Test characteristics fundamentals

The 2x2 Table - The Truth Grid

The 2x2 table is the foundation for evaluating diagnostic tests against a gold standard. It classifies individuals based on test results versus their true disease status.

• Rows represent the test results.

⭐ The vertical columns represent the true disease status, which is the basis for calculating sensitivity $TP/(TP+FN)$ and specificity $TN/(TN+FP)$.

Sensitivity & Specificity - SnNOut & SpPIn Show

• Sensitivity: True Positive Rate. Proportion of people with a disease who test positive. Rules OUT disease if negative.

  • Formula: $TP / (TP + FN)$
  • 📌 Sn-N-Out: A highly Sensitive test, when Negative, rules Out the disease.

• Specificity: True Negative Rate. Proportion of people without a disease who test negative. Rules IN disease if positive.

  • Formula: $TN / (TN + FP)$
  • 📌 Sp-P-In: A highly Specific test, when Positive, rules In the disease.

⭐ High-sensitivity tests are used for screening (e.g., initial HIV screen). High-specificity tests are used for confirmation (e.g., Western blot for HIV).

Predictive Values - Crystal Ball Values

• Positive Predictive Value (PPV): Probability of having the disease with a positive test.

  • Formula: $PPV = \frac{TP}{TP + FP}$
  • Directly varies with prevalence. Higher prevalence → Higher PPV.

• Negative Predictive Value (NPV): Probability of being disease-free with a negative test.

  • Formula: $NPV = \frac{TN}{TN + FN}$
  • Inversely varies with prevalence. Higher prevalence → Lower NPV.

📌 Mnemonic: Prevalence Positively affects PPV.

⭐ As disease prevalence decreases, PPV decreases. In a population with very low prevalence, most positive results are actually false positives.

ROC Curves - Curve Appeal

curve showing True Positive Rate vs False Positive Rate)

• Plots True Positive Rate ($TPR$, Sensitivity) vs. False Positive Rate ($FPR$, 1-Specificity) across various cut-off thresholds.
• The Area Under the Curve (AUC) is a measure of overall test accuracy.
  • AUC = 1.0: Perfect test.
  • AUC = 0.5: Useless test (represented by the diagonal line).
• The ideal cut-off point is often the "knee" of the curve, maximizing the distance from the diagonal.

⭐ The optimal threshold balances sensitivity and specificity, often found by maximizing the Youden Index.

High‑Yield Points - ⚡ Biggest Takeaways

• Sensitivity is the True Positive Rate (TPR), ideal for screening; a negative result in a high-sensitivity test helps rule OUT disease (SNOUT).
• Specificity is the True Negative Rate (TNR), used for confirmation; a positive result in a high-specificity test helps rule IN disease (SPIN).
• Positive Predictive Value (PPV) is directly related to prevalence; as prevalence increases, PPV increases.
• Negative Predictive Value (NPV) is inversely related to prevalence; as prevalence increases, NPV decreases.
• Sensitivity and specificity are intrinsic test characteristics, independent of disease prevalence.