Morning Rounds \u00b7 PSM Numericals \u00b7 Round 03<\/title>\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=Playfair+Display:ital,wght@0,400;0,600;0,700;1,400;1,600&family=Source+Serif+4:ital,wght@0,300;0,400;0,600;1,400&display=swap\" rel=\"stylesheet\">\n<style>\n#nps03 *,#nps03 *::before,#nps03 *::after{box-sizing:border-box;margin:0;padding:0}\n#nps03{\n --ob:#1A5F7A;--ob-light:#236E8C;--ob-pale:#E6F3F7;--ob-dark:#114455;\n --correct:#2D6B47;--correct-bg:#EAF6EF;--correct-border:#3A9960;\n --wrong:#B83232;--wrong-bg:#FDF0F0;--wrong-border:#E53935;\n --ink:#0F2A35;--ink-mid:#2A4D5A;--ink-soft:#5A7D8A;\n --line:#B8D8E3;--cream:#F2F8FA;--warm:#F8FCFD;\n font-family:'Source Serif 4',Georgia,serif;\n font-size:16px;color:var(--ink);background:var(--cream);\n line-height:1.7;padding:0 0 64px;\n}\n#nps03 .mr-header{background:linear-gradient(135deg,var(--ob-dark) 0%,var(--ob) 60%,var(--ob-light) 100%);color:#E4F4F9;padding:36px 24px 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.mr-ring::before{content:'';position:absolute;width:76px;height:76px;border-radius:50%;background:var(--warm);}\n#nps03 .mr-ring-in{position:relative;display:flex;flex-direction:column;align-items:center;line-height:1.2}\n#nps03 .mr-ring-pct{font-family:'Playfair Display',serif;font-size:1.3rem;font-weight:700;color:var(--ob)}\n#nps03 .mr-ring-sub{font-size:0.54rem;color:var(--ink-soft);text-transform:uppercase;letter-spacing:0.06em}\n#nps03 .mr-score-title{font-family:'Playfair Display',serif;font-size:1.15rem;font-weight:700;color:var(--ink);margin-bottom:4px}\n#nps03 .mr-score-net{font-size:0.9rem;color:var(--ob);font-weight:600;margin-bottom:4px}\n#nps03 .mr-verdict{font-size:0.83rem;color:var(--ink-soft);font-style:italic;margin-bottom:18px;padding:0 12px}\n#nps03 .mr-bands{display:flex;justify-content:center;gap:10px;flex-wrap:wrap}\n#nps03 .mr-band{padding:5px 13px;border-radius:16px;font-size:0.78rem;font-weight:600}\n#nps03 .mr-band-c{background:var(--correct-bg);color:var(--correct)}\n#nps03 .mr-band-w{background:var(--wrong-bg);color:var(--wrong)}\n#nps03 .mr-band-s{background:var(--ob-pale);color:var(--ob)}\n#nps03 .mr-retry{display:block;margin:18px auto 4px;background:transparent;border:2px solid var(--ob);color:var(--ob);border-radius:8px;padding:9px 28px;font-family:'Playfair Display',serif;font-size:0.92rem;font-weight:700;cursor:pointer;}\n#nps03 .mr-retry:hover{background:var(--ob);color:#E4F4F9}\n@media(max-width:480px){\n #nps03 .mr-title{font-size:1.4rem}\n #nps03 .mr-num{font-size:1.7rem}\n #nps03 .mr-stem{font-size:0.9rem}\n #nps03 .mr-opt-text{font-size:0.86rem}\n}\n<\/style>\n\n<div id=\"nps03\">\n\n <div class=\"mr-header\">\n <div class=\"mr-series-tag\">Numerical Series · PSM Biostatistics<\/div>\n <div class=\"mr-eyebrow\">Morning Rounds · Round 03 of 07<\/div>\n <div class=\"mr-title\">PPV, NPV &<br><em>The Prevalence Effect<\/em><\/div>\n <div class=\"mr-subtitle\">Five questions · Row-based metrics, how prevalence shifts them & what a positive result actually means<\/div>\n <div class=\"mr-chips\">\n <span class=\"mr-chip\">5 Questions<\/span>\n <span class=\"mr-chip\">+4 \/ −1 scoring<\/span>\n <span class=\"mr-chip\">Options reshuffled<\/span>\n <\/div>\n <\/div>\n\n <div class=\"mr-sentinel\" id=\"nps03-sentinel\"><\/div>\n\n <div class=\"mr-progress\" id=\"nps03-progress\">\n <div class=\"mr-prog-inner\">\n <div class=\"mr-pips\" id=\"nps03-pips\"><\/div>\n <\/div>\n <\/div>\n\n <div class=\"mr-body\">\n <div id=\"nps03-cases\"><\/div>\n <div class=\"mr-submit-wrap\">\n <button class=\"mr-btn\" id=\"nps03-submit\">Submit for Debrief<\/button>\n <\/div>\n <div class=\"mr-score\" id=\"nps03-score\">\n <div class=\"mr-score-in\">\n <div class=\"mr-score-ey\">Round Complete<\/div>\n <div class=\"mr-ring\" id=\"nps03-ring\">\n <div class=\"mr-ring-in\">\n <span class=\"mr-ring-pct\" id=\"nps03-pct\">0%<\/span>\n <span class=\"mr-ring-sub\">net<\/span>\n <\/div>\n <\/div>\n <div class=\"mr-score-title\">Your Debrief<\/div>\n <div class=\"mr-score-net\" id=\"nps03-net\"><\/div>\n <div class=\"mr-verdict\" id=\"nps03-verdict\"><\/div>\n <div class=\"mr-bands\">\n <span class=\"mr-band mr-band-c\" id=\"nps03-ct-c\"><\/span>\n <span class=\"mr-band mr-band-w\" id=\"nps03-ct-w\"><\/span>\n <span class=\"mr-band mr-band-s\" id=\"nps03-ct-s\"><\/span>\n <\/div>\n <button class=\"mr-retry\" id=\"nps03-retry\">↻ New Round<\/button>\n <\/div>\n <\/div>\n <\/div>\n\n<\/div>\n\n<script>\n(function () {\n 'use strict';\n\n var NS = 'nps03';\n var TOTAL = 5;\n var MAX = 20;\n var LTRS = ['A','B','C','D'];\n\n var QS = [\n\n {\n id: 1,\n tag: 'PPV — Calculation from the Table',\n stem: 'A screening test for hepatitis C yields the following results in 1000 patients: <strong>TP=90, FN=10, FP=180, TN=720<\/strong>. What is the <strong>positive predictive value (PPV)<\/strong>?',\n correct: '33.3%',\n opts: [\n '33.3%',\n '90%',\n '50%',\n '80%'\n ],\n exp: 'PPV = <strong>TP ÷ (TP + FP)<\/strong> \u2014 of all who test positive, what proportion truly have the disease?<span class=\"calc\">All test-positive = TP + FP = 90 + 180 = 270<br>PPV = 90 ÷ 270 = <strong>0.333 = 33.3%<\/strong><\/span>This means only 1 in 3 people with a positive result actually has hepatitis C. Two in three positives are false alarms. This is the clinical weight of PPV: it tells the clinician what to do with a positive result.<br><br>Trap 90% is the sensitivity (TP ÷ disease total = 90 ÷ 100). Trap 80% is the specificity (TN ÷ non-disease total = 720 ÷ 900). Trap 50% has no basis in this table. The denominator for PPV is the <strong>positive test row<\/strong> \u2014 TP+FP \u2014 not any disease column. This is the row vs column distinction that separates PPV from sensitivity.'\n },\n\n {\n id: 2,\n tag: 'NPV — Calculation and Meaning',\n stem: 'Using the same hepatitis C data (TP=90, FN=10, FP=180, TN=720), what is the <strong>negative predictive value (NPV)<\/strong>, and what does it tell the clinician?',\n correct: '98.6%; of all who test negative, 98.6% are truly disease-free \u2014 a negative result is highly reliable here',\n opts: [\n '98.6%; of all who test negative, 98.6% are truly disease-free \u2014 a negative result is highly reliable here',\n '98.6%; of all disease-free patients, 98.6% test negative \u2014 confirming high specificity of the test',\n '72%; calculated as TN divided by the total population, reflecting the proportion correctly identified overall',\n '93.5%; calculated as the complement of the false negative rate, which equals FNR subtracted from 100%'\n ],\n exp: 'NPV = <strong>TN ÷ (TN + FN)<\/strong> \u2014 of all who test negative, what proportion are truly disease-free?<span class=\"calc\">All test-negative = TN + FN = 720 + 10 = 730<br>NPV = 720 ÷ 730 = <strong>0.9863 = 98.6%<\/strong><\/span>A negative result in this test is very reassuring \u2014 98.6% chance the patient is truly disease-free. This high NPV is largely because the disease is rare in this sample (prevalence = 100 ÷ 1000 = 10%), so most negatives are true negatives.<br><br>Trap B describes specificity, not NPV. Specificity = TN ÷ (TN+FP); NPV = TN ÷ (TN+FN) \u2014 different denominators, different meanings. Trap C divides by total population. Trap D confuses complement of FNR (= sensitivity) with NPV. NPV denominator = all test-negative = TN+FN.'\n },\n\n {\n id: 3,\n tag: 'Prevalence Effect — PPV Falls as Prevalence Falls',\n stem: 'The same test (sensitivity 90%, specificity 80%) is applied in <strong>two populations of 1000<\/strong>: Population A has <strong>10% prevalence<\/strong>, Population B has <strong>1% prevalence<\/strong>. Without calculating, which statement correctly predicts what happens to PPV?',\n correct: 'PPV falls substantially in Population B; lower prevalence floods the positive pool with false positives from the large non-diseased majority',\n opts: [\n 'PPV falls substantially in Population B; lower prevalence floods the positive pool with false positives from the large non-diseased majority',\n 'PPV rises in Population B; a lower prevalence means fewer diseased people compete for positive test slots, increasing the proportion of true positives',\n 'PPV remains unchanged in Population B; it is a fixed property of the test like sensitivity and specificity',\n 'PPV falls in Population B only if specificity is below 90%; at 80% specificity the effect is too small to be clinically significant'\n ],\n exp: 'This is the central insight of this round. As prevalence falls, the non-diseased population grows. Even a small false positive rate (here 20%) applied to a large non-diseased population generates <strong>many false positives<\/strong>. Meanwhile, the true positive pool shrinks because fewer people have the disease.<span class=\"calc\">Population A (10% prevalence, n=1000):<br>Diseased=100, Non-diseased=900<br>TP = 0.90×100 = 90, FP = 0.20×900 = 180<br>PPV = 90÷(90+180) = 90÷270 = <strong>33.3%<\/strong><br><br>Population B (1% prevalence, n=1000):<br>Diseased=10, Non-diseased=990<br>TP = 0.90×10 = 9, FP = 0.20×990 = 198<br>PPV = 9÷(9+198) = 9÷207 = <strong>4.3%<\/strong><\/span>PPV crashed from 33% to 4% with the same test. Sensitivity and specificity did not change. This is why a positive result from a screening programme applied to a low-prevalence general population requires confirmation before action.'\n },\n\n {\n id: 4,\n tag: 'Prevalence Effect — NPV Rises as Prevalence Falls',\n stem: 'Using the same two populations from Q3 (sensitivity 90%, specificity 80%), what happens to <strong>NPV<\/strong> as prevalence falls from 10% to 1%?',\n correct: 'NPV rises from 98.6% to 99.9%; lower prevalence means most test-negatives are true negatives, making a negative result even more reliable',\n opts: [\n 'NPV rises from 98.6% to 99.9%; lower prevalence means most test-negatives are true negatives, making a negative result even more reliable',\n 'NPV falls as prevalence falls; fewer diseased people means fewer true negatives, reducing the reliability of a negative result',\n 'NPV remains at 98.6% in both populations; like specificity, it is independent of disease prevalence',\n 'NPV rises to 99.9% but becomes clinically useless; in low-prevalence settings negative results carry no diagnostic weight'\n ],\n exp: '<span class=\"calc\">Population A (10% prevalence):<br>FN = 0.10×100 = 10, TN = 0.80×900 = 720<br>NPV = 720÷(720+10) = 720÷730 = <strong>98.6%<\/strong><br><br>Population B (1% prevalence):<br>FN = 0.10×10 = 1, TN = 0.80×990 = 792<br>NPV = 792÷(792+1) = 792÷793 = <strong>99.9%<\/strong><\/span>As prevalence falls: TN pool grows (more disease-free people correctly cleared), FN pool shrinks (fewer diseased people to miss). NPV = TN÷(TN+FN) rises toward 100%.<br><br>The paired lesson: <strong>PPV and NPV move in the same direction as prevalence<\/strong> \u2014 both rise with rising prevalence, both fall with falling prevalence? No \u2014 they move in <em>opposite<\/em> directions. PPV rises with prevalence. NPV falls with prevalence. This asymmetry is the exam trap. Trap B incorrectly inverts NPV direction. Trap D is wrong: a highly reliable negative result is clinically valuable, not useless.'\n },\n\n {\n id: 5,\n tag: 'PPV — Clinical Application in Low-Prevalence Screening',\n stem: 'A national programme screens all adults for a rare autoimmune condition (prevalence <strong>0.5%<\/strong>). The test has sensitivity 95% and specificity 95%. A 35-year-old woman tests positive. She is told she \"almost certainly has the disease.\" Is this statement accurate?',\n correct: 'No; with 0.5% prevalence and 95% specificity, PPV is approximately 8.7% \u2014 fewer than 1 in 10 positive results represent true disease',\n opts: [\n 'No; with 0.5% prevalence and 95% specificity, PPV is approximately 8.7% \u2014 fewer than 1 in 10 positive results represent true disease',\n 'Yes; a test with 95% sensitivity and 95% specificity is highly accurate and a positive result reliably indicates disease',\n 'No; with 0.5% prevalence, the test should not have been offered at all since no screening test performs adequately below 1% prevalence',\n 'Yes; sensitivity of 95% means 95% of positive results are true positives, confirming the statement is correct'\n ],\n exp: '<span class=\"calc\">Population of 10,000 (prevalence 0.5%):<br>Diseased = 50, Non-diseased = 9950<br>TP = 0.95 × 50 = 47.5 ≈ 48<br>FP = 0.05 × 9950 = 497.5 ≈ 498<br>PPV = 48 ÷ (48+498) = 48 ÷ 546 = <strong>8.8%<\/strong><\/span>Even with a 95%\/95% test \u2014 which sounds excellent \u2014 fewer than 1 in 10 positive results represents true disease when prevalence is 0.5%. The other 9 in 10 are false alarms.<br><br>This is the <strong>base rate fallacy<\/strong> in medicine: interpreting test results without accounting for prior probability (prevalence). The statement \"almost certainly has the disease\" is dangerously wrong. This woman needs confirmatory testing before any diagnosis or treatment. Trap B confuses test accuracy with PPV. Trap D is the most common misconception: sensitivity tells you about diseased people, not about positive results. Trap C invents a 1% rule that does not exist.'\n }\n\n ];\n\n var answers = {}, answered = 0, shuffled = {}, done = false;\n\n function gid(s) { return document.getElementById(NS + '-' + s); }\n function byId(s) { return document.getElementById(s); }\n\n function shuffleArr(arr) {\n var a = arr.slice(), i, j, t;\n for (i = a.length - 1; i > 0; i--) {\n j = Math.floor(Math.random() * (i + 1));\n t = a[i]; a[i] = a[j]; a[j] = t;\n }\n return a;\n }\n\n function countVal(v) {\n var n = 0, k;\n for (k in answers) { if (answers[k] === v) n++; }\n return n;\n }\n\n function buildPips() {\n var cont = gid('pips'), i, q, wLine, wPip, line, pip;\n cont.innerHTML = '';\n for (i = 0; i < QS.length; i++) {\n q = QS[i];\n if (i > 0) {\n wLine = document.createElement('div');\n wLine.className = 'mr-pip-wrap';\n line = document.createElement('div');\n line.className = 'mr-pip-line';\n line.id = NS + '-pl' + q.id;\n wLine.appendChild(line);\n cont.appendChild(wLine);\n }\n wPip = document.createElement('div');\n wPip.className = 'mr-pip-wrap';\n pip = document.createElement('div');\n pip.className = 'mr-pip';\n pip.id = NS + '-pip' + q.id;\n pip.textContent = String(q.id);\n wPip.appendChild(pip);\n cont.appendChild(wPip);\n }\n }\n\n function build() {\n var cont, i, q, opts, card, top, numDiv, meta, tag, stem,\n rule, optsDiv, expDiv, lbl, txt, j, optEl, ltrSpan, txtSpan;\n\n cont = gid('cases');\n cont.innerHTML = '';\n answers = {}; answered = 0; shuffled = {}; done = false;\n gid('score').style.display = 'none';\n buildPips();\n\n for (i = 0; i < QS.length; i++) {\n q = QS[i];\n opts = shuffleArr(q.opts);\n shuffled[q.id] = opts;\n\n card = document.createElement('div');\n card.className = 'mr-case';\n\n top = document.createElement('div');\n top.className = 'mr-case-top';\n\n numDiv = document.createElement('div');\n numDiv.className = 'mr-num';\n numDiv.textContent = q.id < 10 ? 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#nps03 .mr-opt-text{font-size:0.86rem}\n}\n<\/style>\n\n<div id=\"nps03\">\n\n <div class=\"mr-header\">\n <div class=\"mr-series-tag\">Numerical Series · PSM Biostatistics<\/div>\n <div class=\"mr-eyebrow\">Morning Rounds · Round 03 of 07<\/div>\n <div class=\"mr-title\">PPV, NPV &<br><em>The Prevalence Effect<\/em><\/div>\n <div class=\"mr-subtitle\">Five questions · Row-based metrics, how prevalence shifts them & what a positive result actually means<\/div>\n <div class=\"mr-chips\">\n <span class=\"mr-chip\">5 Questions<\/span>\n <span class=\"mr-chip\">+4 \/ −1 scoring<\/span>\n <span class=\"mr-chip\">Options reshuffled<\/span>\n <\/div>\n <\/div>\n\n <div class=\"mr-sentinel\" id=\"nps03-sentinel\"><\/div>\n\n <div class=\"mr-progress\" id=\"nps03-progress\">\n <div class=\"mr-prog-inner\">\n <div class=\"mr-pips\" id=\"nps03-pips\"><\/div>\n <\/div>\n <\/div>\n\n <div class=\"mr-body\">\n <div id=\"nps03-cases\"><\/div>\n <div class=\"mr-submit-wrap\">\n <button class=\"mr-btn\" id=\"nps03-submit\">Submit for Debrief<\/button>\n <\/div>\n <div class=\"mr-score\" id=\"nps03-score\">\n <div class=\"mr-score-in\">\n <div class=\"mr-score-ey\">Round Complete<\/div>\n <div class=\"mr-ring\" id=\"nps03-ring\">\n <div class=\"mr-ring-in\">\n <span class=\"mr-ring-pct\" id=\"nps03-pct\">0%<\/span>\n <span class=\"mr-ring-sub\">net<\/span>\n <\/div>\n <\/div>\n <div class=\"mr-score-title\">Your Debrief<\/div>\n <div class=\"mr-score-net\" id=\"nps03-net\"><\/div>\n <div class=\"mr-verdict\" id=\"nps03-verdict\"><\/div>\n <div class=\"mr-bands\">\n <span class=\"mr-band mr-band-c\" id=\"nps03-ct-c\"><\/span>\n <span class=\"mr-band mr-band-w\" id=\"nps03-ct-w\"><\/span>\n <span class=\"mr-band mr-band-s\" id=\"nps03-ct-s\"><\/span>\n <\/div>\n <button class=\"mr-retry\" id=\"nps03-retry\">↻ New Round<\/button>\n <\/div>\n <\/div>\n <\/div>\n\n<\/div>\n\n<script>\n(function () {\n 'use strict';\n\n var NS = 'nps03';\n var TOTAL = 5;\n var MAX = 20;\n var LTRS = ['A','B','C','D'];\n\n var QS = [\n\n {\n id: 1,\n tag: 'PPV — Calculation from the Table',\n stem: 'A screening test for hepatitis C yields the following results in 1000 patients: <strong>TP=90, FN=10, FP=180, TN=720<\/strong>. What is the <strong>positive predictive value (PPV)<\/strong>?',\n correct: '33.3%',\n opts: [\n '33.3%',\n '90%',\n '50%',\n '80%'\n ],\n exp: 'PPV = <strong>TP ÷ (TP + FP)<\/strong> \u2014 of all who test positive, what proportion truly have the disease?<span class=\"calc\">All test-positive = TP + FP = 90 + 180 = 270<br>PPV = 90 ÷ 270 = <strong>0.333 = 33.3%<\/strong><\/span>This means only 1 in 3 people with a positive result actually has hepatitis C. Two in three positives are false alarms. This is the clinical weight of PPV: it tells the clinician what to do with a positive result.<br><br>Trap 90% is the sensitivity (TP ÷ disease total = 90 ÷ 100). Trap 80% is the specificity (TN ÷ non-disease total = 720 ÷ 900). Trap 50% has no basis in this table. The denominator for PPV is the <strong>positive test row<\/strong> \u2014 TP+FP \u2014 not any disease column. This is the row vs column distinction that separates PPV from sensitivity.'\n },\n\n {\n id: 2,\n tag: 'NPV — Calculation and Meaning',\n stem: 'Using the same hepatitis C data (TP=90, FN=10, FP=180, TN=720), what is the <strong>negative predictive value (NPV)<\/strong>, and what does it tell the clinician?',\n correct: '98.6%; of all who test negative, 98.6% are truly disease-free \u2014 a negative result is highly reliable here',\n opts: [\n '98.6%; of all who test negative, 98.6% are truly disease-free \u2014 a negative result is highly reliable here',\n '98.6%; of all disease-free patients, 98.6% test negative \u2014 confirming high specificity of the test',\n '72%; calculated as TN divided by the total population, reflecting the proportion correctly identified overall',\n '93.5%; calculated as the complement of the false negative rate, which equals FNR subtracted from 100%'\n ],\n exp: 'NPV = <strong>TN ÷ (TN + FN)<\/strong> \u2014 of all who test negative, what proportion are truly disease-free?<span class=\"calc\">All test-negative = TN + FN = 720 + 10 = 730<br>NPV = 720 ÷ 730 = <strong>0.9863 = 98.6%<\/strong><\/span>A negative result in this test is very reassuring \u2014 98.6% chance the patient is truly disease-free. This high NPV is largely because the disease is rare in this sample (prevalence = 100 ÷ 1000 = 10%), so most negatives are true negatives.<br><br>Trap B describes specificity, not NPV. Specificity = TN ÷ (TN+FP); NPV = TN ÷ (TN+FN) \u2014 different denominators, different meanings. Trap C divides by total population. Trap D confuses complement of FNR (= sensitivity) with NPV. NPV denominator = all test-negative = TN+FN.'\n },\n\n {\n id: 3,\n tag: 'Prevalence Effect — PPV Falls as Prevalence Falls',\n stem: 'The same test (sensitivity 90%, specificity 80%) is applied in <strong>two populations of 1000<\/strong>: Population A has <strong>10% prevalence<\/strong>, Population B has <strong>1% prevalence<\/strong>. Without calculating, which statement correctly predicts what happens to PPV?',\n correct: 'PPV falls substantially in Population B; lower prevalence floods the positive pool with false positives from the large non-diseased majority',\n opts: [\n 'PPV falls substantially in Population B; lower prevalence floods the positive pool with false positives from the large non-diseased majority',\n 'PPV rises in Population B; a lower prevalence means fewer diseased people compete for positive test slots, increasing the proportion of true positives',\n 'PPV remains unchanged in Population B; it is a fixed property of the test like sensitivity and specificity',\n 'PPV falls in Population B only if specificity is below 90%; at 80% specificity the effect is too small to be clinically significant'\n ],\n exp: 'This is the central insight of this round. As prevalence falls, the non-diseased population grows. Even a small false positive rate (here 20%) applied to a large non-diseased population generates <strong>many false positives<\/strong>. Meanwhile, the true positive pool shrinks because fewer people have the disease.<span class=\"calc\">Population A (10% prevalence, n=1000):<br>Diseased=100, Non-diseased=900<br>TP = 0.90×100 = 90, FP = 0.20×900 = 180<br>PPV = 90÷(90+180) = 90÷270 = <strong>33.3%<\/strong><br><br>Population B (1% prevalence, n=1000):<br>Diseased=10, Non-diseased=990<br>TP = 0.90×10 = 9, FP = 0.20×990 = 198<br>PPV = 9÷(9+198) = 9÷207 = <strong>4.3%<\/strong><\/span>PPV crashed from 33% to 4% with the same test. Sensitivity and specificity did not change. This is why a positive result from a screening programme applied to a low-prevalence general population requires confirmation before action.'\n },\n\n {\n id: 4,\n tag: 'Prevalence Effect — NPV Rises as Prevalence Falls',\n stem: 'Using the same two populations from Q3 (sensitivity 90%, specificity 80%), what happens to <strong>NPV<\/strong> as prevalence falls from 10% to 1%?',\n correct: 'NPV rises from 98.6% to 99.9%; lower prevalence means most test-negatives are true negatives, making a negative result even more reliable',\n opts: [\n 'NPV rises from 98.6% to 99.9%; lower prevalence means most test-negatives are true negatives, making a negative result even more reliable',\n 'NPV falls as prevalence falls; fewer diseased people means fewer true negatives, reducing the reliability of a negative result',\n 'NPV remains at 98.6% in both populations; like specificity, it is independent of disease prevalence',\n 'NPV rises to 99.9% but becomes clinically useless; in low-prevalence settings negative results carry no diagnostic weight'\n ],\n exp: '<span class=\"calc\">Population A (10% prevalence):<br>FN = 0.10×100 = 10, TN = 0.80×900 = 720<br>NPV = 720÷(720+10) = 720÷730 = <strong>98.6%<\/strong><br><br>Population B (1% prevalence):<br>FN = 0.10×10 = 1, TN = 0.80×990 = 792<br>NPV = 792÷(792+1) = 792÷793 = <strong>99.9%<\/strong><\/span>As prevalence falls: TN pool grows (more disease-free people correctly cleared), FN pool shrinks (fewer diseased people to miss). NPV = TN÷(TN+FN) rises toward 100%.<br><br>The paired lesson: <strong>PPV and NPV move in the same direction as prevalence<\/strong> \u2014 both rise with rising prevalence, both fall with falling prevalence? No \u2014 they move in <em>opposite<\/em> directions. PPV rises with prevalence. NPV falls with prevalence. This asymmetry is the exam trap. Trap B incorrectly inverts NPV direction. Trap D is wrong: a highly reliable negative result is clinically valuable, not useless.'\n },\n\n {\n id: 5,\n tag: 'PPV — Clinical Application in Low-Prevalence Screening',\n stem: 'A national programme screens all adults for a rare autoimmune condition (prevalence <strong>0.5%<\/strong>). The test has sensitivity 95% and specificity 95%. A 35-year-old woman tests positive. She is told she \"almost certainly has the disease.\" Is this statement accurate?',\n correct: 'No; with 0.5% prevalence and 95% specificity, PPV is approximately 8.7% \u2014 fewer than 1 in 10 positive results represent true disease',\n opts: [\n 'No; with 0.5% prevalence and 95% specificity, PPV is approximately 8.7% \u2014 fewer than 1 in 10 positive results represent true disease',\n 'Yes; a test with 95% sensitivity and 95% specificity is highly accurate and a positive result reliably indicates disease',\n 'No; with 0.5% prevalence, the test should not have been offered at all since no screening test performs adequately below 1% prevalence',\n 'Yes; sensitivity of 95% means 95% of positive results are true positives, confirming the statement is correct'\n ],\n exp: '<span class=\"calc\">Population of 10,000 (prevalence 0.5%):<br>Diseased = 50, Non-diseased = 9950<br>TP = 0.95 × 50 = 47.5 ≈ 48<br>FP = 0.05 × 9950 = 497.5 ≈ 498<br>PPV = 48 ÷ (48+498) = 48 ÷ 546 = <strong>8.8%<\/strong><\/span>Even with a 95%\/95% test \u2014 which sounds excellent \u2014 fewer than 1 in 10 positive results represents true disease when prevalence is 0.5%. The other 9 in 10 are false alarms.<br><br>This is the <strong>base rate fallacy<\/strong> in medicine: interpreting test results without accounting for prior probability (prevalence). The statement \"almost certainly has the disease\" is dangerously wrong. This woman needs confirmatory testing before any diagnosis or treatment. Trap B confuses test accuracy with PPV. Trap D is the most common misconception: sensitivity tells you about diseased people, not about positive results. Trap C invents a 1% rule that does not exist.'\n }\n\n ];\n\n var answers = {}, answered = 0, shuffled = {}, done = false;\n\n function gid(s) { return document.getElementById(NS + '-' + s); }\n function byId(s) { return document.getElementById(s); }\n\n function shuffleArr(arr) {\n var a = arr.slice(), i, j, t;\n for (i = a.length - 1; i > 0; i--) {\n j = Math.floor(Math.random() * (i + 1));\n t = a[i]; a[i] = a[j]; a[j] = t;\n }\n return a;\n }\n\n function countVal(v) {\n var n = 0, k;\n for (k in answers) { if (answers[k] === v) n++; }\n return n;\n }\n\n function buildPips() {\n var cont = gid('pips'), i, q, wLine, wPip, line, pip;\n cont.innerHTML = '';\n for (i = 0; i < QS.length; i++) {\n q = QS[i];\n if (i > 0) {\n wLine = document.createElement('div');\n wLine.className = 'mr-pip-wrap';\n line = document.createElement('div');\n line.className = 'mr-pip-line';\n line.id = NS + '-pl' + q.id;\n wLine.appendChild(line);\n cont.appendChild(wLine);\n }\n wPip = document.createElement('div');\n wPip.className = 'mr-pip-wrap';\n pip = document.createElement('div');\n pip.className = 'mr-pip';\n pip.id = NS + '-pip' + q.id;\n pip.textContent = String(q.id);\n wPip.appendChild(pip);\n cont.appendChild(wPip);\n }\n }\n\n function build() {\n var cont, i, q, opts, card, top, numDiv, meta, tag, stem,\n rule, optsDiv, expDiv, lbl, txt, j, optEl, ltrSpan, txtSpan;\n\n cont = gid('cases');\n cont.innerHTML = '';\n answers = {}; answered = 0; shuffled = {}; done = false;\n gid('score').style.display = 'none';\n buildPips();\n\n for (i = 0; i < QS.length; i++) {\n q = QS[i];\n opts = shuffleArr(q.opts);\n shuffled[q.id] = opts;\n\n card = document.createElement('div');\n card.className = 'mr-case';\n\n top = document.createElement('div');\n top.className = 'mr-case-top';\n\n numDiv = document.createElement('div');\n numDiv.className = 'mr-num';\n numDiv.textContent = q.id < 10 ? 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