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Difficulty: HardDiagnostic and Screening Test Performance

A city health department is evaluating a new rapid antigen test for a circulating strain of influenza. Surveillance data indicates that the prevalence of this influenza strain among symptomatic patients presenting to urgent care clinics is 20%20\%. In this specific clinical setting, validation studies demonstrate that the rapid antigen test has a positive predictive value of 50%50\% and a sensitivity of 80%80\%.

Based on these findings, what is the specificity of this new rapid antigen test? (Enter the value as a percentage)

Answer: 80 %

Answer

80
Specificity is defined as the proportion of patients without the disease who correctly test negative. By using the provided prevalence (20%20\%) and sensitivity (80%80\%), we determine the true positive rate for a hypothetical cohort. We then use the positive predictive value (50%50\%) formula algebraically to deduce the absolute number of false positives. Subtracting false positives from the total disease-negative population yields the true negatives, allowing us to calculate a final specificity of 80%80\%.

Step-by-Step Solution

1
Set up a hypothetical population to calculate absolute numbers based on the given prevalence.
In a population of 1000 patients with a 20% prevalence, there are 200 patients with influenza and 800 patients without influenza.
Using a hypothetical round number (like 1000) simplifies the translation of probabilities into a standard 2x2 contingency table without dealing with decimals.
2
Calculate the True Positives (TP) using the given sensitivity.
TP = 200 * 0.80 = 160 patients.
Sensitivity is defined as the proportion of actual positive cases that are correctly identified by the test.
3
Use the Positive Predictive Value (PPV) formula to solve for False Positives (FP).
0.50 = 160 / (160 + FP) => 0.50 * (160 + FP) = 160 => 80 + 0.50 * FP = 160 => FP = 160 patients.
PPV is the probability that a positive test result is a true positive. Working backward from PPV allows us to identify how many false positives occurred.
4
Calculate True Negatives (TN) by subtracting False Positives from the total disease-free population.
TN = 800 (Total without disease) - 160 (FP) = 640 patients.
The entire disease-free population must either test positive (False Positives) or negative (True Negatives).
5
Calculate the specificity of the test.
Specificity = 640 / 800 = 0.80 or 80%.
Specificity is defined as the proportion of individuals without the disease who correctly test negative (TN / Total without disease).

Key Concept

Calculating Specificity using Prevalence, Sensitivity, and Positive Predictive Value
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Topics

Diagnostic and Screening Test Performance

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