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Difficulty: MediumDiagnostic and Screening Test Performance

A 32-year-old man comes to an outpatient community clinic in early autumn complaining of fever, cough, and myalgias. Epidemiological surveillance estimates that the prevalence of influenza A among symptomatic patients in this community is currently 20%20\%. The physician decides to use a new rapid point-of-care antigen test for influenza A. During its initial validation study at a tertiary care center during peak flu season (prevalence of 50%50\%), the test demonstrated a sensitivity of 80%80\% and a specificity of 90%90\%. Assuming the test's sensitivity and specificity remain constant, if this patient's test yields a positive result, which of the following best estimates the probability that he actually has influenza A?

  1. A
    16%16\%
  2. 67%67\%Answer
  3. C
    80%80\%
  4. D
    89%89\%
  5. E
    95%95\%

Answer

The probability that the patient actually has influenza A given a positive test is approximately 67%67\%.
The probability that the patient actually has influenza A given a positive test result is the positive predictive value (PPV). Predictive values depend heavily on the prevalence of the disease in the tested population. To calculate the new PPV, a 2×22 \times 2 contingency table can be constructed based on the community's prevalence of 20%20\%. In a hypothetical population of 100100 patients, 2020 will have influenza A and 8080 will not. With a sensitivity of 80%80\%, there will be 1616 true-positive results (0.80×200.80 \times 20). With a specificity of 90%90\%, there will be 7272 true-negative results (0.90×800.90 \times 80), leaving 88 false-positive results (80−7280 - 72). The total number of positive test results is the sum of true positives and false positives (16+8=2416 + 8 = 24). The PPV is the ratio of true positives to total positives: 16/24=2/316 / 24 = 2/3, which is approximately 67%67\%.

Step-by-Step Solution

1
Identify the current pre-test probability (prevalence) of influenza A.
The current prevalence in the community clinic is 20%20\%.
Predictive values are highly dependent on the prevalence of the disease in the specific population being tested, not the prevalence from the validation study.
2
Determine the number of patients with and without disease in a hypothetical population of 100.
2020 patients have the disease (Disease Positive) and 8080 patients do not (Disease Negative).
Using a hypothetical cohort of 100 makes calculating the components of the 2×22 \times 2 contingency table straightforward.
3
Calculate the expected number of true-positive and false-positive test results.
True Positives = 0.80×20=160.80 \times 20 = 16. False Positives = (1−0.90)×80=0.10×80=8(1 - 0.90) \times 80 = 0.10 \times 80 = 8.
Sensitivity (80%80\%) determines the proportion of diseased patients who test positive. Specificity (90%90\%) determines the proportion of healthy patients who test negative, leaving 10%10\% to incorrectly test positive.
4
Calculate the positive predictive value (PPV).
PPV = True Positives / (True Positives + False Positives) = 16/(16+8)=16/24=2/3≈67%16 / (16 + 8) = 16 / 24 = 2/3 \approx 67\%.
The question asks for the probability of having the disease given a positive test, which is the definition of PPV.

Key Concept

The positive predictive value (PPV) of a test changes dynamically with the prevalence of the disease in the tested population, even when intrinsic test characteristics (sensitivity and specificity) remain constant.
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Topics

Diagnostic and Screening Test Performance

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