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Difficulty: MediumDiagnostic Testing Performance

A 32-year-old man presents to the clinic with an intermittent low-grade fever, fatigue, and a new heart murmur. The physician suspects infective endocarditis. Based on the clinical presentation and local epidemiological data, the physician estimates the patient's pretest probability for the disease to be 10%10\%. A novel rapid serum biomarker assay is performed, which has a reported positive likelihood ratio (LR+LR^+) of 9.09.0 and a negative likelihood ratio (LR−LR^-) of 0.20.2. The test result comes back positive. Which of the following is the best estimate of this patient's post-test probability of having infective endocarditis?

  1. 50%50\%Answer
  2. B
    90%90\%
  3. C
    99%99\%
  4. D
    100%100\%
  5. E
    2%2\%

Answer

The correct post-test probability is 50%50\%.
To calculate the post-test probability, the pretest probability (10%10\%) must first be converted into pretest odds (0.10/0.90=1/90.10 / 0.90 = 1/9). Since the test is positive, we multiply the pretest odds by the positive likelihood ratio (LR+LR^+). Multiplying 1/91/9 by an LR+LR^+ of 9.09.0 yields post-test odds of 1.01.0 (or 1:11:1). Finally, post-test odds of 1.01.0 are converted back to a post-test probability using the formula Probability = Odds / (1 + Odds), which results in 1.0/2.0=50%1.0 / 2.0 = 50\%.

Step-by-Step Solution

1
Convert the pretest probability into pretest odds.
Pretest odds = 0.11−0.1=19\frac{0.1}{1 - 0.1} = \frac{1}{9}.
Likelihood ratios are multipliers for odds, not probabilities. You must convert probability to odds before applying the test characteristics.
2
Apply the appropriate likelihood ratio based on the test result.
Post-test odds = Pretest odds ×LR+=19×9.0=1.0\times LR^+ = \frac{1}{9} \times 9.0 = 1.0.
Because the diagnostic test result was positive, the positive likelihood ratio (LR+LR^+) is used to calculate the post-test odds.
3
Convert the resulting post-test odds back into a post-test probability.
Post-test probability = 1.01.0+1.0=0.5=50%\frac{1.0}{1.0 + 1.0} = 0.5 = 50\%.
The clinical question asks for the final post-test probability of disease, which requires converting the odds back to a percentage.

Key Concept

Calculating Post-Test Probability Using Likelihood Ratios
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Topics

Diagnostic Testing Performance

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