Sensitivity and specificity Study Guide

📖 Core Concepts Sensitivity (True Positive Rate): Probability test is positive given the person truly has the disease. Specificity (True Negative Rate): Probability test is negative given the person truly does not have the disease. Both are intrinsic properties of a test – they do not change with disease prevalence. Positive Predictive Value (PPV) = probability disease is present given a positive result. Negative Predictive Value (NPV) = probability disease is absent given a negative result. Likelihood Ratios combine sensitivity and specificity to show how much a result shifts disease odds. --- 📌 Must Remember Formulas Sensitivity $= \dfrac{TP}{TP+FN}$ Specificity $= \dfrac{TN}{TN+FP}$ PPV $= \dfrac{TP}{TP+FP}$ NPV $= \dfrac{TN}{TN+FN}$ Positive LR $= \dfrac{\text{sensitivity}}{1-\text{specificity}}$ Negative LR $= \dfrac{1-\text{sensitivity}}{\text{specificity}}$ Mnemonics SnNout – a Sensitive test that is Negative rules out disease. SpPin – a Specific test that is Positive rules in disease. Trade‑off: Raising the cutoff ↑ sensitivity ↓ specificity; lowering the cutoff does the opposite. ROC Curve plots sensitivity vs. $1-\text{specificity}$ for every possible cutoff; the area under the curve (AUC) summarizes overall discriminative ability. Power = Sensitivity in hypothesis‑testing language; higher power → fewer type II (false‑negative) errors. --- 🔄 Key Processes Compute Sensitivity & Specificity from a 2 × 2 table Fill counts: TP, FP, TN, FN. Apply formulas above. Derive Predictive Values (need disease prevalence or pre‑test probability). Create an ROC Curve For each possible cutoff, calculate sensitivity & $1-\text{specificity}$. Plot points, connect them; compute AUC if required. Calculate Likelihood Ratios Use LR⁺ and LR⁻ formulas; then apply Bayes’ theorem to update pre‑test odds to post‑test odds. Construct a 95 % Confidence Interval (e.g., Wilson score) for sensitivity or specificity when sample size is modest. --- 🔍 Key Comparisons Sensitivity vs. Specificity Goal: Sensitivity → “rule out” (SnNout); Specificity → “rule in” (SpPin). Screening Test vs. Diagnostic Test Screening: high sensitivity, tolerates false positives. Diagnostic: high specificity, tolerates false negatives. PPV vs. Sensitivity PPV depends on prevalence; Sensitivity does not. ROC AUC vs. Single Cutoff Metrics AUC reflects overall test performance across all thresholds; a single sensitivity/specficity pair reflects performance at one chosen threshold. --- ⚠️ Common Misunderstandings “100 % sensitivity = perfect test” – only true for ruling out disease; the test may have 0 % specificity (all positives). Confusing PPV with sensitivity – PPV changes with prevalence, sensitivity does not. Assuming LR⁺ > 1 always means disease is present – must still consider pre‑test probability; a modest LR⁺ on a low‑prevalence disease may not change odds much. Treating a single measure (e.g., only sensitivity) as sufficient – clinical decisions require both sensitivity, specificity, and prevalence context. --- 🧠 Mental Models / Intuition “Net” analogy: Sensitivity is the size of the net catching diseased fish; specificity is the tightness that lets healthy fish slip through. Likelihood Ratio as “Odds Multiplier”: LR⁺ multiplies pre‑test odds to give post‑test odds when the test is positive; LR⁻ does the same when negative. ROC Curve as “Performance Landscape”: The farther the curve bows toward the upper left corner, the better the test can separate disease from health regardless of cutoff. --- 🚩 Exceptions & Edge Cases Very low prevalence → PPV can be low even with high specificity; NPV remains high. Small sample sizes → point estimates of sensitivity/specificity become unstable; confidence intervals widen dramatically. Tests with perfect sensitivity or specificity are rare; if observed, suspect verification bias or mis‑classification of the gold standard. --- 📍 When to Use Which Screening → Choose a test with ≥ 90 % sensitivity; accept lower specificity. Confirmatory Diagnosis → Prioritize ≥ 90 % specificity; tolerate lower sensitivity. Estimating disease probability → Use LR⁺ / LR⁻ with Bayes’ theorem instead of raw sensitivity/specificity. Comparing two tests → Look at AUC of ROC curves; if AUCs are similar, compare at the clinically relevant cutoff. --- 👀 Patterns to Recognize High sensitivity + negative result → disease is unlikely (SnNout). High specificity + positive result → disease is likely (SpPin). ROC curve hugging the left‑hand border → excellent discrimination. LR⁺ > 10 or LR⁻ < 0.1 → strong evidence to rule in/out disease. --- 🗂️ Exam Traps Choosing PPV when the question asks for sensitivity – remember PPV varies with prevalence. Selecting a test with 100 % sensitivity as “best” – ignore the accompanying 0 % specificity unless the question explicitly wants a rule‑out scenario. Confusing false‑positive rate with (1‑specificity) – they are the same, but many students write the opposite; double‑check the formula. Misreading “SnNout” as “sensitive test, negative = rule in” – the mnemonic’s “OUT” signals rule out. Assuming ROC AUC = 0.5 means the test is useless – 0.5 is indeed random, but sometimes a question will give an AUC of 0.7 and expect you to say “moderate discrimination”. ---