A multicenter study evaluates the diagnostic accuracy of a novel serological marker (anti-… — USMLE Step 2 CK

A multicenter study evaluates the diagnostic accuracy of a novel serological marker (anti-tissue transglutaminase isoform X) for identifying celiac disease. Researchers enroll $500$ adult patients presenting with chronic diarrhea and weight loss. All patients undergo both the novel serological test and a duodenal biopsy, which serves as the gold standard for diagnosis.

The biopsy results confirm celiac disease in $100$ of the enrolled patients. Among these $100$ patients, $85$ have a positive result on the novel serological test.

Among the $400$ patients who do not have celiac disease according to the biopsy, $360$ have a negative result on the novel serological test.

Based on these study results, what is the positive likelihood ratio ( $LR+$ ) of the novel serological test for diagnosing celiac disease?

Answer: 8.5

Answer

8.5

The positive likelihood ratio (

LR+

) represents how much more likely a positive test result is to occur in a patient with the disease compared to a patient without the disease. It is calculated using the formula

LR+ = \frac{Sensitivity}{1 - Specificity}

. Based on the study data, the sensitivity (true positive rate) is

85 / 100 = 0.85

, and the specificity (true negative rate) is

360 / 400 = 0.90

. The false positive rate (

1 - Specificity

) is therefore

0.10

. Dividing the sensitivity by the false positive rate gives

0.85 / 0.10 = 8.5

Step-by-Step Solution

Determine the distribution of test results among patients with and without the disease.

TP = 85

;

FN = 100 - 85 = 15

;

TN = 360

;

FP = 400 - 360 = 40

Accurate categorization into a 2x2 contingency table is required to compute performance metrics.

Calculate the Sensitivity of the test.

Sensitivity = \frac{TP}{TP + FN} = \frac{85}{100} = 0.85

Sensitivity is the proportion of true positives among all patients who actually have the disease.

Calculate the Specificity of the test.

Specificity = \frac{TN}{TN + FP} = \frac{360}{400} = 0.90

Specificity is the proportion of true negatives among all patients who do not have the disease.

Calculate the Positive Likelihood Ratio (

LR+

LR+ = \frac{Sensitivity}{1 - Specificity} = \frac{0.85}{1 - 0.90} = \frac{0.85}{0.10} = 8.5

LR+

quantifies how much more likely a positive test result is to occur in a patient with the disease compared to a patient without the disease.

Key Concept

Calculating the Positive Likelihood Ratio (LR+) from raw clinical data requires determining Sensitivity and Specificity first.

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