The analytical process is summarised in Figs. 3 and and4.4. A fundamental assumption when using a case-only design in this context is that the SNPs and mutation carrier status are independent61. To confirm independence, SNPs likely to be in linkage disequilibrium (LD) with BRCA1 or BRCA2 mutations, i.e., those located in or within 500 kb of either gene, were excluded. However, LD also exists between variants at long-distance on the same chromosome or even on a different chromosome (interchromosomal LD)62,71. Therefore, control-only analyses were performed to further exclude SNPs associated with mutation carrier status in unaffected women72, using a stringent statistical significance level of 10−8).

After excluding SNPs in LD or in interchromosomal LD with BRCA1 or BRCA2 mutations, case-only analyses were performed to assess the association between SNPs and BRCA1 or BRCA2 mutation carrier status. We considered two categories of SNPs depending on whether they had been previously found to be associated with BC in published BCAC studies35,48. For known BC susceptibility SNPs (Fig. 3) we used a significance threshold of 2.7 × 10−4 (applying Bonferroni correction to 179 tests) and for potential novel SNP modifier (Fig. 4) a stringent significance threshold of 10−8 was used.

Because BRCA1mutation-associated tumours are more often ER-negative than those in the general population73, a subsequent case-only analysis was performed restricting the BCAC cases to those with ER-negative disease. We used this strategy for two reasons. First, we wished to exclude associations driven by differences in the tumour ER-status distributions between BRCA1 carriers and BCAC cases. Therefore, in the BRCA1 analysis, SNPs were considered to be associated with mutation carrier status only if they were also associated in the ER-negative case-only analysis at a prior defined significance threshold of 10−7 for novel SNP modifiers (Fig. 4) and of 0.05 for the established BC susceptibility SNPs after a pre-selection at P < 2.7 × 10−4 in the BRCA1 overall case-only analysis (Fig. 3). The second reason we applied this strategy was to identify novel SNP modifiers specific to BRCA1/ER-negative tumours that had not been detected in the overall analysis; for this we applied a significance threshold of 10−8.

To confirm that potentially novel associations in the case-only analysis were not driven by differences in the imputation accuracy between the CIMBA and BCAC data, each of the regions defined as ±500 kb around the associated SNP, were re-imputed for the combined CIMBA and BCAC samples. The more accurate one-stage imputation was carried out, using IMPUTE2 without pre-phasing. Associations with all the SNPs in the re-imputed regions were then re-evaluated using the control-only and case-only analytical approaches described above. Finally, we used a step-wise regression analysis using a significance threshold of 10−8 in order to determine whether associations with SNPs in the same region are independent and to define the conditionally independent SNPs (top SNPs).

Among the 179 established BC susceptibility SNPs, 107 were genotyped and 71 were imputed. As previously, although none of these 71 SNPs were excluded based on their Δr², to exclude potentially spurious associations, regions around these 71 SNPs were re-imputed using the one-stage imputation applied to BCAC and CIMBA data combined, and before performing the control-only and case-only analyses.

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