A 62-year-old man presents to the emergency department with sudden-onset left-sided weakne… — USMLE Step 3

A 62-year-old man presents to the emergency department with sudden-onset left-sided weakness and slurred speech. He has a history of hypertension and type 2 diabetes. A new point-of-care biomarker assay is being evaluated in the emergency department to aid in the diagnosis of acute ischemic stroke. The prevalence (pre-test probability) of acute ischemic stroke in patients presenting to this department with similar symptoms is estimated to be $30\%$ . The biomarker assay has a reported sensitivity of $90\%$ and a specificity of $85\%$ . The patient undergoes the assay, and the result is positive.

Based on these parameters, what is the probability (in percentage) that this patient actually has an acute ischemic stroke?

Answer: 72 %

Answer

The correct answer is

72

. The positive predictive value (PPV) calculates the probability that a patient has the disease given a positive test result. This value heavily depends on the sensitivity, specificity, and prevalence (pre-test probability) of the disease. Using a

2 \times 2

table for a hypothetical cohort of

1000

patients:

300

have the disease and

700

do not. The test correctly identifies

270

of the

300

diseased patients (

90\%

sensitivity). It incorrectly identifies

105

of the

700

healthy patients (

100\% - 85\%

specificity). The total number of positive tests is

270 + 105 = 375

. The PPV is the number of true positives divided by the total positives:

\frac{270}{375} = 72\%

Step-by-Step Solution

Determine the disease and non-disease populations

Disease = 300, No Disease = 700

Using a hypothetical cohort of 1000 patients and a prevalence of 30% simplifies the calculation.

Calculate True Positives (TP)

TP = 270

Sensitivity is 90%, so 90% of the 300 patients with the disease will correctly test positive.

Calculate False Positives (FP)

FP = 105

Specificity is 85%, so 15% of the 700 patients without the disease will incorrectly test positive.

Calculate the Positive Predictive Value (PPV)

PPV = 72%

PPV is the proportion of true positives out of all positive tests: TP / (TP + FP) = 270 / 375 = 0.72.

Key Concept

Positive Predictive Value calculation using pre-test probability (prevalence), sensitivity, and specificity.

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