Various common genetic susceptibility loci have been identified for breast cancer; however, it is unclear how they combine with lifestyle/environmental risk factors to influence risk. We undertook an international collaborative study to assess gene-environment interaction for risk of breast cancer. Data from 24 studies of the Breast Cancer Association Consortium were pooled. Using up to 34,793 invasive breast cancers and 41,099 controls, we examined whether the relative risks associated with 23 single nucleotide polymorphisms were modified by 10 established environmental risk factors (age at menarche, parity, breastfeeding, body mass index, height, oral contraceptive use, menopausal hormone therapy use, alcohol consumption, cigarette smoking, physical activity) in women of European ancestry. We used logistic regression models stratified by study and adjusted for age and performed likelihood ratio tests to assess gene–environment interactions. All statistical tests were two-sided. We replicated previously reported potential interactions between LSP1-rs3817198 and parity (Pinteraction = 2.4×10−6) and between CASP8-rs17468277 and alcohol consumption (Pinteraction = 3.1×10−4). Overall, the per-allele odds ratio (95% confidence interval) for LSP1-rs3817198 was 1.08 (1.01–1.16) in nulliparous women and ranged from 1.03 (0.96–1.10) in parous women with one birth to 1.26 (1.16–1.37) in women with at least four births. For CASP8-rs17468277, the per-allele OR was 0.91 (0.85–0.98) in those with an alcohol intake of <20 g/day and 1.45 (1.14–1.85) in those who drank ≥20 g/day. Additionally, interaction was found between 1p11.2-rs11249433 and ever being parous (Pinteraction = 5.3×10−5), with a per-allele OR of 1.14 (1.11–1.17) in parous women and 0.98 (0.92–1.05) in nulliparous women. These data provide first strong evidence that the risk of breast cancer associated with some common genetic variants may vary with environmental risk factors.

Genome-wide association studies (GWAS) of breast cancer defined by hormone receptor status have revealed loci contributing to susceptibility of estrogen receptor (ER)-negative subtypes. To identify additional genetic variants for ER-negative breast cancer, we conducted the largest meta-analysis of ER-negative disease to date, comprising 4754 ER-negative cases and 31 663 controls from three GWAS: NCI Breast and Prostate Cancer Cohort Consortium (BPC3) (2188 ER-negative cases; 25 519 controls of European ancestry), Triple Negative Breast Cancer Consortium (TNBCC) (1562 triple negative cases; 3399 controls of European ancestry) and African American Breast Cancer Consortium (AABC) (1004 ER-negative cases; 2745 controls). We performed in silico replication of 86 SNPs at P ≤ 1 × 10(-5) in an additional 11 209 breast cancer cases (946 with ER-negative disease) and 16 057 controls of Japanese, Latino and European ancestry. We identified two novel loci for breast cancer at 20q11 and 6q14. SNP rs2284378 at 20q11 was associated with ER-negative breast cancer (combined two-stage OR = 1.16; P = 1.1 × 10(-8)) but showed a weaker association with overall breast cancer (OR = 1.08, P = 1.3 × 10(-6)) based on 17 869 cases and 43 745 controls and no association with ER-positive disease (OR = 1.01, P = 0.67) based on 9965 cases and 22 902 controls. Similarly, rs17530068 at 6q14 was associated with breast cancer (OR = 1.12; P = 1.1 × 10(-9)), and with both ER-positive (OR = 1.09; P = 1.5 × 10(-5)) and ER-negative (OR = 1.16, P = 2.5 × 10(-7)) disease. We also confirmed three known loci associated with ER-negative (19p13) and both ER-negative and ER-positive breast cancer (6q25 and 12p11). Our results highlight the value of large-scale collaborative studies to identify novel breast cancer risk loci.

Recent work by Ding and Kay has demonstrated that the Bayesian information criterion (BIC) is an inconsistent estimator of model order in nested model selection as the noise variance τ*→ 0. Unfortunately, Ding and Kay have erroneously concluded that the minimum description length (MDL) principle also leads to inconsistent estimates of model order in this setting by equating BIC with MDL. This correspondence shows that only the earlier MDL criterion based on asymptotic assumptions has this problem, and proves that the new MDL linear regression criteria based on normalized maximum likelihood and Bayesian mixture codes satisfy the notion of consistency as τ*→ 0. The main result may be used as a basis to easily establish similar consistency results for other closely related information theoretic regression criteria.

Most published GWAS do not examine SNP interactions due to the high computational complexity of computing p-values for the interaction terms. Our aim is to utilize supercomputing resources to apply complex statistical techniques to the world's accumulating GWAS, epidemiology, survival and pathology data to uncover more information about genetic and environmental risk, biology and aetiology. We performed the Bayesian Posterior Probability test on a pseudo data set with 500,000 single nucleotide polymorphism and 100 samples as proof of principle. We carried out strong scaling simulations on 2 to 4,096 processing cores with factor 2 increments in partition size. On two processing cores, the run time is 317h, i.e. almost two weeks, compared to less than 10 minutes on 4,096 processing cores. The speedup factor is 2,020 that is very close to the theoretical value of 2,048. This work demonstrates the feasibility of performing exhaustive higher order analysis of GWAS studies using independence testing for contingency tables. We are now in a position to employ supercomputers with hundreds of thousands of threads for higher order analysis of GWAS data using complex statistics.