Beta-Thalassaemia Risk in a Consanguineous-Like Family History
At a township hospital in Mandalay, a couple seeks genetic counselling. The husband is healthy, but his younger brother died at age 6 from transfusion-dependent beta-thalassaemia. The wife is also healthy; her brother is now 12 and receives monthly transfusions for the same condition. Both sets of parents are healthy. The couple has one healthy 3-year-old son. DNA testing shows the husband carries a beta-globin mutation, but the wife has not been tested. The counsellor explains that beta-thalassaemia is autosomal recessive and that an unaffected sibling of an affected child has a two-in-three chance of being a carrier before any other information is used. The couple asks about the risk to their next child, whether their healthy son should be tested, and whether prenatal diagnosis is worthwhile. The counsellor must use the pedigree and the existing child to update the risk, and must explain the limits of the calculation.
1. Explain why the wife's prior carrier probability is 2/3, while the husband's is 1 after testing.
Read the worked answer
Beta-thalassaemia is autosomal recessive. The wife's affected brother must have inherited one mutation from each parent, so both of her parents are carriers. The wife is unaffected, so she cannot be homozygous affected. The original Mendelian ratio for their children is AA : Aa : aa = 1 : 2 : 1. Given that she is unaffected, aa is excluded, leaving AA : Aa = 1 : 2. Therefore P(carrier) = 2/3. It is not 1/2, because being unaffected is extra information that removes the affected genotype from the possible outcomes.
The husband also has an affected brother, so his parents are carriers too; before testing his probability would also be 2/3. However, DNA testing detected a beta-globin mutation in him, so his carrier status is confirmed. His probability is therefore 1, assuming the test detects the family mutation. The wife's 2/3 remains a prior probability until she is tested.
2. Calculate the risk that the next child will be affected using only the prior 2/3, and then after incorporating the healthy 3-year-old son. Comment on the size of the change.
Read the worked answer
Using only the prior probability: P(affected child) = P(husband carrier) × P(wife carrier) × 1/4 = 1 × 2/3 × 1/4 = 1/6 = 16.7%.
Now incorporate the healthy son using Bayes' theorem. Before the son, the wife's prior odds of carrier : non-carrier are 2 : 1. If she is a carrier, the chance of a healthy child is 3/4. If she is not a carrier, the chance of a healthy child is 1. Posterior P(carrier) = (2/3 × 3/4) ÷ [(2/3 × 3/4) + (1/3 × 1)] = (1/2) ÷ (1/2 + 1/3) = (1/2) ÷ (5/6) = 3/5 = 0.60.
The next child's risk is then 0.60 × 1 × 1/4 = 0.15 = 15%. The change is small, from 16.7% to 15%. One healthy child is weak evidence because a carrier couple already has a 3/4 chance of a healthy child. More unaffected children or a DNA test would change the estimate much more.
3. Should the wife be tested, should the 3-year-old be tested, and is prenatal diagnosis justified? Give reasoning.
Read the worked answer
The wife should be tested first. If she is not a carrier, the couple's chance of an affected child is very low, because the husband alone cannot produce an affected child. Their children would still have a 50% chance of being carriers. If she is a carrier, each pregnancy has a 25% risk of beta-thalassaemia major, and prenatal diagnosis is justified. Chorionic villus sampling at about 11–14 weeks or amniocentesis at about 15–18 weeks can determine whether the fetus is affected, but the couple must receive counselling about the limits and the options.
The healthy 3-year-old does not need urgent testing for his own health. He is not affected now. If both parents are carriers, an unaffected child has a 2/3 chance of being a carrier; if only the father is a carrier, the chance is 1/2. Carrier status is asymptomatic and becomes relevant mainly at reproductive age. Testing a young child raises consent and confidentiality issues and gives no immediate medical benefit, so it can be deferred until he can understand and agree. Prenatal diagnosis should not be offered unless the wife's carrier status is known, because an invasive test carries a small miscarriage risk.