For individual cancer sites, we only observed nominally significant associations with breast cancer for homozygosity at HLA-C locus (adjusted OR = 1.38, 95% CI = 1.02–1.87, P = 0.036, Supplementary Table 6) and lung cancer for homozygosity at HLA-DQB1 locus (adjusted OR = 1.15, 95% CI = 1.02–1.29, P = 0.022, Supplementary Table 10). This evidence concerns the gene HLA-C and breast cancer.