A rural community health center introduces a new rapid point-of-care test for Lyme disease… — USMLE Step 2 CK

A rural community health center introduces a new rapid point-of-care test for Lyme disease during the summer months. Based on epidemiological data, the pre-test probability of a patient having Lyme disease when presenting with non-specific flu-like symptoms in this region is $25\%$ . The rapid test has a documented sensitivity of $84\%$ and a specificity of $92\%$ . A 32-year-old forestry worker presents with malaise and myalgia and tests positive on this new assay. What is the positive predictive value of this test for this patient? Express your answer as a percentage rounded to one decimal place.

Answer: 77.8 %

Answer

77.8

The positive predictive value (PPV) is the probability that a patient with a positive test result actually has the disease. It is calculated by dividing the true positive results by the total positive results (true positives + false positives). Using the given prevalence of

25\%

, sensitivity of

84\%

, and specificity of

92\%

, a hypothetical population of 10,000 yields 2,100 true positives and 600 false positives, resulting in a PPV of

\frac{2,100}{2,700} \approx 77.8\%

Step-by-Step Solution

Identify the given statistical parameters for the clinical scenario.

Prevalence =

25\%

(

0.25

), Sensitivity =

84\%

(

0.84

), Specificity =

92\%

(

0.92

These are the necessary components to calculate predictive values.

Set up a hypothetical population to calculate exact patient numbers.

Assume a population of

10,000

patients.

Using whole numbers makes calculating true positives and false positives more intuitive than calculating compound probabilities.

Calculate the number of patients who actually have the disease (Disease Positive) and those who do not (Disease Negative).

Disease Positive =

10,000 \times 0.25 = 2,500

. Disease Negative =

10,000 - 2,500 = 7,500

Prevalence dictates the baseline disease status in the population.

Calculate True Positives (TP) and False Positives (FP).

TP =

2,500 \times 0.84 = 2,100

. FP =

7,500 \times (1 - 0.92) = 7,500 \times 0.08 = 600

TP is derived from sensitivity applied to diseased patients. FP is derived from the false positive rate (

1 - \text{Specificity}

) applied to healthy patients.

Calculate the Positive Predictive Value (PPV).

PPV =

\frac{\text{TP}}{\text{TP} + \text{FP}} = \frac{2,100}{2,100 + 600} = \frac{2,100}{2,700} \approx 0.7777

77.8\%

PPV represents the proportion of all positive test results that are true positives.

Key Concept

Positive Predictive Value (PPV) Calculation and Dependence on Prevalence

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