💡 Key idea: Every diagnostic test gives results that may be true or false relative to the real disease state. The goal is to quantify how well a test distinguishes between health and disease.

🧩 Basic Terms

True Positive (TP): Patient has the disease ➜ test correctly positive.
False Positive (FP): Patient does not have the disease ➜ test incorrectly positive.
True Negative (TN): Patient does not have the disease ➜ test correctly negative.
False Negative (FN): Patient has the disease ➜ test incorrectly negative.

🔬 Sensitivity

Formula: Sensitivity = TP / (TP + FN)

Measures a test’s ability to correctly identify those who have the disease.
High sensitivity = few false negatives → useful for screening.
Example: If 19 of 20 diseased patients test positive → sensitivity = 19/20 = 95%.

🩺 Tip: “SnNout” — when a test is highly SeNsitive, a Negative result rules disease out.

🧪 Specificity

Formula: Specificity = TN / (TN + FP)

Measures a test’s ability to correctly identify those without the disease.
High specificity = few false positives → useful for confirmation.
Example: If 80 of 100 healthy people test negative → specificity = 80/100 = 80%.

💡 Tip: “SpPin” — when a test is highly SPecific, a Positive result rules disease in.

📊 Using Two-Step Testing

Begin with a high sensitivity test (broad screening) → captures nearly everyone with disease.
Follow with a high specificity test (confirmatory) → filters out false positives.
Example: HIV testing uses this principle — ELISA (sensitive) followed by Western blot (specific).

📈 Positive Predictive Value (PPV)

Formula: PPV = TP / (TP + FP)

Answers: “Given a positive test, what is the probability the patient actually has the disease?”
Strongly influenced by disease prevalence — PPV rises as disease becomes more common.
Example: In a high-prevalence population, even modest tests yield high PPV.

📉 Negative Predictive Value (NPV)

Formula: NPV = TN / (TN + FN)

Answers: “Given a negative test, what is the probability the patient truly does not have the disease?”
Also depends on prevalence — NPV rises when disease is rare.

⚖️ Likelihood Ratios (LR)

Formulae:
LR⁺ = Sensitivity / (1 − Specificity)
LR⁻ = (1 − Sensitivity) / Specificity

Express how much a test result changes the probability of disease.
LR⁺ > 10 → strong evidence to rule in disease.
LR⁻ < 0.1 → strong evidence to rule out disease.
Useful for Bayesian reasoning in clinical decision-making.

🧮 Example Table (2×2 Matrix)

	Disease Present	Disease Absent
Test Positive	True Positive (TP)	False Positive (FP)
Test Negative	False Negative (FN)	True Negative (TN)

🧠 Teaching Commentary

Sensitivity and specificity are intrinsic properties of the test — they do not change with prevalence.
PPV and NPV depend on disease prevalence — a low-prevalence condition produces many false positives.
In acute medicine, start broad (sensitive test) and narrow down (specific test).
Likelihood ratios integrate both metrics, helping clinicians interpret tests across populations rather than within one study.

📚 References

Lalkhen AG, McCluskey A. Clinical tests: sensitivity and specificity. CEACCP 2008;8(6):221–223.
BMJ Best Practice. Diagnostic test evaluation.
Akobeng AK. Understanding diagnostic tests 1: sensitivity, specificity and predictive values. Arch Dis Child 2007.

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Testing

🧠 Understanding Sensitivity, Specificity, and Predictive Values