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.
- $NPV = TN / (TN + FN)$
- PPV: Probability of disease if test is positive. Directly related to prevalence.
⭐ 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 Present | Disease Absent | |
|---|---|---|
| Test Positive | True Positive (TP) | False Positive (FP) |
| Test Negative | False 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.

⭐ 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

-
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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