An Unaffected Sibling Asks for a Recurrence Risk
A couple, both unaffected, have two children. Their son is affected by a rare metabolic disorder confirmed to be autosomal recessive; their daughter is unaffected and is now 24 years old. The family lives in a district where newborn screening is not routine, and the carrier frequency in the general population is estimated as 1 in 50. The daughter's partner is unrelated and has no family history of the disorder. The daughter asks a genetic counsellor: 'My brother has it, so what is the chance my first child will be affected?' The counsellor also has access to carrier testing for the known pathogenic variant, but the daughter has not yet been tested. The counsellor must give a probability before testing and explain how testing would change it.
1. Assign genotypes to the parents and both children. Calculate the probability that the unaffected daughter is a carrier, and explain why it is not 1/2.
Read the worked answer
Let A be the normal allele and a the pathogenic allele. Both parents are unaffected but have an affected child, so both must be Aa. The affected son is aa. The unaffected daughter can be AA or Aa. From Aa × Aa, the offspring probabilities are 1/4 AA, 1/2 Aa, 1/4 aa. Given that she is unaffected, aa is excluded, so the remaining possibilities are AA (1/4) and Aa (1/2), total 3/4. Her carrier probability is (1/2)/(3/4) = 2/3. It is not 1/2 because we are conditioning on the observed fact that she is unaffected; the two carrier-producing outcomes are weighted against the three unaffected outcomes, not against all four.
2. Using the population carrier frequency, calculate the probability that the daughter's first child will be affected before any testing. Show the multiplication.
Read the worked answer
Assume the partner's carrier probability is the population value, 1/50, and that the couple's genotypes are independent. Probability child is affected = P(daughter carrier) × P(partner carrier) × P(child aa | both carriers). = (2/3) × (1/50) × (1/4) = 2/600 = 1/300 ≈ 0.0033, or about 0.33%. This is a conditional risk given the family history; it is not the population risk of 1/50 × 1/50 × 1/4. The calculation assumes the partner has no family history and that the population frequency applies to his ancestry.
3. If carrier testing shows the daughter is a carrier, but the partner tests negative for the known variant, what is the residual risk that their child is affected? State one limitation of the test that affects your answer.
Read the worked answer
If the daughter is confirmed Aa and the partner's test is perfect and fully informative, his carrier risk is essentially zero for this variant, so the couple's risk is near 0. But carrier tests usually detect only a defined set of variants. If the test detects, say, 90% of pathogenic variants in this population, a negative partner still has a residual carrier probability of about (1/50) × 0.10 = 1/500. Then risk = 1 × (1/500) × (1/4) = 1/2000, or 0.05%. The exact residual risk depends on the test's sensitivity and on whether the familial variant is included. A negative result lowers but does not always eliminate risk; genetic counselling should state the detection rate.