An international health consortium is assessing a novel rapid antigen test for detecting a… — USMLE Step 2 CK

An international health consortium is assessing a novel rapid antigen test for detecting a newly identified strain of avian influenza in symptomatic individuals. During the initial clinical validation phase, the test was administered to $2,000$ patients with respiratory symptoms. Confirmatory polymerase chain reaction (PCR) testing, acting as the gold standard, diagnosed the influenza strain in $400$ of these patients. The novel rapid test returned a positive result in $360$ of the infected patients. Among the patients confirmed to be uninfected by PCR, the rapid test incorrectly indicated a positive result in $240$ individuals.

Based on these performance metrics, the consortium decides to implement the rapid test at a dedicated respiratory triage center where historical epidemiological data indicates the prevalence of this specific influenza strain is $30\%$ among presenting patients.

Assuming the intrinsic diagnostic properties of the test remain constant, what is the positive predictive value of the rapid antigen test in this triage center? (Express your answer as a percentage)

Answer: 72 %

Answer

The correct calculation accounts for the shift in prevalence while maintaining the intrinsic test properties. From the validation study, Sensitivity is 90% (

360/400

) and Specificity is 85% (

1360/1600

). In a new population with

30\%

prevalence, a cohort of

1,000

patients yields

300

diseased and

700

non-diseased individuals. The test will accurately identify

270

of the diseased patients (True Positives =

300 \times 0.90

) and inaccurately identify

105

of the non-diseased patients as positive (False Positives =

700 \times 0.15

). The Positive Predictive Value is the ratio of True Positives to all positives:

270 / (270 + 105) = 270 / 375 = 0.72

, or

72\%

Step-by-Step Solution

Calculate the test's sensitivity and specificity from the initial validation cohort.

Sensitivity = 90%, Specificity = 85%

Sensitivity and specificity are intrinsic properties of the test and remain constant regardless of disease prevalence. Sensitivity = TP / Total Disease Positive = 360 / 400 = 0.90. Specificity = TN / Total Disease Negative = (1600 - 240) / 1600 = 1360 / 1600 = 0.85.

Establish the disease distribution in the new triage center population.

Disease positive = 30%, Disease negative = 70%

The new clinical setting has a known prevalence of 30%, which acts as the pre-test probability.

Calculate the expected number of True Positives (TP) and False Positives (FP) for a hypothetical cohort of 1,000 patients in the triage center.

TP = 270, FP = 105

TP is calculated as (Prevalence) * (Sensitivity) * 1000 = 300 * 0.90 = 270. FP is calculated as (1 - Prevalence) * (1 - Specificity) * 1000 = 700 * 0.15 = 105.

Calculate the Positive Predictive Value (PPV) using the new TP and FP values.

PPV = 72%

PPV represents the probability that a positive test result is a true positive. PPV = TP / (TP + FP) = 270 / (270 + 105) = 270 / 375 = 0.72, or 72%.

Key Concept

While sensitivity and specificity are intrinsic to a diagnostic test and do not change with disease prevalence, predictive values (PPV and NPV) are highly dependent on the prevalence of the disease in the tested population.

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