A new rapid antigen test for a respiratory virus is evaluated in a cohort of 1,000 symptomatic adults. The researchers compare the rapid test against the gold standard polymerase chain reaction (PCR) test. The following data are observed:
- 210 patients tested positive on both the rapid test and PCR.
- 40 patients tested negative on the rapid test but positive on PCR.
- 90 patients tested positive on the rapid test but negative on PCR.
- 660 patients tested negative on both tests.
An adult from the same community presents with similar symptoms and receives a negative rapid antigen test. Based on these validation data, what is the approximate probability that this patient actually has the viral infection?
- 5.7%Answer
- B12.0%
- C16.0%
- D25.0%
- E94.3%
Answer
5.7%
The question asks for the probability that a patient has the disease given a negative test result. This metric is the False Omission Rate (FOR), which is the complement of the Negative Predictive Value (NPV). To calculate this, divide the number of patients with the disease who tested negative (False Negatives = 40) by the total number of patients who tested negative (False Negatives + True Negatives = 40 + 660 = 700). The calculation is 40 / 700, which equals approximately 5.7%.
Step-by-Step Solution
Key Concept
The False Omission Rate (FOR) represents the probability that a patient has the disease despite a negative test result, calculated as False Negatives divided by Total Negative Tests. It is the mathematical complement to the Negative Predictive Value (1 - NPV).
Alternative Method
Instead of calculating the False Omission Rate directly, you can calculate the Negative Predictive Value (NPV = 660 / 700 = 94.3%) and subtract it from 100%. If there is a 94.3% probability the patient is truly negative, there is a 5.7% probability they are a false negative (100% - 94.3% = 5.7%).
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