Question

A new screening test is applied. It yields 90 true positives and 50 false positives. What is the positive predictive value (PPV) of the test?

• A. 64.3%
• B. 90%
• C. 50%
• D. 35.7%

Hint:

PPV = true positives ÷ all who tested positive (TP + FP).

Answer 1

The Correct Option is A

Step 1: Recall the definition of PPV. The positive predictive value is the probability that a person who tests positive truly has the disease. It uses only those who tested positive:
\[ PPV = \frac{\text{True Positives}}{\text{True Positives} + \text{False Positives}} \]

Step 2: Identify the numbers. True positives (TP) = 90 and false positives (FP) = 50, so the total number testing positive = 90 + 50 = 140.

Step 3: Substitute.
\[ PPV = \frac{90}{140} = 0.643 = 64.3\% \]

Step 4: Interpret. About 64% of those flagged positive by the test actually have the disease; the remaining ~36% are false alarms.

Step 5: Why the others are wrong. 90% wrongly treats all 90 TP as the whole positive group. 50% has no valid derivation. 35.7% is the complement (50/140), i.e. the false-positive proportion among positives, not the PPV.

Key fact: PPV = TP / (TP + FP) = 90/140 ≈ 64.3%.