Key Facts

RR and OR quantify the strength of association between an exposure and outcome. Correct interpretation requires understanding which study design produces which measure and the limitations of each.

Relative Risk

• RR = [a/(a+b)] / [c/(c+d)] from 2×2 table
• Measures how many times more (or less) likely exposed individuals are to develop the outcome compared to unexposed
• Only valid when incidence can be calculated (cohort studies, RCTs)
• RR = 2.0 means exposed group has twice the risk
• RR = 0.5 means exposed group has half the risk (50% reduction)

Odds Ratio

• OR = (a × d) / (b × c) from 2×2 table
• Measures the ratio of odds of exposure in cases vs controls
• Can be calculated from case-control studies, cross-sectional studies, and logistic regression
• OR approximates RR when disease is rare (<10% prevalence)
• OR always overestimates RR when RR >1 and underestimates when RR <1

Hazard Ratio

• From Cox proportional hazards regression (survival analysis)
• Accounts for time-to-event and censored data
• Interpreted similarly to RR
• Used in most RCTs with time-to-event outcomes
• HR = 0.7 means 30% reduction in hazard (instantaneous rate) at any time point

Confidence Intervals and Statistical Significance

• 95% CI: range within which the true value lies with 95% probability
• If 95% CI for RR, OR, or HR crosses 1.0: NOT statistically significant
• Wider CI = less precision (small sample size)
• Narrow CI = more precision (large sample size)

Clinical Interpretation Examples

• Smoking and lung cancer RR = 15: smokers have 15× the risk of lung cancer
• Statins in 4S trial: RR for major coronary events = 0.66 (34% relative risk reduction)
• COC and VTE: OR approximately 3-4 (3-4× increased odds of VTE)
• ARISTOTLE trial: apixaban vs warfarin HR for stroke = 0.79 (21% reduction in stroke/SE)

Common Mistakes

• Using OR when RR is appropriate (and vice versa)
• Interpreting RR of 2.0 as '100% will get disease' (it's relative, not absolute)
• Confusing statistical significance (p-value/CI) with clinical significance (effect size/NNT)
• Failing to consider baseline risk (large RR with tiny baseline risk = tiny absolute difference)
• Interpreting association as causation without considering confounding

When to Use Which Measure

• RR: cohort studies, RCTs (where incidence can be calculated)
• OR: case-control studies, logistic regression, meta-analyses (can pool ORs)
• HR: time-to-event analyses (Kaplan-Meier curves, Cox regression)
• Rate ratio: when person-time data available (accounting for variable follow-up)

Reporting Standards

• Always report 95% CI alongside point estimate
• Present both relative (RR/OR/HR) and absolute measures (ARR, NNT)
• Specify the reference group clearly
• State whether adjusted or unadjusted (and for which confounders)

From Measures of Association to Clinical Action

• Large RR/OR with narrow CI and biological plausibility → strong evidence of association
• Translate to absolute measures for patient communication (NNT, NNH)
• Consider dose-response relationship (biological gradient)
• Apply Bradford Hill criteria for causality assessment
• Use risk calculators (QRISK, FRAX) that incorporate multiple RRs for clinical decisions

• RR and OR are essential for understanding the magnitude of treatment effects and risk factor associations
• Relative measures alone can be misleading; absolute measures provide clinical context
• Meta-analyses often pool ORs across studies to generate summary estimates
• Understanding these measures is fundamental to interpreting clinical guidelines and making evidence-based decisions
• Personalised medicine increasingly uses individual risk profiles incorporating multiple RRs

OR vs RR Divergence with Prevalence

OR always overestimates RR when RR >1; more so with higher prevalence

RR Interpretation Guide