MD measures were collected from seven studies involving participants sequenced through the BRIDGES project within the Breast Cancer Association Consortium (BCAC), comprising 3,133 breast cancer cases and 9,451 controls. All individuals were of European ancestry (Table S1). An additional 3,676 cases and 8,738 controls from 14 BCAC studies with CHEK2 c.1100delC array genotyping and MD data were included in analyses of CHEK2 PVs. ^12–14 All studies were approved by the relevant ethical review boards, and all participants included in these studies provided appropriate consent.

MD parameters were measured using STRATUS¹⁵ for the KARMA study, and Cumulus6¹⁶ for all other studies (Table S1). We utilised four MD parameters: dense area (cm²; DA); percent density (PD), non-dense area (cm²; NDA), and the absolute difference in PD between left- and right-side breast (ADPD). All the MD was measured by either mediolateral or craniocaudal views by studies. For controls, we used the average MD of both breasts. For cases, we preferentially included mammograms more than one year prior to diagnosis. Where only mammograms at diagnosis were available, we included measurements from the breast contralateral to the tumour. We excluded cases without information on the timing of the mammograms, cases with mammograms within 1 year of diagnosis lacking tumour side information or with (synchronous) bilateral cancer, and individuals without BMI data at the time of the mammogram or recruitment.

The BRIDGES project performed targeted sequencing of 34 putative breast cancer susceptibility genes in 60,466 female breast cancer cases and 53,461 controls from BCAC. Detailed methods are provided elsewhere.¹ Analyses focused on the burden of likely pathogenic protein truncating variants (PVs) in eight genes (ATM, BARD1, BRCA1, BRCA2, CHEK2, PALB2, RAD51C and RAD51D; supplementary notes, Table S2). BRCA1, BRCA2 and PALB2 were considered “high-risk” genes and the remaining genes “moderate-risk”. Details of the iCOGS and OncoArray genotyping have been provided elsewhere. ^12–14

Each of the four MD measures was square-root transformed to provide a distribution that was approximately Gaussian. The associations between the burden of PVs in breast cancer susceptibility genes and transformed MD measures were assessed using linear regression, adjusting for study and age and BMI at mammogram as covariates. Subgroup analyses were performed based on the MD measurement methods (Cumulus6 or STRATUS), menopausal status, breast cancer status and estrogen-receptor (ER) status. Sensitivity analyses were performed by further adjusting for menopausal status, family history of breast cancer, parity, age at menarche, age at first childbirth, and current use of HRT.

To assess the combined effect of gene variants and MD on breast cancer risk, we restricted the analysis to genes with at least 10 PV carriers. First, we obtained residuals of the MD measures by fitting the square root of those measures in a generalised linear regression model, respectively, adjusting for age and 1/BMI at mammogram and study.¹⁷ We then estimated the association between residual of the MD measurements, gene variant burden and breast cancer in a logistic regression model adjusted for age, BMI and study. Departures from a multiplicative model assumption were assessed by fitting an MD × gene burden interaction term and performing likelihood ratio tests (LRT). Subgroup analyses were performed based on the MD measurement method, menopausal status and ER status.

Association and interaction analyses for CHEK2 c.1100delC and MD, using the iCOGS and OncoArray data, were conducted in the same way, additionally adjusting for the array. The results were then combined with the CHEK2 PV results from the BRIDGES dataset using a fixed-effect meta-analysis.

To further investigate the association between MD and breast cancer risk among BRCA1 and BRCA2 PV gene variant carriers, two-sample MR analyses were performed using summary statistics for breast cancer risk among BRCA1 and BRCA2 PV carriers from the Consortium of Investigators of Modifiers of BRCA1/2 (CIMBA), ^{18, 19} and summary statistics from two MD GWAS as instrumental variables (supplementary notes). ^{4, 6} For comparison, we also conducted MR analyses for overall breast cancer and breast cancer subtypes, using summary statistics from GWAS carried out by the BCAC.^{12, 20} We tested the association between SNPs-represented MD measures and breast cancer and its subtypes using the weighted median ²¹ and inverse variance-weighted method.²² Cochran’s Q statistic was used to investigate heterogeneity across SNP effects. A non-zero intercept of MR-Egger (at p<0.05) was considered indicative of directional pleiotropy or a violation of the InSIDE assumption. ²³ Additionally, MR-PRESSO was applied to identify horizontal pleiotropic outliers.²⁴

Analyses were conducted using R, version 4.2.2. Packages ‘MendelianRandomization’, ‘MRPRESSO’ and ‘TwoSampleMR’ were used. Statistical significance was defined as P<0.05.

We analysed data on 3,133 cases and 9,451 controls who had both assessable MD measures and sequencing data on the eight breast cancer susceptibility genes (Table 1). The mean age at mammogram was 57.9 (SD=9.7) years in cases and 59.3 (SD=8.9) in controls. The majority of women were post-menopausal. In the array data, similar participant characteristics were observed, with the exception that controls were younger than cases. (Table S3).

All the MD measures were associated with breast cancer status (Table S4) with no significant heterogeneity across studies (Table S5). Among the four MD measures, PD had the strongest association with breast cancer risk, with an estimated 1.47-fold increased risk per SD of the residual of PD (95%CI=1.41,1.54; P=1.45×10^-63) in BRIDGES and an estimated 1.46-fold increase in the iCOGS and OncoArray data (95%CI=1.39,1.52; P=4.54 ×10^-64). In the subgroup of individuals in BRIDGES, the burden of PVs in ATM, BRCA1, BRCA2, CHEK2 and RAD51C was associated with an increased risk of breast cancer (Table S6).

PV carrier status for any single gene was not associated with any MD measure. There was, however, some evidence that overall PV burden was associated with higher NDA and lower PD in cases (NDA: beta=0.34; P=0.103; PD: beta=-0.39; P=0.005; Figure 1, Table S7) and of the opposite effect in controls (NDA: beta=-0.34; P=0.056, P_int=0.084; PD: beta=0.15; P = 0.244; P_int =0.046; Table S7, Figure 1-2).

For individual genes, the strongest association between PV status and MD measures was for BRCA1: BRCA1 PVs were associated with higher NDA (beta=1.33, P=0.016, Table S7). No significant heterogeneity in the effect size was observed by MD measurement method, menopausal status, or ER status. In the meta-analysis of the BRIDGES and array data, there was no evidence of an association between CHEK2 c.1100delC status and any MD measure (Figure 1, Table S8). Adjusting for additional covariates did not materially affect the results (Table S9-10).

We next conducted logistic regression analyses with breast cancer as the outcome, and PV carrier status and MD measures were included in the same model. In the model with no interaction term, the effect sizes for PVs and MD measures were not materially affected by mutual adjustment (Table S11). However, when including an interaction term, we observed some evidence of a negative interaction between the overall burden of PVs and PD for breast cancer risk (OR_int=0.79; 95%CI_int=0.62,1.00; P_LRT=0.047, Table S12). This appeared to be largely driven by a positive interaction between NDA and PV burden (OR_int=1.28; 95%CI_int=0.97,1.71). For individual genes, the interaction was nominally significant for ATM and PD and DA (OR_int=0.52; 95%CI_int=0.26,0.99 and 0.50; 95%CI_int=0.24,0.98 respectively), CHEK2 and NDA (OR_int=1.49; 95%CI_int=1.01,2.23) and PALB2 and DA (OR_int=3.70; 95%CI_int=1.22,16.67). After synthesising sequencing and array genotyping data, the evidence of interaction was stronger for CHEK2 c.1100delC and NDA (OR_int=1.42; 95%CI_int=1.04,1.95, Table S13).

The joint effects were also examined by considering the associations between MD and breast cancer among PV carriers. For example, the ORs for the association between PD and breast cancer were 1.47 (95%CI=1.41,1.54) in the overall population and 1.19 (95%CI=0.93,1.52) in PV carriers (Table S14). The weaker effect size was more apparent for PVs in the moderate-risk genes (OR=1.14; 95%CI=0.84,1.56) than in the high-risk genes (OR=1.41; 95%CI=0.91,2.22).

We conducted MR analyses based on genetic instruments for MD derived from the SNP associations identified by Sieh(2020) ⁴ and Chen(2022) ⁷ (Table S15). There was evidence for an association between genetically predicted MD measures and breast cancer risk (Figure 3, Table S16, Figure S1-6). The ORs per standard deviation from weighted-median MR for the association between PD and overall breast cancer were 1.54 (95%CI=1.31,1.80) for Sieh(2020) and 1.74 (95%CI=1.49,2.03) for Chen(2022). In addition, associations were seen for all subtypes but were somewhat weaker for triple-negative breast cancer (TNBC): for PD, the ORs were 1.28 (95%CI=0.99,1.66) and 1.48 (95%CI=1.16,1.88) using the Sieh and Chen data, respectively.

The associations between genetically predicted MD measures and breast cancer risk in BRCA1 PV carriers, using summary statistics from CIMBA, were significantly attenuated compared to the overall breast cancer effect sizes. The ORs for genetically predicted PD and breast cancer in BRCA1 PV carriers were 1.02 (95%CI=0.78,1.34) using Sieh(2020) and 1.20 (95%CI=0.92,1.55) using Chen(2022). For BRCA2 PV carriers, the effect sizes were similar to those for overall breast cancer (OR=1.55; 95%CI=1.08,2.24, P=0.019 and OR=1.80; 95%CI=1.30,2.51, P=4.65×10^-4).

The intercepts from the MR-Egger analyses indicated no evidence of pleiotropy, but the Q-statistics indicated significant heterogeneity among the effect estimates. Re-estimation of associations after removing outlier SNPs identified yielded similar effect estimates, both in the overall breast cancer, by subtype and in BRCA1 and BRCA2 carriers (Table S16, Figure S1-6).