Case 5: One affected child, two more pregnancies, one anxious sister
A couple, neither of whom has cystic fibrosis, have a two-year-old son who has just been diagnosed with the condition. Neither parent knew of any family history. The midwife explains that the risk to a future child is 1 in 4. The father says: 'We've used up our bad luck - the next two will be fine.' The mother's sister, aged 24, is planning a pregnancy and asks whether she should be tested. She says testing is pointless because 'nobody in the family has it'. In this population about 1 in 25 people is a carrier of a cystic fibrosis mutation, and the standard screening test detects about 90% of carrier mutations.
1. Using a genetic diagram, explain why two unaffected parents can have an affected child and why the risk to each further pregnancy is 1 in 4.
Read the worked answer
Because both parents are unaffected but have an affected child, the condition must be caused by a recessive allele: one working copy of the gene is enough for normal chloride transport, so carriers (heterozygous) show no symptoms. Both parents must be carriers, genotype Ff.
Genetic diagram:
| F (father) | f (father) | |
|---|---|---|
| F (mother) | FF | Ff |
| f (mother) | Ff | ff |
Offspring: 1 FF : 2 Ff : 1 ff.
- FF (1 in 4) - unaffected, not a carrier.
- Ff (2 in 4) - unaffected carrier, like both parents.
- ff (1 in 4) - affected, because no working allele is present.
So there is a 1 in 4 chance that any given pregnancy produces an affected child, and a 3 in 4 chance of an unaffected child. Among unaffected children, 2 in 3 will be carriers. The 1 in 4 applies afresh to each pregnancy; it is a probability, not a quota, which is why families with one affected child can have another.
2. Assess the father's statement that the next two children 'will be fine' because the family has 'used up its bad luck'.
Read the worked answer
The statement confuses past outcomes with future probabilities, and the parent's genotypes have not changed.
Each pregnancy is an independent event with the same 1 in 4 chance of an affected child and 3 in 4 chance of an unaffected child. The probability that the next two children are both unaffected is 3/4 × 3/4 = 9/16 ≈ 0.56. So there is roughly a 0.44 (44%) chance that at least one of the next two is affected - not a negligible risk, and certainly not certainty. The chance that both are affected is 1/4 × 1/4 = 1/16.
A useful analogy is rolling a die: a six does not become less likely because a six came up last time. The 3 : 1 ratio in a Punnett square describes expected proportions over many families, not a fixed sequence within one family.
If the couple want to reduce risk rather than accept it, the options are carrier testing of both parents (already effectively known here), prenatal testing of the fetus, or pre-implantation genetic testing with IVF. Each has its own limitations and should be discussed with a genetic counsellor.
3. The mother's sister asks about her own risk. Explain what her chance of being a carrier is likely to be, the risk to a child with a partner from the population, and why a negative screening test cannot give complete reassurance.
Read the worked answer
Her carrier chance is much higher than the population figure. Her sister (the affected boy's mother) is a confirmed carrier Ff, so at least one of their parents carries the allele. If one parent is Ff and the other FF, the sister had a 1 in 2 chance of inheriting the f allele - 1/2, compared with 1/25 for a random person in the population. 'Nobody in the family has it' is wrong: a recessive allele can pass silently through several generations of carriers.
Risk to a child with a partner of unknown genotype: 1/2 (she is a carrier) × 1/25 (partner is a carrier) × 1/4 (both pass on the allele) = 1/200, about 0.5% per pregnancy.
Why a negative test is not a guarantee: the test detects about 90% of carrier mutations, so roughly 1 in 10 carriers test negative. A simple estimate of her residual chance of being a carrier after a negative result is about 1/2 × 1/10 = 1 in 20 (strictly a little lower once the test's specificity is allowed for), which still leaves a child risk of the order of 1 in 2,000. Testing therefore reduces her anxiety and her risk substantially, and is worth doing, but it cannot reduce the risk to zero; partner testing and genetic counselling give the fuller picture.