Recurrence Risk in a Family with an Affected Daughter
Both parents are healthy and have three children: an unaffected son (age 9), an affected daughter (age 6), and an affected son (age 3). The two affected children have the same rare metabolic disorder, which has an incidence of about 1 in 60,000 in the general population. There is no known consanguinity and no other affected relatives. The parents ask about the chance that a future child will be affected. They also ask whether their unaffected son could be a carrier and what the risk would be for the affected daughter's future children. The family's ethnic group has a carrier frequency for this disorder of about 1/60. The parents are considering another pregnancy and want a number they can understand, not just a statement that the condition is recessive.
1. Which mode of inheritance is most consistent with this family, and why is X-linked recessive effectively ruled out? Explain how the affected daughter's sex and the father's phenotype interact.
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Autosomal recessive is the best fit. Both parents are unaffected but have two affected children of different sexes, which is the signature of two carrier parents. X-linked recessive is effectively ruled out by the affected daughter. A female has two X chromosomes and inherits one from each parent. For her to be affected by an X-linked recessive trait, she would need an affected X from her father; but a father has only one X, so an affected X would make him affected. The father is healthy, so he cannot transmit an affected X-linked allele. An affected daughter therefore cannot occur in X-linked recessive inheritance with an unaffected father. Autosomal dominant is also unlikely because neither parent is affected and the disorder is rare; a new mutation in both affected children would be extraordinarily unlikely. Mitochondrial inheritance is inconsistent with the family pattern because an affected daughter and son from an unaffected mother would require unusual heteroplasmy. Molecular testing would confirm, but the pedigree strongly favors autosomal recessive.
2. Calculate the recurrence risk for the next pregnancy and the probability that the unaffected 9-year-old son is a carrier. Show each step.
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Label the parents Aa and Aa. Their possible offspring are AA (1/4), Aa (1/2), and aa (1/4). The affected children are aa, confirming both parents carry a. For each future pregnancy, the chance of aa is 1/4, or 25%; the chance of an unaffected child is 3/4. For the unaffected son, condition on his being unaffected: he is either AA or Aa. The prior probabilities are AA 1/4 and Aa 1/2, so among unaffected children the proportions are (1/4)/(3/4) = 1/3 AA and (1/2)/(3/4) = 2/3 Aa. Thus his carrier probability is 2/3, not 1/2. The recurrence risk is independent of previous children; having two affected children does not change the 1/4 risk for the next pregnancy, just as coin flips do not 'correct' past outcomes. If the parents used prenatal testing, that would provide direct information, but the Mendelian risk remains 25% before testing.
3. The affected daughter later partners with a man whose brother has the same disorder. How does that change her child's risk compared with using the population carrier frequency of 1/60? Explain the reasoning.
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The daughter is aa, so she always passes a. Her partner's brother is affected, which implies the partner's parents are both carriers (Aa × Aa), assuming the same autosomal recessive disorder. The partner is unaffected, so his possible genotypes are AA (1/3) or Aa (2/3), exactly the same conditional logic as the 9-year-old son. His carrier probability is therefore 2/3. The child is affected only if the partner is a carrier and passes a: (2/3) × (1/2) = 1/3. Using the population carrier frequency of 1/60 gives (1/60) × (1/2) = 1/120. The family history raises the risk from about 0.83% to about 33%, a 40-fold increase. The population frequency is a prior that assumes no relevant family history; a close affected relative updates that prior strongly. If the brother's disorder were a different condition, the calculation would not apply, so confirmation is important.