Clinical Scenario:
The Denver Developmental Screening Test II is evaluated as a screening tool for developmental delay. In a population where the prevalence of developmental delay is 10%, the test has a sensitivity of 80% and a specificity of 90%.
A child has a positive screening result. What is the approximate probability that this child actually has developmental delay?
A. 25%
B. 47%
C. 64%
D. 80%
E. 90%
Correct answer & Explanation:
Answer: B. 47%
Explanation
Assume a cohort of 1,000 children:
- 100 have developmental delay. With 80% sensitivity, 80 are true positives.
- 900 do not have developmental delay. With 90% specificity, 90 are false positives.
Therefore:
PPV = True positives / (True positives + False positives)
PPV = 80 / (80 + 90) ≈ 47%
Thus, a positive screening result means that the child has approximately a 47% probability of actually having developmental delay.
The important principle is that positive predictive value depends strongly on disease prevalence. Even a test with good sensitivity and specificity can have a relatively modest PPV when used in a population where the condition is uncommon.
