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Difficulty: MediumDiagnostic and Screening Test Performance

A university health center is implementing a new point-of-care screening assay for a highly contagious viral pharyngitis during a campus outbreak. Epidemiological surveillance indicates that the prevalence of this specific viral infection among students presenting with a sore throat is 10%10\%. The manufacturer of the point-of-care assay reports a sensitivity of 90%90\% and a specificity of 90%90\%. A student presenting with a sore throat is tested using this new assay, and the result is positive.

Based on the provided test characteristics, which of the following best represents the probability that this student actually has the viral infection?

  1. A
    10%10\%
  2. 50%50\%Answer
  3. C
    81%81\%
  4. D
    90%90\%
  5. E
    99%99\%

Answer

50%50\%
The positive predictive value (PPV) is the probability that a patient with a positive test actually has the disease. It depends heavily on the prevalence of the disease in the tested population. Using a 2×22 \times 2 contingency table for a hypothetical cohort of 1,0001,000 students, a 10%10\% prevalence means 100100 students have the disease and 900900 do not. A test with 90%90\% sensitivity yields 9090 true positives (0.90×1000.90 \times 100). A test with 90%90\% specificity has a false positive rate of 10%10\%, which yields 9090 false positives (0.10×9000.10 \times 900). The total number of positive tests is 180180 (9090 true + 9090 false). The PPV is the ratio of true positives to total positives, which is 90/18090 / 180, resulting in 50%50\%.

Step-by-Step Solution

1
Establish a hypothetical population to simplify calculations.
Assume a population of 1,0001,000 students presenting with a sore throat.
Using absolute numbers instead of pure probabilities makes calculating positive predictive value (PPV) more intuitive.
2
Calculate the true positives based on prevalence and sensitivity.
A prevalence of 10%10\% means 100100 students have the disease. A sensitivity of 90%90\% means there are 9090 true positive results (0.90×100=900.90 \times 100 = 90).
Sensitivity identifies the proportion of actually diseased individuals who test positive.
3
Calculate the false positives based on the healthy population and specificity.
900900 students do not have the disease. A specificity of 90%90\% means a 10%10\% false positive rate (1−0.90=0.101 - 0.90 = 0.10). Thus, there are 9090 false positive results (0.10×900=900.10 \times 900 = 90).
The false positive rate applied to the healthy individuals gives the number of people who incorrectly test positive.
4
Calculate the positive predictive value.
PPV=True PositivesTrue Positives+False Positives=9090+90=50%\text{PPV} = \frac{\text{True Positives}}{\text{True Positives} + \text{False Positives}} = \frac{90}{90 + 90} = 50\%.
PPV defines the probability that a positive test result represents a true infection.

Key Concept

Calculation of Positive Predictive Value (PPV) and the impact of disease prevalence on false positive rates.
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Topics

Diagnostic and Screening Test Performance

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