Question

Difficulty: MediumDiagnostic Testing Performance

A 72-year-old woman comes to the clinic due to a 4-week history of new-onset headaches and generalized fatigue. She has no vision changes, jaw claudication, or scalp tenderness. She has a history of osteoarthritis and hypertension. Her temperature is 37.2°C (99.0°F), blood pressure is 140/85 mm Hg, and pulse is 78/min. Physical examination shows normal, non-tender temporal arteries. Laboratory studies show an erythrocyte sedimentation rate of 45 mm/h (reference range: 0-30 mm/h). Given the atypical presentation but elevated inflammatory markers in an older adult, the physician suspects giant cell arteritis (GCA) but estimates the pre-test probability to be only 20%. To aid in the diagnosis before deciding on an invasive temporal artery biopsy, the physician orders a high-resolution color Doppler ultrasound of the temporal arteries. Evidence shows that a 'halo sign' (hypoechoic wall thickening) on this ultrasound has a positive likelihood ratio of 12.0 and a negative likelihood ratio of 0.2 for GCA. The patient's ultrasound reveals a clear halo sign. Which of the following is the best estimate of this patient's post-test probability of having giant cell arteritis?

  1. A
    5%
  2. B
    20%
  3. C
    71%
  4. 75%Answer
  5. E
    92%

Answer

75%
The correct answer accurately calculates post-test probability using the standard three-step approach. First, the pre-test probability of 20%20\% is converted to odds: 0.201−0.20=0.25\frac{0.20}{1 - 0.20} = 0.25. Next, because the ultrasound result is positive, the pre-test odds are multiplied by the positive likelihood ratio to find the post-test odds: 0.25×12.0=3.00.25 \times 12.0 = 3.0. Finally, the post-test odds are converted back into a probability: 3.01+3.0=0.75\frac{3.0}{1 + 3.0} = 0.75, which equals 75%75\%.

Step-by-Step Solution

1
Convert the pre-test probability to pre-test odds.
Pre-test odds = 0.201−0.20=0.200.80=0.25\frac{0.20}{1 - 0.20} = \frac{0.20}{0.80} = 0.25.
Likelihood ratios can only be multiplied by odds, not by percentages or probabilities.
2
Calculate the post-test odds by multiplying the pre-test odds by the positive likelihood ratio (LR+).
Post-test odds = 0.25×12.0=3.00.25 \times 12.0 = 3.0.
The test result was positive, so the positive likelihood ratio (12.0) must be used to update the odds.
3
Convert the post-test odds back to a post-test probability.
Post-test probability = 3.01+3.0=3.04.0=0.75\frac{3.0}{1 + 3.0} = \frac{3.0}{4.0} = 0.75, or 75%75\%.
Clinical decision-making relies on probability (percentage risk), so the odds must be converted back to a standard probability format.

Key Concept

Using likelihood ratios to calculate post-test probability requires converting probability to odds, multiplying by the likelihood ratio, and converting back to probability.
Rate this question