Relative risk Study Guide

📖 Core Concepts Relative Risk (RR) – Ratio of the probability (risk) of an outcome in an exposed group to that in an unexposed group. Incidence Rate – New cases ÷ persons at risk in a given time period; used in the RR formula. Protective vs. Risk Factor – RR < 1 → exposure lowers risk (protective); RR > 1 → exposure raises risk (risk factor). Absolute Risk – Probability of the outcome in a single group, without comparison. Relative Risk Reduction (RRR) – $1 - RR$; expresses the proportionate drop in risk due to an exposure. --- 📌 Must Remember RR formula: $RR = \dfrac{I{\text{exposed}}}{I{\text{unexposed}}} = \dfrac{a/(a+b)}{c/(c+d)}$. Standard error of $\ln RR$: $\text{SE}(\ln RR)=\sqrt{\frac{1}{a}-\frac{1}{a+b}+\frac{1}{c}-\frac{1}{c+d}}$. CI for RR: compute CI on $\ln RR$ → exponentiate limits. RR > 1 does not prove causation; confounding can create spurious associations. Rare disease rule: When the outcome is rare, odds ratio ≈ RR. Always pair RR with absolute risk (or risk difference) to avoid the base‑rate fallacy. --- 🔄 Key Processes Build a 2 × 2 table | | Outcome Yes (a/c) | Outcome No (b/d) | |----------------|-------------------|------------------| | Exposed | a | b | | Unexposed | c | d | Compute point estimate $RR = \dfrac{a/(a+b)}{c/(c+d)}$. Calculate SE of $\ln RR$ using the formula above. Construct confidence interval $\ln RR \pm z{\alpha/2}\times \text{SE}(\ln RR)$. Exponentiate lower and upper bounds to get CI for RR. Interpret RR < 1 → protective; RR > 1 → risk factor. Check absolute risks to gauge real‑world impact. --- 🔍 Key Comparisons RR vs. Odds Ratio (OR) RR compares probabilities; OR compares odds. OR ≈ RR only when the outcome is rare. Cohort/Randomized Trial vs. Case‑Control Cohort/RT → can estimate RR directly. Case‑Control → incidence fixed; use OR instead. Relative vs. Absolute Measures RR tells how many times risk changes. Absolute risk shows the actual probability change. --- ⚠️ Common Misunderstandings “RR = 2 means 200 % increase” – Correct phrasing: “risk is twice as high.” Ignoring baseline risk – A large RR with a tiny baseline risk may be clinically negligible. Treating OR as RR for common outcomes – Leads to exaggerated effect size. Assuming causality from RR > 1 – Confounders can produce spurious associations. --- 🧠 Mental Models / Intuition “Risk multiplier” – Think of RR as a slider that multiplies the baseline probability. If baseline = 5 % and RR = 3, the new risk ≈ 15 %. “Log‑scale symmetry” – Working with $\ln RR$ makes the confidence interval symmetric; exponentiating brings it back to the original scale. “Base‑rate anchor” – Always anchor the RR to the underlying absolute risk; the anchor tells you whether the multiplier matters. --- 🚩 Exceptions & Edge Cases Very rare outcomes – OR ≈ RR; reporting OR is acceptable. Very common outcomes – OR can vastly overstate effect; prefer RR. Zero cells in 2 × 2 table – Add a continuity correction (e.g., +0.5) before computing RR and SE. --- 📍 When to Use Which Use RR when you have incidence data (cohort, RCT) and want an intuitive risk comparison. Use OR in case‑control studies or when fitting logistic regression; convert to RR only if the outcome is rare. Present both RR and absolute risk (or risk difference) when the baseline rate is low or high, to avoid the base‑rate fallacy. --- 👀 Patterns to Recognize RR > 1 + low baseline → small absolute change (e.g., RR = 4 but baseline 0.1 % → absolute increase ≈ 0.3 %). RR ≈ 1 + high baseline → potentially important absolute change (e.g., RR = 1.2 with baseline 30 % → absolute increase ≈ 6 %). Confidence interval crossing 1 → effect not statistically significant. --- 🗂️ Exam Traps Choosing OR when RR is available – test‑writers often expect RR for cohort data. Interpreting “2‑fold increase” as 200 % increase – answer choice may say “risk doubles,” which is correct; “risk increases by 200 %” is wrong. Ignoring the confidence interval – a point estimate of RR = 1.5 with CI = 0.9–2.5 is not a significant finding. Base‑rate fallacy – a large RR (e.g., 5) with a tiny baseline (0.01 %) may be a distractor; the correct answer will emphasize the small absolute risk. ---