A Negative Carrier Test in a Family With Cystic Fibrosis
A couple, both aged 29, attend genetic counselling because each has a brother with cystic fibrosis (CF); neither has symptoms. CF is autosomal recessive and caused by variants in CFTR. The local population carrier frequency is about 1 in 25, but having an affected sibling changes the prior probability. Both take a 50-variant panel that detects about 90% of CFTR variants in this population. The woman's result is negative; the man's result is positive for F508del. The woman is already 8 weeks pregnant, and the couple want a risk figure before deciding on prenatal testing or IVF with preimplantation genetic testing. They ask whether the woman should have full-gene sequencing, which costs €600, takes 3 weeks and identifies about 99% of carriers. The clinic has a 2-week window before the IVF decision.
1. Calculate the probability that their first child will have cystic fibrosis, using the panel result. Then calculate the probability if the woman has full-gene sequencing and tests negative.
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The prior probability that each unaffected sibling of an affected child carries a CF variant is 2/3, because the possible genotypes are AA, Aa and aA (aa is excluded by being unaffected). The man tests positive for F508del, so treat his carrier probability as about 1; a second rare variant in trans is possible but very unlikely. For the woman, use Bayes:
P(carrier | negative) = (0.10 × 2/3) / [(0.10 × 2/3) + (1.00 × 1/3)] = 0.0667 / 0.400 = 1/6.
Child risk = P(woman carrier) × P(man carrier) × 1/4 = 1/6 × 1 × 1/4 = 1/24 ≈ 4.2%.
If full-gene sequencing detects 99% of carriers, her residual carrier probability becomes (0.01 × 2/3)/[(0.01 × 2/3) + (1/3)] = 0.0067/0.340 ≈ 0.020, or 1 in 50. Child risk then falls to about 0.020 × 1 × 1/4 = 0.005, i.e. 0.5% or 1 in 200.
2. Explain why the prior probability is 2/3 rather than 1/2, and why a negative panel result does not mean the woman is definitely not a carrier.
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The 2/3 figure comes from conditional probability, not from the population carrier frequency. The couple already know that each has an affected sibling, so the relevant sample space is the unaffected siblings of an affected child: AA, Aa and aA are expected with equal probability before observation, and aa is excluded. Two of the three remaining possibilities carry a variant. The 1 in 25 population figure is irrelevant for these two people once the family history is known. A negative panel is not proof of non-carrier status: the panel detects about 90% of carrier variants in this population, so about 1 in 10 carriers test negative. The residual risk is therefore not zero; it is the prior probability multiplied by the chance the test missed a variant, then renormalised. That is why the result is 1/6 rather than 0 or 2/3.
3. Advise the couple on whether to order full-gene sequencing, given the 2-week IVF window and the 3-week turnaround. Show the reasoning behind your advice.
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Order the sequencing, but do not delay the IVF decision for it. The 3-week turnaround misses the 2-week window, so the couple must decide on current information. The current risk is about 4%, which many couples regard as high enough to justify IVF with preimplantation genetic testing. Sequencing can still be useful: if it identifies a second variant, her carrier status becomes certain and the child risk rises to 1/4; if it is negative, the risk falls to about 1 in 200. Because she is already 8 weeks pregnant, the result should also be timed for possible chorionic villus sampling at 11–13 weeks. Counselling should state that a negative sequencing result reduces but does not abolish risk, and that the man's other allele has not been fully sequenced. The couple's values, not just the number, should drive the choice.