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Prevalence effects on predictive values

Prevalence effects on predictive values

Prevalence effects on predictive values

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Core Concepts - The Diagnostic Toolkit

  • Sensitivity: Rules OUT disease (SNOUT). High sensitivity tests are good for screening.
    • $Sensitivity = TP / (TP + FN)$
  • Specificity: Rules IN disease (SPIN). High specificity tests are good for confirmation.
    • $Specificity = TN / (TN + FP)$
  • Predictive Values: Depend on disease prevalence.
    • PPV: Probability of disease if test is positive. Directly related to prevalence.
      • $PPV = TP / (TP + FP)$
    • NPV: Probability of no disease if test is negative. Inversely related to prevalence.
      • $NPV = TN / (TN + FN)$

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⭐ As prevalence decreases, PPV decreases and NPV increases. Sensitivity and specificity remain unchanged as they are intrinsic properties of the test.

Prevalence Effects - The Value Proposition

Prevalence, the proportion of a population with a disease, directly impacts a test's predictive values. It does not affect sensitivity or specificity.

  • High Prevalence: More true positives (TP) and false negatives (FN).
  • Low Prevalence: More true negatives (TN) and false positives (FP).
Disease PresentDisease Absent
Test PositiveTrue Positive (TP)False Positive (FP)
Test NegativeFalse Negative (FN)True Negative (TN)
-   $PPV = TP / (TP + FP)$
  • Negative Predictive Value (NPV): Probability of not having the disease with a negative test.
    • $NPV = TN / (TN + FN)$

As prevalence changes, so do the predictive values:

  • ↑ Prevalence → ↑ PPV & ↓ NPV.
  • ↓ Prevalence → ↓ PPV & ↑ NPV.

Prevalence effects on PPV and NPV

⭐ Sensitivity and Specificity are intrinsic to the test and are not affected by disease prevalence. A test is just as good at detecting disease in a high-prevalence or low-prevalence population.

Predictive Value Curves - See the Shift

Prevalence effects on PPV and NPV with varying cut-offs

  • Positive Predictive Value (PPV): Directly proportional to prevalence.

    • As disease prevalence ↑, PPV ↑.
    • A positive test in a high-prevalence population is more likely a true positive.
  • Negative Predictive Value (NPV): Inversely proportional to prevalence.

    • As disease prevalence ↑, NPV ↓.
    • A negative test is most reliable when the disease is rare.

⭐ When prevalence is low, a positive result has a high chance of being a false positive, even with a good test. This is why we don't screen for rare diseases in the general population.

  • Prevalence directly influences a test's predictive values but not its sensitivity or specificity.
  • As disease prevalence increases, the Positive Predictive Value (PPV) also increases.
  • Conversely, as disease prevalence decreases, the Negative Predictive Value (NPV) increases.
  • In high-prevalence settings, a positive result is more likely to be a true positive.
  • In low-prevalence settings, a negative result is more likely to be a true negative.

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