Question

Difficulty: MediumDiagnostic and Screening Test Performance

Physicians at a tertiary care center are evaluating a novel immunoassay for diagnosing acute mesenteric ischemia. To determine the test's clinical utility, they apply it to a cohort of patients presenting with acute abdominal pain.

Among 120120 patients who are ultimately diagnosed with acute mesenteric ischemia via angiography, the immunoassay returns a positive result in 102102 cases. In another group of 400400 patients whose abdominal pain is confirmed to be non-ischemic in origin, the immunoassay is positive in 4040 cases.

Based on these findings, what is the positive likelihood ratio of this novel immunoassay?

Answer: 8.5

Answer

8.5
The positive likelihood ratio (LR+LR+) is calculated by dividing a test's sensitivity by its false positive rate (1−Specificity1 - \text{Specificity}). The sensitivity is the proportion of true positives among all those with the disease (102/120=0.85102/120 = 0.85). The false positive rate is the proportion of false positives among all those without the disease (40/400=0.1040/400 = 0.10). Dividing 0.850.85 by 0.100.10 yields 8.58.5. This indicates that a positive test result is 8.5 times more likely to be observed in a patient with acute mesenteric ischemia than in a patient without it.

Step-by-Step Solution

1
Calculate the sensitivity of the assay.
0.85
Sensitivity represents the proportion of patients with the disease who test positive (102/120102 / 120).
2
Calculate the false positive rate (1−Specificity1 - \text{Specificity}).
0.10
The false positive rate represents the proportion of disease-free patients who incorrectly test positive (40/40040 / 400).
3
Calculate the positive likelihood ratio (LR+LR+).
8.5
LR+LR+ is the ratio of sensitivity to the false positive rate (0.85/0.100.85 / 0.10).

Key Concept

The positive likelihood ratio (LR+LR+) indicates how much more likely a positive test result is to occur in a patient with the disease compared to a patient without the disease, calculated as Sensitivity / (1−Specificity1 - \text{Specificity}).
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