A physician-validated, board-style question from the Active Transport QBank. Try it, then check the reasoning for every option.
A 14-month-old boy is brought in by his parents with an 8-month history of diarrhea, abdominal tenderness and concomitant failure to thrive. The pediatric attending physician believes that Crohn’s disease is the best explanation of this patient’s symptoms. Based on the pediatric attending physician’s experience, the pretest probability of this diagnosis is estimated at 40%. According to Fagan nomogram (see image). If the likelihood ratio of a negative test result (LR-) for Crohn’s disease is 0.04, what is the chance that this is the correct diagnosis in this patient with a negative test result?
-
A
2.5%Correct. Pretest odds 0.667 × LR− 0.04 = posttest odds 0.0267, which converts to posttest probability ≈ 2.5%.
-
B
25%Incorrect. 25% would imply an LR− of about 0.5, which barely moves the probability — not consistent with LR− 0.04.
-
C
40%Incorrect. 40% is the pretest probability itself; the question asks how a negative test result changes it.
-
D
97.5%Incorrect. 97.5% would be the posttest probability after a strongly POSITIVE test, not a negative one.
-
E
Approximately 60%Incorrect. 60% would represent a post-test probability after a mildly positive test (LR+ ~2); a negative test with LR− 0.04 lowers, rather than raises, the probability of disease.
↑ Tap an answer to reveal the reasoning
Answer: A. Using Bayes' theorem (or Fagan nomogram): pretest odds = 0.4 / 0.6 ≈ 0.667. Posttest odds (negative test) = pretest odds × LR− = 0.667 × 0.04 = 0.0267. Posttest probability = 0.0267 / (1 + 0.0267) ≈ 2.6%, rounding to 2.5%.
The conceptual point: a very small LR− (0.04) means a negative test is extremely useful for ruling out disease ('SnNout' — a highly sensitive test with a negative result rules out). Even at a 40% pretest probability, a negative result drops the posttest probability to about 2.5%, essentially excluding Crohn disease in this child.
LR− = (1 − sensitivity) / specificity. An LR− < 0.1 produces a large (~45%) reduction in probability; an LR− between 0.1 and 0.2 produces a moderate reduction. Likelihood ratios are independent of prevalence, which is why they outperform raw predictive values when applying test results to individual patients.
**Why each option:**
**A.** Correct. Pretest odds 0.667 × LR− 0.04 = posttest odds 0.0267, which converts to posttest probability ≈ 2.5%.
**B.** 25% would imply an LR− of about 0.5, which barely moves the probability — not consistent with LR− 0.04.
**C.** 40% is the pretest probability itself; the question asks how a negative test result changes it.
**D.** 97.5% would be the posttest probability after a strongly POSITIVE test, not a negative one.