Definitions and calculations

The 2x2 Table - Stats Ground Zero

The foundational tool for calculating a test's accuracy. It cross-tabulates the test result against the true disease status (gold standard).

• Specificity: Identifies true negatives. $Specificity = TN / (TN + FP)$

⭐ 📌 SNOUT & SPIN: A highly Sensitive test, when negative, rules out disease. A highly Specific test, when positive, rules in disease.

Sensitivity & Specificity - SNOUT & SPIN

• Sensitivity: True Positive Rate (TPR). Proportion of individuals with the disease who test positive.

  • Formula: $Sensitivity = TP / (TP + FN)$
  • 📌 SNOUT: A highly Sensitive test, when Negative, helps rule OUT the disease.

• Specificity: True Negative Rate (TNR). Proportion of individuals without the disease who test negative.

  • Formula: $Specificity = TN / (TN + FP)$
  • 📌 SPIN: A highly Specific test, when Positive, helps rule IN the disease.

⭐ High sensitivity tests are crucial for screening, minimizing false negatives (e.g., initial HIV screen). High specificity tests are used for confirmation, minimizing false positives (e.g., Western blot for HIV).

Predictive Values - Prevalence Power

• Positive Predictive Value (PPV): Probability that a person with a positive test result truly has the disease.

  • Formula: $PPV = \frac{TP}{TP + FP}$

• Negative Predictive Value (NPV): Probability that a person with a negative test result is truly disease-free.

  • Formula: $NPV = \frac{TN}{TN + FN}$

• Prevalence Dependence: Unlike sensitivity and specificity, predictive values are heavily influenced by the pre-test probability (prevalence).

  • If Prevalence ↑: PPV ↑, NPV ↓
  • If Prevalence ↓: PPV ↓, NPV ↑

⭐ A screening test is most useful when applied to a high-prevalence population because the PPV will be higher, leading to fewer false-positive scares.

Likelihood Ratios - Odds On Favourite

• Likelihood Ratios (LRs) quantify how much a test result changes the likelihood of having a disease. They are independent of prevalence.

• Positive LR (LR+): The increase in odds of disease given a positive test.

  • $LR+ = \frac{Sensitivity}{(1 - Specificity)}$
  • A useful test has an LR+ > 10.

• Negative LR (LR-): The decrease in odds of disease given a negative test.

  • $LR- = \frac{(1 - Sensitivity)}{Specificity}$
  • A useful test has an LR- < 0.1.

• Application: Post-test odds = Pre-test odds × LR.

⭐ An LR of 1 means the test result does not change the likelihood of disease at all. The post-test probability equals the pre-test probability.

shift pre-test probability to post-test probability)

High‑Yield Points - ⚡ Biggest Takeaways

• Sensitivity measures how well a test identifies people with the disease (true positive rate). It is vital for screening tests.
• Use the SNOUT mnemonic: a SeNsitive test with a Negative result helps rule OUT the disease.
• Specificity measures how well a test identifies people without the disease (true negative rate). It is crucial for confirmatory tests.
• Use the SPIN mnemonic: a SPecific test with a Positive result helps rule IN the disease.
• Both are intrinsic properties of a test and are not affected by disease prevalence.