Core Curriculum
Module 3: Measures of Association & Data Analysis
Core Topics
Relative risk, odds ratio, hazard ratio, NNT, NNH, PAR% — the essential tools for quantifying exposure‑outcome relationships and assessing clinical and public health impact.
📊 3.1 Relative Risk (RR) and Odds Ratio (OR)
Relative Risk (RR) compares the likelihood of an outcome between exposed and unexposed groups. Used in cohort studies and RCTs.
Odds Ratio (OR) is used in case‑control studies and logistic regression. OR = (a×d) / (b×c). Under the rare disease assumption (outcome prevalence <10%), OR ≈ RR. For common outcomes, OR overestimates RR (further from 1).
📌 Clinical takeaway: RR is the preferred measure when incidence can be calculated; OR is the only valid measure in case‑control designs.
⏱️ 3.2 Hazard Ratio (HR) and Survival Analysis
Hazard Ratio (HR) is the ratio of instantaneous event rates between two groups over time, derived from Cox proportional hazards regression. It handles censored data and does not require specifying the baseline hazard.
HR = (hazard in exposed) / (hazard in unexposed)
HR = 1 → no difference; HR > 1 → higher instantaneous risk; HR < 1 → lower risk.
Proportional hazards assumption: The HR is constant over time. If survival curves cross, the assumption is violated.
📈 HR vs. RR: RR measures cumulative risk over the entire follow‑up; HR measures risk at any moment. HR is preferred for time‑to‑event outcomes (cancer survival, cardiovascular events).
💊 3.3 Absolute Measures and Clinical Impact
Absolute Risk Reduction (ARR)
= Riskcontrol – Risktreatment
Number Needed to Treat (NNT)
= 1 / ARR
(e.g., NNT = 20 → treat 20 to prevent 1 event)
Absolute Risk Increase (ARI)
= Riskexposed – Riskunexposed
Number Needed to Harm (NNH)
= 1 / ARI
(e.g., NNH = 50 → expose 50 to cause 1 harm)
Attributable Risk (AR) = Incidenceexposed – Incidenceunexposed (excess risk due to exposure).
📐 Clinical relevance: NNT and NNH communicate absolute effects to patients; they vary with baseline risk and are essential for shared decision making.
🌍 3.4 Population‑Level Impact
Population Attributable Risk (PAR) = Incidencetotal – Incidenceunexposed — the excess burden of disease in the entire population attributable to the exposure.
PAR% (Population Attributable Risk Percent)
PAR% = [Pe(RR – 1)] / [1 + Pe(RR – 1)] × 100
where Pe = proportion of the population exposed.
PAR% represents the proportion of disease in the total population that would be eliminated if the exposure were removed. It guides public health priorities (e.g., smoking and lung cancer).
📌 Example: If 40% of the population smokes and RR for lung cancer is 10, PAR% = [0.4×9]/[1+0.4×9] = 3.6/4.6 ≈ 78% of lung cancer cases attributable to smoking.