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Difficulty: HardDiagnostic Testing Performance

A 42-year-old man comes to the urgent care clinic complaining of fever, severe myalgias, and a retro-orbital headache for the past 3 days. He recently returned from a business trip to a tropical region experiencing an outbreak of a novel mosquito-borne viral illness. The local health department recently provided urgent care centers with a new rapid antigen test for this virus. According to the validation literature provided with the test kits, the test has a sensitivity of 90% and a specificity of 90%. The literature notes that in the validation cohort, which consisted of highly symptomatic patients admitted to a tropical disease hospital, the prevalence of the disease was 50%. However, an epidemiological alert for your specific community urgent care setting estimates the prevalence of this viral illness among patients presenting with similar symptoms to be 10%. The physician performs the rapid antigen test on this patient, and the result is positive.

Based on the epidemiological data for this urgent care setting, which of the following is the best estimate of the probability that this patient actually has the novel viral illness?

  1. A
    9%
  2. B
    10%
  3. 50%Answer
  4. D
    90%
  5. E
    99%

Answer

50%
The probability that a patient with a positive test actually has the disease is defined as the Positive Predictive Value (PPV). Unlike sensitivity and specificity, which are intrinsic properties of the test, PPV is highly dependent on the disease prevalence in the tested population. In this urgent care setting, the prevalence is 10%. Using a hypothetical cohort of 1,000 patients, 100 will have the disease and 900 will not. With a sensitivity of 90%, there will be 90 true positives. With a specificity of 90%, 810 of the 900 healthy individuals will appropriately test negative, leaving 90 false positives. The total number of positive test results is 180 (90 true positives + 90 false positives). The PPV is the ratio of true positives to total positive results: 90/180=50%90 / 180 = 50\%. Therefore, despite the test's high sensitivity and specificity, the low prevalence in this setting means a positive result is essentially a coin flip.

Step-by-Step Solution

1
Identify the goal and the relevant testing population parameters.
The goal is to find the Positive Predictive Value (PPV) in the urgent care setting. The prevalence (pre-test probability) is 10%, sensitivity is 90%, and specificity is 90%.
PPV depends heavily on the disease prevalence of the specific testing population. The 50% prevalence from the validation cohort is no longer applicable.
2
Construct a hypothetical cohort of 1,000 patients to represent the urgent care population.
With a 10% prevalence, 100 patients have the disease and 900 do not.
Using a fixed population size makes it straightforward to calculate the raw numbers of true positives and false positives without complex formulas.
3
Calculate the number of True Positives (TP).
100×0.90=90100 \times 0.90 = 90 True Positives.
Sensitivity (90%) is the proportion of patients with the disease who correctly test positive.
4
Calculate the number of False Positives (FP).
Specificity is 90%, meaning 900×0.90=810900 \times 0.90 = 810 True Negatives. The remaining 900−810=90900 - 810 = 90 patients are False Positives.
False positives occur in the healthy population when the test incorrectly returns a positive result (1−Specificity1 - \text{Specificity}).
5
Calculate the Positive Predictive Value (PPV).
PPV=TPTP+FP=9090+90=90180=50%PPV = \frac{TP}{TP + FP} = \frac{90}{90 + 90} = \frac{90}{180} = 50\%.
PPV represents the probability that a patient with a positive test result actually has the disease.

Key Concept

Positive Predictive Value (PPV) calculation in shifting prevalence settings
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Topics

Diagnostic Testing Performance

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