A Negative Carrier Test in an X-Linked Disorder
After a genetics unit, a 16-year-old female student asks a teacher candidate a personal question. Her mother's two brothers have Duchenne muscular dystrophy (DMD), an X-linked recessive disorder. Her mother is unaffected and has not been tested. The student has no brothers and has already received deletion/duplication carrier testing on a cheek swab; the result is negative. No mutation has been identified in her affected uncles, so the test is estimated to detect about 70% of carrier females in this situation. The student asks whether a negative result means her future sons cannot have DMD. School policy directs health-related questions to the school nurse or a genetic counselor, but the student wants an explanation now. The teacher candidate must respond without diagnosing, while using the moment to teach conditional probability, test sensitivity, and the limits of a negative result.
1. Calculate the student's prior probability of being a carrier and her approximate residual probability after the negative deletion/duplication test. Show each step and state your assumptions.
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Step 1: Grandmother. Two affected sons make the maternal grandmother an obligate carrier, assuming no other explanation, which is reasonable here.
Step 2: Mother. An unaffected daughter of an obligate carrier has prior carrier probability 1/2.
Step 3: Student. A daughter of a woman with carrier probability 1/2 has prior probability 1/2 × 1/2 = 1/4.
Step 4: Negative test. Sensitivity is about 0.70, so P(negative | carrier) = 0.30. Specificity is effectively 1 for this calculation. P(carrier | negative) = (0.25 × 0.30) / [(0.25 × 0.30) + (0.75 × 1.00)] = 0.075 / 0.825 ≈ 0.091.
Result: about 9% residual carrier probability, not zero. Assumptions: the 70% sensitivity applies, no familial mutation is known, and the test is specific. If the uncles' mutation were identified, targeted testing would change the estimate substantially.
2. Explain why the statement a negative test means zero risk is wrong, and translate the residual risk into approximate risks for a future son and daughter.
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A negative test lowers the probability but cannot eliminate it because deletion/duplication testing misses some carrier females. With a residual carrier probability of about 9%, each future son has about 0.09 × 1/2 ≈ 4.5% risk of DMD, and each daughter has about 4.5% risk of being a carrier. These are approximate and assume the test result is valid. The key teaching point is conditional probability: the test result updates a prior risk; it does not erase the family history. The candidate should also distinguish population risk from this family's risk and avoid saying the sons are safe. A genetic counselor can discuss confirmatory testing, prenatal options, and the uncertainty in more detail.
3. Draft a three-sentence response that stays within the teacher's role and redirects the student appropriately.
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Model response: I can explain the probability, but I cannot interpret your test or tell you what to do medically. A negative test lowers your chance of being a carrier but does not make it zero, because the test misses some carriers; that is why the school nurse or a genetic counselor should review the result with you. If you want, I can walk you through the pedigree and the math so you can ask them better questions. This is three sentences, stays within the teacher's role, is empathetic, and redirects to the appropriate professional without giving a diagnosis.