Sensitivity, specificity, positive predictive value, and negative predictive value are core measures used to judge how well a medical test performs. They help students and clinicians decide whether a test is good for screening, confirming disease, or reassuring a patient after a negative result. These ideas connect statistics directly to patient care, because the same test can be useful in one setting and misleading in another. Understanding them prevents common errors in interpreting lab tests, imaging, and bedside screening tools.

Sensitivity and specificity describe the test itself by comparing results to the true disease status, while PPV and NPV describe what a positive or negative result means for the patient in a specific population. The standard framework is the 2 x 2 table with true positives, false positives, true negatives, and false negatives. Disease prevalence strongly affects PPV and NPV, even when sensitivity and specificity stay the same. In practice, highly sensitive tests are often used to rule out disease, and highly specific tests are often used to rule in disease.

Key Facts

  • Sensitivity = TP / (TP + FN)
  • Specificity = TN / (TN + FP)
  • PPV = TP / (TP + FP)
  • NPV = TN / (TN + FN)
  • Accuracy = (TP + TN) / (TP + TN + FP + FN)
  • Higher prevalence increases PPV and decreases NPV, even if sensitivity and specificity do not change.

Vocabulary

Sensitivity
Sensitivity is the proportion of people with the disease who test positive.
Specificity
Specificity is the proportion of people without the disease who test negative.
Positive predictive value
Positive predictive value is the probability that a person with a positive test truly has the disease.
Negative predictive value
Negative predictive value is the probability that a person with a negative test truly does not have the disease.
Prevalence
Prevalence is the proportion of a population that has the disease at a given time.

Common Mistakes to Avoid

  • Confusing sensitivity with PPV, because sensitivity is based on people who truly have disease, while PPV is based on people who tested positive. These answer different clinical questions and cannot be used interchangeably.
  • Ignoring prevalence when interpreting PPV and NPV, because predictive values change with how common the disease is in the tested population. A test can have the same sensitivity and specificity but very different PPV in a low-prevalence setting.
  • Using a highly specific test to rule out disease, because specificity mainly helps confirm disease when the result is positive. To rule out disease, a highly sensitive test is usually more helpful.
  • Reading percentages from a 2 x 2 table incorrectly, because the denominator must match the definition of the statistic. For example, sensitivity uses TP + FN, not all positive test results.

Practice Questions

  1. 1 A screening test is given to 200 people. Of the 50 who truly have disease, 45 test positive. Of the 150 without disease, 30 test positive. Calculate sensitivity and specificity.
  2. 2 In a clinic, a test gives the following results: TP = 36, FP = 12, TN = 108, FN = 4. Calculate PPV and NPV.
  3. 3 A disease is rare in Population A and common in Population B. The same test with the same sensitivity and specificity is used in both groups. Explain how PPV and NPV are expected to differ between the two populations and why.