harm is less frequent, implying better safety.⁴

Example

If a nerve block reduces the incidence of chronic postsurgical pain from 15% to 5%, the ARR is 10%, meaning there’s a 10% absolute reduction in risk. The number needed to treat is 10, meaning that 10 patients must receive the intervention to prevent one case of chronic postsurgical pain.

In this example, if the risk for nerve injury increases from 1% to 5%, the Absolute Risk Increase (ARI) would be 4%. Therefore, the number needed to harm is 25, meaning that for every 25 patients who receive the nerve block, one additional patient will experience a nerve injury.

Calculation

Assumptions and Limitations

• ARR assumes the baseline risk does not change between groups.⁶
• This measure is highly sensitive to sample size, i.e., smaller studies may produce wide variability in ARR estimates.⁷
• A narrow CI around ARR reflects greater precision and confidence in the result, while a wide CI suggests uncertainty.⁶

Attributable Risk

Definition

AR, also known as risk difference, measures the difference in risk between exposed and unexposed groups.⁸

Formula

AR = (Risk in Exposed Group) – (Risk in Unexposed Group)

Interpretation

AR indicates the proportion of incidents in the exposed group that can be attributed to the exposure.⁸

Example

If the incidence of perioperative respiratory complications is 8% in smokers and 2% in nonsmokers, the AR is 6%, suggesting that smoking accounts for a 6% increase in complications. The AR percentage is 75%, meaning that 75% of complications in smokers can be attributed to smoking.

Calculation