A guideline says something specific
The most important thing on this page is not a genotype. It is that two large trials gave these to smokers and counted more cancers, not fewer.
Circulating carotenoid and tocopherol levels are partly heritable — rs12272004 near APOA5 is one of the positions found for them. That is the genetics, and it is the least important thing here.
The reasoning that sold these supplements looked solid. People with more carotenoids and vitamin E in their blood get less lung cancer, so raising the level should prevent it. Two trials tested that directly, in the people with the most to gain.
ATBC randomised 29,133 male smokers in Finland to alpha-tocopherol, beta-carotene, both, or placebo. Lung cancer incidence among the men given beta-carotene was 18% higher (95% CI 3–36%) and total mortality 8% higher (1–16%). Alpha-tocopherol did not reduce lung cancer, and there were more deaths from haemorrhagic stroke among the men who took it.
CARET gave beta-carotene with retinol to 18,314 smokers, former smokers and asbestos-exposed workers. Relative risk of lung cancer in the treated group: 1.28 (1.04–1.57). Death from lung cancer: 1.46 (1.07–2.00). Death from any cause: 1.17 (1.03–1.33). The trial was stopped 21 months early.
This is the clearest demonstration on this site of why a blood level that travels with good health is not therefore a target to raise with a pill. The nutrient in food and the nutrient in a capsule were not the same intervention, and in the group most likely to benefit they went the wrong way.
No genotype changes that, and no genotype is used to select these supplements for anyone.
Nothing on this page recommends taking anything. If a result here matters to you, take it to a doctor or a pharmacist rather than to a shop.