DNA methylation can mimic the effects of germline mutations in cancer predisposition genes. Recently, we identified twenty‐four heritable methylation marks associated with breast cancer risk. As breast and prostate cancer share genetic risk factors, including rare, high‐risk mutations (eg, in BRCA2), we hypothesized that some of these heritable methylation marks might also be associated with the risk of prostate cancer.

Background Clustering of breast and colorectal cancer has been observed within some families and cannot be explained by chance or known high-risk mutations in major susceptibility genes. Potential shared genetic susceptibility between breast and colorectal cancer, not explained by high-penetrance genes, has been postulated. We hypothesized that yet undiscovered genetic variants predispose to a breast-colorectal cancer phenotype. Methods To identify variants associated with a breast-colorectal cancer phenotype, we analyzed genome-wide association study (GWAS) data from cases and controls that met the following criteria: cases (n = 985) were women with breast cancer who had one or more first- or second-degree relatives with colorectal cancer, men/women with colorectal cancer who had one or more first- or second-degree relatives with breast cancer, and women diagnosed with both breast and colorectal cancer. Controls (n = 1769), were unrelated, breast and colorectal cancer-free, and age- and sex- frequency-matched to cases. After imputation, 6,220,060 variants were analyzed using the discovery set and variants associated with the breast-colorectal cancer phenotype at P<5.0E-04 (n = 549, at 60 loci) were analyzed for replication (n = 293 cases and 2,103 controls). Results Multiple correlated SNPs in intron 1 of the ROBO1 gene were suggestively associated with the breast-colorectal cancer phenotype in the discovery and replication data (most significant; rs7430339, Pdiscovery = 1.2E-04; rs7429100, Preplication = 2.8E-03). In meta-analysis of the discovery and replication data, the most significant association remained at rs7429100 (P = 1.84E-06). Conclusion The results of this exploratory analysis did not find clear evidence for a susceptibility locus with a pleiotropic effect on hereditary breast and colorectal cancer risk, although the suggestive association of genetic variation in the region of ROBO1, a potential tumor suppressor gene, merits further investigation.

Background/Objectives:There is increasing evidence of a relationship between blood DNA methylation and body mass index (BMI). We aimed to assess associations of BMI with individual methylation measures (CpGs) through a cross-sectional genome-wide DNA methylation association study and a longitudinal analysis of repeated measurements over time.Subjects/Methods:Using the Illumina Infinium HumanMethylation450 BeadChip, DNA methylation measures were determined in baseline peripheral blood samples from 5361 adults recruited to the Melbourne Collaborative Cohort Study (MCCS) and selected for nested case–control studies, 2586 because they were subsequently diagnosed with cancer (cases) and 2775 as controls. For a subset of 1088 controls, these measures were repeated using blood samples collected at wave 2 follow-up, a median of 11 years later; weight was measured at both time points. Associations between BMI and blood DNA methylation were assessed using linear mixed-effects regression models adjusted for batch effects and potential confounders. These were applied to cases and controls separately, with results combined through fixed-effects meta-analysis.Results:Cross-sectional analysis identified 310 CpGs associated with BMI with P<1.0 × 10−7, 225 of which had not been reported previously. Of these 225 novel associations, 172 were replicated (P<0.05) using the Atherosclerosis Risk in Communities (ARIC) study. We also replicated using MCCS data (P<0.05) 335 of 392 associations previously reported with P<1.0 × 10−7, including 60 that had not been replicated before. Associations between change in BMI and change in methylation were observed for 34 of the 310 strongest signals in our cross-sectional analysis, including 7 that had not been replicated using the ARIC study.Conclusions:Together, these findings suggest that BMI is associated with blood DNA methylation at a large number of CpGs across the genome, several of which are located in or near genes involved in ATP-binding cassette transportation, tumour necrosis factor signalling, insulin resistance and lipid metabolism.

Before SNP-based risk can be incorporated in colorectal cancer (CRC) screening, the ability of these SNPs to estimate CRC risk for persons with and without a family history of CRC, and the screening implications need to be determined. We estimated the association with CRC of a 45 SNP-based risk using 1181 cases and 999 controls, and its correlation with CRC risk predicted from detailed family history. We estimated the predicted change in the distribution across predefined risk categories, and implications for recommended screening commencement age, from adding SNP-based risk to family history. The inter-quintile risk ratio for colorectal cancer risk of the SNP-based risk was 3.28 (95% CI 2.54–4.22). SNP-based and family history-based risks were not correlated (r = 0.02). For persons with no first-degree relatives with CRC, screening could commence 4 years earlier for women (5 years for men) in the highest quintile of SNP-based risk. For persons with two first-degree relatives with CRC, screening could commence 16 years earlier for men and women in the highest quintile, and 7 years earlier for the lowest quintile. This 45 SNP panel in conjunction with family history, can identify people who could benefit from earlier screening. Risk reclassification by 45 SNPs could inform targeted screening for CRC prevention, particularly in clinical genetics settings when mutations in high-risk genes cannot be identified. Yet to be determined is cost-effectiveness, resources requirements, community, patient and clinician acceptance, and feasibility with potentially ethical, legal and insurance implications.

This paper applies the minimum message length principle to inference of linear regression models with Student-t errors. A new criterion for variable selection and parameter estimation in Student-t regression is proposed. By exploiting properties of the regression model, we derive a suitable non-informative proper uniform prior distribution for the regression coefficients that leads to a simple and easy-to-apply criterion. Our proposed criterion does not require specification of hyperparameters and is invariant under both full rank transformations of the design matrix and linear transformations of the outcomes. We compare the proposed criterion with several standard model selection criteria, such as the Akaike information criterion and the Bayesian information criterion, on simulations and real data with promising results.

Global-local shrinkage hierarchies are an important innovation in Bayesian estimation. We propose the use of log-scale distributions as a novel basis for generating familes of prior distributions for local shrinkage hyperparameters. By varying the scale parameter one may vary the degree to which the prior distribution promotes sparsity in the coefficient estimates. By examining the class of distributions over the logarithm of the local shrinkage parameter that have log-linear, or sub-log-linear tails, we show that many standard prior distributions for local shrinkage parameters can be unified in terms of the tail behaviour and concentration properties of their corresponding marginal distributions over the coefficients $\beta_j$. We derive upper bounds on the rate of concentration around $|\beta_j|=0$, and the tail decay as $|\beta_j| \to \infty$, achievable by this wide class of prior distributions. We then propose a new type of ultra-heavy tailed prior, called the log-$t$ prior with the property that, irrespective of the choice of associated scale parameter, the marginal distribution always diverges at $\beta_j = 0$, and always possesses super-Cauchy tails. We develop results demonstrating when prior distributions with (sub)-log-linear tails attain Kullback--Leibler super-efficiency and prove that the log-$t$ prior distribution is always super-efficient. We show that the log-$t$ prior is less sensitive to misspecification of the global shrinkage parameter than the horseshoe or lasso priors. By incorporating the scale parameter of the log-scale prior distributions into the Bayesian hierarchy we derive novel adaptive shrinkage procedures. Simulations show that the adaptive log-$t$ procedure appears to always perform well, irrespective of the level of sparsity or signal-to-noise ratio of the underlying model.

Roger Milne and colleagues conduct a genome-wide association study for estrogen receptor (ER)-negative breast cancer combined with BRCA1 mutation carriers in a large cohort. They identify ten new risk variants and find high genetic correlation between breast cancer risk for BRCA1 mutation carriers and risk of ER-negative breast cancer in the general population. Most common breast cancer susceptibility variants have been identified through genome-wide association studies (GWAS) of predominantly estrogen receptor (ER)-positive disease1. We conducted a GWAS using 21,468 ER-negative cases and 100,594 controls combined with 18,908 BRCA1 mutation carriers (9,414 with breast cancer), all of European origin. We identified independent associations at P < 5 × 10−8 with ten variants at nine new loci. At P < 0.05, we replicated associations with 10 of 11 variants previously reported in ER-negative disease or BRCA1 mutation carrier GWAS and observed consistent associations with ER-negative disease for 105 susceptibility variants identified by other studies. These 125 variants explain approximately 16% of the familial risk of this breast cancer subtype. There was high genetic correlation (0.72) between risk of ER-negative breast cancer and breast cancer risk for BRCA1 mutation carriers. These findings may lead to improved risk prediction and inform further fine-mapping and functional work to better understand the biological basis of ER-negative breast cancer.

Association analysis identifies 65 new breast cancer risk loci, predicts target genes for known risk loci and demonstrates a strong overlap with somatic driver genes in breast tumours. Genome-wide association studies for breast cancer have identified common genetic variation that influences susceptibility to this disease, but much of the genetic risk remains unexplained. Doug Easton and colleagues report a genome-wide association study for breast cancer in more than 122,000 cases and 105,000 controls. The authors genotyped a subset of these cases using OncoArray, a new, custom genome-wide single-nucleotide polymorphism (SNP) array for cancer genomics. Overall, they identify 65 loci newly associated with breast cancer susceptibility, and estimate that, together with 107 previously identified breast cancer susceptibility loci, these explain about 18 per cent of the familial relative risk of breast cancer. Polygenic risk scores may be used in risk prediction models and may improve early detection and targeted prevention of the disease. Breast cancer risk is influenced by rare coding variants in susceptibility genes, such as BRCA1, and many common, mostly non-coding variants. However, much of the genetic contribution to breast cancer risk remains unknown. Here we report the results of a genome-wide association study of breast cancer in 122,977 cases and 105,974 controls of European ancestry and 14,068 cases and 13,104 controls of East Asian ancestry1. We identified 65 new loci that are associated with overall breast cancer risk at P < 5 × 10−8. The majority of credible risk single-nucleotide polymorphisms in these loci fall in distal regulatory elements, and by integrating in silico data to predict target genes in breast cells at each locus, we demonstrate a strong overlap between candidate target genes and somatic driver genes in breast tumours. We also find that heritability of breast cancer due to all single-nucleotide polymorphisms in regulatory features was 2–5-fold enriched relative to the genome-wide average, with strong enrichment for particular transcription factor binding sites. These results provide further insight into genetic susceptibility to breast cancer and will improve the use of genetic risk scores for individualized screening and prevention.

Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of attention in the problem of estimating sparse, high-dimensional linear models. This paper extends these ideas, and presents a Bayesian grouped model with continuous global-local shrinkage priors to handle complex group hierarchies that include overlapping and multilevel group structures. As the posterior mean is never a sparse estimate of the linear model coefficients, we extend the recently proposed decoupled shrinkage and selection (DSS) technique to the problem of selecting groups of variables from posterior samples. To choose a final, sparse model, we also adapt generalised information criteria approaches to the DSS framework. To ensure that sparse groups, in which only a few predictors are active, can be effectively identified, we provide an alternative degrees of freedom estimator for sparse Bayesian linear models that takes into account the effects of shrinkage on the model coefficients. Simulations and real data analysis using our proposed method show promising performance in terms of correct identification of active and inactive groups, and prediction, in comparison with a Bayesian grouped slab-and-spike approach.