{
  "ok": true,
  "tool": "fagan-nomogram",
  "input": {
    "mode": "sens_spec",
    "pretest_pct": 20,
    "sens_pct": 90,
    "spec_pct": 80
  },
  "result": {
    "pre_test_probability_pct": 20,
    "lr_pos": 4.5,
    "lr_neg": 0.125,
    "positive": {
      "lr": 4.5,
      "pre_test_odds": 0.25,
      "post_test_odds": 1.125,
      "post_test_probability_pct": 52.94,
      "interpretation": "Small increase in probability"
    },
    "negative": {
      "lr": 0.125,
      "pre_test_odds": 0.25,
      "post_test_odds": 0.0312,
      "post_test_probability_pct": 3.03,
      "interpretation": "Moderate decrease in probability"
    }
  },
  "warnings": [],
  "explanation": "Bayes' theorem in odds form: pre-test odds = p / (1 − p) = 0.2 / (1 − 0.2); post-test odds = pre-test odds × LR; post-test probability = odds / (1 + odds). LR+ = sensitivity / (1 − specificity); LR− = (1 − sensitivity) / specificity. If positive: LR+ 4.5; pre-test odds 0.25 × 4.5 = post-test odds 1.13; post-test probability = 1.13 / (1 + 1.13) = 52.9%. If negative: LR− 0.125; pre-test odds 0.25 × 0.125 = post-test odds 0.0312; post-test probability = 0.0312 / (1 + 0.0312) = 3.0%.",
  "sources": [
    {
      "title": "Fagan TJ. Nomogram for Bayes theorem. N Engl J Med. 1975;293(5):257.",
      "url": "https://doi.org/10.1056/NEJM197507312930513"
    },
    {
      "title": "Deeks JJ, Altman DG. Diagnostic tests 4: likelihood ratios. BMJ. 2004;329(7458):168-169.",
      "url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC478236/"
    },
    {
      "title": "McGee S. Simplifying likelihood ratios. J Gen Intern Med. 2002;17(8):647-650.",
      "url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC1495095/"
    },
    {
      "title": "Centre for Evidence-Based Medicine, University of Oxford. Likelihood ratios.",
      "url": "https://www.cebm.ox.ac.uk/resources/ebm-tools/likelihood-ratios"
    }
  ],
  "disclaimer": "This calculator is for education and clinical decision support by health professionals. It does not replace clinical judgement or local guidelines, and no data you enter leaves your browser.",
  "page_url": "https://arkangel.ai/fagan-nomogram?mode=sens_spec&pretest_pct=20&sens_pct=90&spec_pct=80"
}