A carrier risk that depends on which test is done first
A 28-year-old woman asks about her risk of having a child with spinal muscular atrophy, an autosomal recessive condition. Her brother is affected; she is healthy. Her partner is healthy, from the same ethnic subgroup, and has no family history. In that subgroup the carrier frequency is 1/25; in the general population it is 1/40. A colleague writes: 'Risk = (2/3) × (1/25) × (1/4) = 1/150.' The couple is offered a carrier panel that detects 90% of pathogenic variants in this gene; a negative result means no detected variant, not necessarily no carrier status. The partner is reluctant to be tested first because 'the numbers are already small'. The clinic's genetic counselor wants a written justification of the 1/150 figure, an estimate of what a negative panel result would mean for the woman, and advice on the order of testing.
1. Justify or correct the 1/150 figure, listing every assumption it depends on.
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Chain of reasoning:
- The affected brother means both parents are carriers (assuming no de novo event and no misattributed paternity).
- An unaffected sibling of an affected child has prior carrier probability 2/3, because the possible genotypes at conception are AA, Aa, aA, aa with equal probability, and aa is excluded by her being healthy.
- The partner's prior is the carrier frequency of his own subgroup, 1/25, not 1/40. Strictly, conditioning on his being unaffected gives 2pq/(1 − q²) with q = 1/50, which is 1/25 to four significant figures because q² is negligible.
- If both are carriers, each child has probability 1/4 of being affected.
Product: (2/3)(1/25)(1/4) = 2/300 = 1/150 ≈ 0.67%.
Hidden assumptions: autosomal recessive inheritance with full penetrance; the panel has not yet been done; no consanguinity; the 1/25 figure is appropriate for this couple's actual ancestry; the brother's diagnosis is confirmed molecularly.
2. The woman takes the panel and tests negative. What is her residual carrier probability, and what is the couple's revised risk?
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Use Bayes. Prior P(carrier) = 2/3, P(not carrier) = 1/3. Sensitivity = 0.90, so P(negative | carrier) = 0.10 and P(negative | not carrier) = 1.
P(carrier | negative) = (2/3 × 0.10) / (2/3 × 0.10 + 1/3 × 1.00) = 0.0667 / (0.0667 + 0.3333) = 0.0667/0.4000 = 1/6 ≈ 0.167.
Her risk fell fourfold (from 0.667 to 0.167) but did not vanish. Revised child risk = (1/6)(1/25)(1/4) = 1/600 ≈ 0.17%.
Key point: a 90%-sensitive panel cannot reduce a prior of 2/3 below about 1/6, because the residual probability is dominated by the 10% of carriers the panel misses. Quoting 'negative, so no risk' would be wrong.
3. Advise on the order of testing. Which sample gives the most information per test, and how does that change the counseling?
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The highest-information sample is the affected brother's DNA, not the couple's. If his two pathogenic variants are identified, the family-specific variant is known, and testing the woman for just those variants is close to 100% sensitive rather than 90%. Her result then becomes near-binary: carrier (risk to a child with a carrier partner = 1/4) or not (risk ≈ 0, apart from de novo and missed-variant error).
If the brother is unavailable, test the woman first: her prior (2/3) is far higher than the partner's (1/25), so her test has the greater expected yield and a negative result already cuts the couple's risk fourfold. Test the partner second; if he is positive, her residual risk matters and a negative panel on her is not reassuring enough to skip further testing.
Counseling should quote the risk as a range conditional on test status, state that the panel is a detection test and not an exclusion test, and avoid presenting 1/150 as a final number before any testing is done.