Carrier Screening After an Affected Sibling
A healthy 22-year-old woman is 12 weeks pregnant. Her 4-year-old brother has an autosomal recessive disorder caused by mutations in a single gene; their parents are unaffected. Her partner has no family history of the disorder. The population carrier frequency is 1 in 25. The woman takes a carrier screening test that detects 90% of carriers and correctly identifies 95% of non-carriers; her result is negative. She asks, 'Since my test is negative, my baby cannot be affected, right?' The counsellor explains that the test is not diagnostic and that the woman's family history changes her prior risk. The condition is fully penetrant, is not caused by new mutations in this family, and no consanguinity is known. The partner has not been tested.
1. Explain why the woman's prior probability of being a carrier is 2/3, not 1/2 or 1/25.
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The woman's parents must both be carriers because they have an affected son but are themselves unaffected. For an autosomal recessive condition, the possible offspring of two carriers are AA, Aa, Aa and aa. The woman is unaffected, so she cannot be aa; among the remaining three equally likely genotypes, two are carriers. Her prior probability is therefore 2/3. It is not 1/2 because we already know she is unaffected, which removes the aa possibility. It is not 1/25 because the population frequency applies to people with no family history; her family history is strong evidence. The 1/25 figure is used for her partner, who has no family history.
2. Calculate the residual carrier probability after the negative test, and the chance that the baby is affected. State your assumptions.
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Using Bayes' theorem: prior carrier probability = 2/3. The test has sensitivity 90%, so P(negative | carrier) = 0.10. Specificity is 95%, so P(negative | non-carrier) = 0.95. Posterior = (2/3 × 0.10) / [(2/3 × 0.10) + (1/3 × 0.95)] = 0.0667 / 0.3833 = 0.174. The partner's prior carrier probability is 1/25 = 0.04. The chance that both are carriers is 0.174 × 0.04 = 0.00696. If both are carriers, the chance that the baby inherits two mutant alleles is 1/4. So the risk is 0.00696 × 0.25 = 0.00174, about 1 in 575. This assumes the population frequency applies to the partner, the test result is independent of other risk factors, and the condition is fully penetrant.
3. Explain why a negative test does not mean the baby cannot be affected, and describe one further test that could clarify the risk.
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A negative carrier test does not prove that the woman is not a carrier, because the test misses about 10% of carriers. The residual risk is about 1 in 575, not zero. The couple could be offered testing of the partner; if he is also negative, the risk falls further, though it is not eliminated. Prenatal diagnosis, such as chorionic villus sampling or amniocentesis, can determine the baby's genotype if both parents are known carriers. The couple should also receive genetic counselling about the uncertainties of screening and the options available. The woman's brother's condition does not change the 1/4 risk for a pregnancy once both parents are known carriers.