Positive predictive value

Positive Predictive Value - Predicting the Positive

• Definition: The probability that a person with a positive test result actually has the disease.
• Formula: $PPV = TP / (TP + FP)$
  • PPV is directly proportional to disease prevalence and specificity.
  • ↑ prevalence → ↑ PPV.
  • ↑ specificity → ↑ PPV.
• 📌 Mnemonic: PPV asks, 'Given a Positive test, what's the probability of Positive disease?'

⭐ PPV is the answer to the patient's question: 'I tested positive, do I actually have the disease?'

PPV & Prevalence - The Prevalence Effect

• Positive Predictive Value (PPV) is critically dependent on disease prevalence (i.e., pre-test probability) in the tested population.

• The relationship is directly proportional:

  • If prevalence ↑, then PPV ↑.
  • If prevalence ↓, then PPV ↓.

• High-Prevalence Setting:

  • A positive result is more likely to be a true positive.
  • Seen when testing symptomatic individuals or high-risk groups.

• Low-Prevalence (Screening) Setting:

  • A positive result has a higher chance of being a false positive.
  • This is a major challenge for general population screening tests.

⭐ In a low-prevalence population, even a highly specific test will have a low PPV, leading to many false positives.

📌 Mnemonic: High Prevalence → High PPV. Low Prevalence → Low PPV.

Diagnostic Metrics - The Whole Squad

-   $Sensitivity = TP / (TP + FN)$
-   📌 **SNOUT**: a highly **S**e**n**sitive test, when **N**egative, helps rule **OUT** disease.

• Specificity (Sp): Rules in. Proportion of people without the disease who test negative.

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

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

  • $NPV = TN / (TN + FN)$

⭐ Sensitivity and Specificity are intrinsic properties of a diagnostic test and do NOT change with disease prevalence.

High‑Yield Points - ⚡ Biggest Takeaways

• Positive Predictive Value (PPV) is the probability that a patient with a positive test result truly has the disease.
• It is calculated as True Positives / (True Positives + False Positives).
• Unlike sensitivity and specificity, PPV is highly dependent on the pretest probability or disease prevalence.
• As prevalence increases, the PPV increases.
• As prevalence decreases, the PPV decreases.
• This is critical for interpreting screening tests in low-risk vs. high-risk populations.