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Difficulty: MediumDiagnostic Testing Performance

A 55-year-old man presents to the emergency department with sudden-onset, tearing chest pain radiating to his back. The physician suspects acute aortic dissection. Based on his history, physical examination, and initial chest x-ray findings, the pre-test probability of an acute aortic dissection is estimated to be 20%20\%. The physician orders a rapid D-dimer assay, which for this specific cutoff has a reported sensitivity of 80%80\% and a specificity of 95%95\% for aortic dissection in this clinical setting. The patient's D-dimer result returns negative.

Based on these test characteristics, what is the probability (expressed as a percentage) that this patient actually has an acute aortic dissection despite the negative test result?

Answer: 5 %

Answer

The probability that the patient has an aortic dissection despite a negative test result is 5%.
The patient's probability of having the disease despite a negative test is the false omission rate. Using a 2x2 table for a theoretical cohort of 100 patients with a 20%20\% pre-test probability: 20 have the disease, and 80 do not. With 80%80\% sensitivity, there are 4 false negatives. With 95%95\% specificity, there are 76 true negatives. The total number of negative tests is 80 (4 false negatives + 76 true negatives). The probability that a negative result is false (the patient actually has the disease) is 4/80=0.054 / 80 = 0.05, or 5%5\%.

Step-by-Step Solution

1
Determine the disease distribution in a theoretical cohort of 100 patients.
20 patients have the disease (Pre-test probability = 20%20\%) and 80 patients do not have the disease.
Establishing a standard population makes calculating true and false test results straightforward.
2
Calculate the number of false negative results.
Out of 20 patients with the disease, 20%20\% will falsely test negative (100%−80%100\% - 80\% sensitivity). 20×0.20=420 \times 0.20 = 4 false negative patients.
Sensitivity identifies the true positive rate; its complement provides the false negative rate.
3
Calculate the number of true negative results.
Out of 80 patients without the disease, 95%95\% will correctly test negative (Specificity = 95%95\%). 80×0.95=7680 \times 0.95 = 76 true negative patients.
Specificity is the proportion of patients without the disease who correctly test negative.
4
Calculate the post-test probability of having the disease given a negative test.
Total negative tests = 4+76=804 + 76 = 80. Probability = False Negatives / Total Negatives = 4/80=0.054 / 80 = 0.05, or 5%5\%.
This calculation represents the False Omission Rate, which is the probability of the disease actually being present when the test result is negative.

Key Concept

The post-test probability after a negative test (False Omission Rate) is calculated by dividing the number of false negatives by the total number of negative test results. It depends on sensitivity, specificity, and the pre-test probability of the disease.
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Diagnostic Testing Performance

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