An educational tool for medical students and junior doctors to understand diagnostic reasoning, likelihood ratios, and clinical thresholds
Every diagnostic decision follows the same pattern:
| LR+ Value | Effect on Probability | Clinical Meaning |
|---|---|---|
| >10 | Large increase | Strong evidence for disease |
| 5–10 | Moderate increase | Good evidence for disease |
| 2–5 | Small increase | Weak evidence for disease |
| 1–2 | Minimal change | Finding doesn't help much |
| LR− Value | Effect on Probability | Clinical Meaning |
|---|---|---|
| <0.1 | Large decrease | Strong evidence against disease |
| 0.1–0.2 | Moderate decrease | Good evidence against disease |
| 0.2–0.5 | Small decrease | Weak evidence against disease |
| 0.5–1.0 | Minimal change | Absence doesn't help much |
Imagine 100 patients in your GP surgery who have lower respiratory infections, based on NICE guideline data 5–12% will be diagnosed and managed as community-acquired pneumonia.
LR− = 0.25 means the finding is 4 times less common in people WITH pneumonia than those WITHOUT.
This is a conceptual illustration showing approximately how findings distribute across diseased vs well patients. The exact numbers depend on the test's sensitivity and specificity.
Key insight: A negative finding (LR− 0.25) reduces probability from 10% → ~2.7% using Bayes' theorem.
Clinical decisions aren't just about calculating probability—you need to know what probability should trigger action. This is where thresholds come in.
Thresholds depend on several factors:
| Condition | Test Threshold | Treatment Threshold | Rationale |
|---|---|---|---|
| Pulmonary Embolism | ~2-5% | ~15-20% | Life-threatening; thresholds vary by Wells score and D-dimer availability |
| Strep Throat | ~10-15% | ~50-60% | Usually self-limiting; antibiotics prevent rare complications |
| Pneumonia (primary care) | ~5-10% | ~30-40% | Can be serious; antibiotics generally safe in short course |
| Bacterial Meningitis | ~1-2% | ~5-10% | Rapidly fatal if untreated; antibiotics relatively safe |
Practice calculating post-test probability using clinical findings from any condition.
Estimate based on:
• Prevalence in your setting
• Patient risk factors
• Clinical presentation
Work through these realistic scenarios applying probabilistic reasoning and thresholds.
Patient: 28-year-old non-smoker, 3-day history of cough with green sputum. No breathlessness. No comorbidities.
Examination: Temperature 37.2°C, HR 75, RR 16, SpO₂ 98%. Chest clear, no focal signs.
Step 1: Pre-test probability ≈ 5% (young, well, no focal signs)
Step 2: Pre-test odds = 0.05 ÷ 0.95 = 0.053
Step 3: Post-test odds = 0.053 × 0.25 = 0.013
Step 4: Post-test probability = 0.013 ÷ 1.013 = 1.3%
Clinical decision: Pneumonia very unlikely. Safety-net advice, no CXR or antibiotics needed. Advise to return if symptoms worsen or don't improve in 3-5 days.
Patient: 67-year-old with COPD, 5-day history of productive cough and breathlessness. Feels unwell.
Examination: Temperature 38.3°C, HR 98, RR 24, SpO₂ 94% on air. Crackles right base, dull to percussion.
Step 1: Pre-test probability ≈ 25% (elderly, COPD, focal signs, systemically unwell)
Step 2: Pre-test odds = 0.25 ÷ 0.75 = 0.333
Step 3: Post-test odds = 0.333 × 3.21 = 1.069
Step 4: Post-test probability = 1.069 ÷ 2.069 = 51.7%
Clinical decision: Pneumonia likely. Consider point-of-care CRP if available. Start empirical antibiotics per local guidelines (example: amoxicillin 500mg TDS for 5 days—actual dosing varies by local antimicrobial guidance, allergy, severity). Arrange CXR if diagnostic uncertainty or high-risk features. Consider CRB-65 for admission decision. Safety-net with clear criteria to re-attend.
Patient: 45-year-old smoker, 4-day cough, mild fever last night, feeling tired.
Examination: Temperature 37.8°C, HR 88, RR 18. Few scattered crackles bilaterally.
Point-of-care CRP: 15 mg/L
Step 1: Pre-test probability ≈ 15% (smoker, mild systemic upset, equivocal chest signs)
Step 2: Pre-test odds = 0.15 ÷ 0.85 = 0.176
Step 3: Post-test odds = 0.176 × 0.52 = 0.092
Step 4: Post-test probability = 0.092 ÷ 1.092 = 8.4%
Clinical decision: CRP <20 mg/L substantially reduces pneumonia probability from 15% to 8%. This falls below typical treatment threshold. Reasonable to withhold antibiotics and provide safety-net advice. Advise return if fever persists >48h or symptoms worsen.
Patient: 52-year-old woman, 3-day history of right calf pain and swelling. Today developed sudden-onset breathlessness and pleuritic chest pain.
Examination: HR 105, RR 22, SpO₂ 94% on air. Right calf swollen and tender. Chest clear.
Wells Score: Clinical DVT signs (3 points) + tachycardia (1.5 points) + PE most likely diagnosis (3 points) = 7.5 points → "PE likely" (high risk)
Pre-test probability analysis: Wells score 7.5 places this patient in the "PE likely" group. Studies show this corresponds to approximately 30-40% probability of PE in ED populations (some studies report 28-40% depending on exact cohort).
Is D-dimer indicated? No—and here's why:
Recommended management (by-the-book): At 30-40% pre-test probability, proceed directly to CTPA, bypassing D-dimer. Consider early anticoagulation if clinically unstable or imaging delayed. This is standard practice for "PE likely" presentations.
⚠️ Real-world practice paradox:
Despite the above reasoning, D-dimer is still very often done in high-risk PE presentations. Why?
Teaching point: In high-risk presentations, the D-dimer result is frequently ignored because it does not alter the decision to proceed to CTPA. This validates what juniors observe: the test gets done, but the decision was already made on clinical grounds.
Key learning: This case demonstrates why Bayesian reasoning sometimes leads you away from testing rather than toward it. At high pre-test probability, additional tests that won't cross thresholds should not be ordered—even though real-world practice may not always follow this principle. Understanding both the ideal reasoning and the practical reality is what makes you a better clinician.
Patient: 68-year-old with diabetes and hypertension. 45 minutes of severe central chest pain radiating to both arms and jaw. Sweating, nausea.
Examination: Pale, clammy. BP 95/60, HR 110. HS normal, chest clear.
ECG: ST elevation 3mm in leads II, III, aVF
Step 1: Pre-test probability ≈ 40% (elderly, diabetes, hypertension, classic radiation pattern)
Step 2: Pre-test odds = 0.40 ÷ 0.60 = 0.667
Step 3: Post-test odds = 0.667 × 13.1 = 8.74
Step 4: Post-test probability = 8.74 ÷ 9.74 = 89.7%
Threshold analysis: Post-test probability (90%) is well above treatment threshold for STEMI (~80%). ECG finding alone provides sufficient certainty.
Clinical decision: This is STEMI. Immediate dual antiplatelet therapy, activate cath lab for primary PCI. Don't wait for troponin—probability already exceeds treatment threshold, and time-to-reperfusion is critical. This illustrates when further testing delays necessary treatment.
Patient: 24-year-old female, sudden onset pleuritic chest pain. No calf swelling, no haemoptysis, no previous clots.
Examination: HR 72, SpO₂ 99% on air. Chest clear. Wells Score ≤4 ("PE Unlikely").
Investigation: D-dimer Negative.
Step 1: Pre-test probability ≈ 10%.
Step 2: Pre-test odds = 0.10 ÷ 0.90 = 0.111.
Step 3: Post-test odds = 0.111 × 0.1 = 0.011.
Step 4: Post-test probability = 0.011 ÷ 1.011 ≈ 1.1%.
Clinical decision: 1.1% is well below the test threshold for CTPA. You have successfully "ruled out" PE. Discharge with safety-netting.
Contrast this with Case 4: The same test (D-dimer) works here because the pre-test probability was low enough.
Patient: 34-year-old father with a sore throat for 2 days. No cough.
Examination: Temp 37.1°C. Tonsils swollen with exudate (pus).
Context: Most adult sore throats are viral. Bacterial prevalence is low (~5-10%).
Step 1: Pre-test probability ≈ 10%.
Step 2: Pre-test odds = 0.10 ÷ 0.90 = 0.111.
Step 3: Post-test odds = 0.111 × 3.5 = 0.388.
Step 4: Post-test probability = 0.388 ÷ 1.388 ≈ 28%.
Clinical decision: Despite the "positive" finding of pus, the probability is only ~28%. This is often below the treatment threshold for antibiotics (usually >40-50% or Centor score 3-4).
The Lesson: This is the "Prevalence Trap" discussed in the Deep Dive tab. In low-prevalence settings, even good signs (LR+ 3.5) often fail to raise probability high enough to treat.
Why is this so confusing?
Medical students often struggle because there are two ways to look at test data:
| Term | The Question it Answers | Clinical Role |
|---|---|---|
| Sensitivity | "If the patient definitely has the disease, how often will the test be positive?" | The Safety Net. High sensitivity means few false negatives. Good for ruling out disease (SnNout). |
| Specificity | "If the patient is definitely healthy, how often will the test be negative?" | The Bouncer. High specificity means few false positives. Good for ruling in disease (SpPin). |
| PPV (Positive Predictive Value) |
"My patient tested positive. What is the chance they actually have the disease?" | Trust Level. Changes based on prevalence. Often much lower than you think! |
| NPV (Negative Predictive Value) |
"My patient tested negative. What is the chance they are actually healthy?" | Reassurance. Usually very high in primary care because disease is rare. |
This is the most common mistake in diagnostic reasoning: Confusing Sensitivity with PPV.
Imagine a test for a cancer (1% prevalence in at risk group) that has 90% Sensitivity and 90% Specificity. Sounds like a great test, right?
If you get a Positive Result, do you have a 90% chance of cancer?
The Result: You have 9 true positives and 99 false positives.
PPV = 9 ÷ (9 + 99) ≈ 8.3%
If PPV changes every time the prevalence changes, how can we remember the numbers? We can't.
That is why Likelihood Ratios (LRs) are superior for clinical reasoning. LRs are calculated from Sensitivity and Specificity, so they (mostly) stay stable regardless of prevalence.
Found a paper reporting Sensitivity/Specificity? Convert it to LRs here to see how useful the test actually is.