Breast cancer risks associated with missense variants in breast cancer susceptibility genes

Protein truncating variants in ATM, BRCA1, BRCA2, CHEK2, and PALB2 are associated with increased breast cancer risk, but risks associated with missense variants in these genes are uncertain. We analyzed data on 59,639 breast cancer cases and 53,165 controls from studies participating in the Breast Cancer Association Consortium BRIDGES project. We sampled training (80%) and validation (20%) sets to analyze rare missense variants in ATM (1146 training variants), BRCA1 (644), BRCA2 (1425), CHEK2 (325), and PALB2 (472). We evaluated breast cancer risks according to five in silico prediction-of-deleteriousness algorithms, functional protein domain, and frequency, using logistic regression models and also mixture models in which a subset of variants was assumed to be risk-associated. The most predictive in silico algorithms were Helix (BRCA1, BRCA2 and CHEK2) and CADD (ATM). Increased risks appeared restricted to functional protein domains for ATM (FAT and PIK domains) and BRCA1 (RING and BRCT domains). For ATM, BRCA1, and BRCA2, data were compatible with small subsets (approximately 7%, 2%, and 0.6%, respectively) of rare missense variants giving similar risk to those of protein truncating variants in the same gene. For CHEK2, data were more consistent with a large fraction (approximately 60%) of rare missense variants giving a lower risk (OR 1.75, 95% CI (1.47–2.08)) than CHEK2 protein truncating variants. There was little evidence for an association with risk for missense variants in PALB2. The best fitting models were well calibrated in the validation set. These results will inform risk prediction models and the selection of candidate variants for functional assays and could contribute to the clinical reporting of gene panel testing for breast cancer susceptibility.

Background Genetic testing for cancer susceptibility is now part of mainstream clinical practice. For breast cancer susceptibility, genetic testing generally focuses on high-risk genes, notably BRCA1, BRCA2, PALB2, and TP53, but testing of larger panels that include so-called "moderaterisk" genes is being increasingly offered [1]. While the evidence that many of these genes are risk associated is clear, for most this evidence is based on carrying a protein truncating variant (PTV). Besides PTVs, genetic testing also identifies missense variants for which the impact on protein function and associated cancer risk is generally unknown ("variants of uncertain significance" (VUS)), resulting in a major problem for genetic counselling. Some missense variants have been shown to confer risk [2,3] with risk estimates comparable to PTVs, and it is possible that missense variants contribute substantially to risk [4,5], at least in some genes. However, defining the set of missense variants in each gene that may confer risk, and their associated risk estimates, presents an ongoing problem.
Resolving this problem is complex as most variants are individually very rare, so the evidence must be based on combining data across multiple variants in a statistical model. To this end, efforts have been made to develop statistical algorithms that score missense variants according to in silico features that may predict pathogenicity.
Here, we have compared the usefulness of five in silico algorithms in predicting breast cancer risk associated with missense variants using sequenced germline DNA from more than 59,000 cases and 53,000 controls from studies in the Breast Cancer Association Consortium (BCAC) [6] participating in the BRIDGES project [7]. We used the most predictive in silico algorithm to estimate the risks of breast cancer associated with subsets of rare missense variants, defined by categories of the in silico score, in ATM, BRCA1, BRCA2, CHEK2, and PALB2. These predictions were then validated using an independent dataset.

Subjects
We included data from female breast cancer patients (cases) and unaffected controls from 44 studies participating in the BRIDGES project, as previously documented [7]. These studies are a subset of studies participating in the Breast Cancer Association Consortium (BCAC) for which targeted sequencing was performed using the BRIDGES panel (see below). Details of the participating studies, including the enrollment of cases and controls and sample sizes, are given in Additional File 1: Tables S1 and S2. Of these, 30 were population-based or hospital-based studies (hereafter: population studies) including cases and controls sampled independently of family history. A further 14 studies oversampled cases with a family history of breast cancer (hereafter: familial studies). All studies were approved by the relevant ethical review boards and used appropriate consent procedures. Five duplicated samples were identified and removed. After quality control procedures (see below), 53,165 controls and 59,639 cases with an invasive (53,838; 90.3%) or in situ (4,153; 7.0%) tumor, or tumor of unknown invasiveness (1648; 2.7%), were included in the analyses. Of these, 50,414 controls and 48,230 cases were from population studies.

Laboratory methods, variant calling, and classification
The BRIDGES project performed targeted sequencing on a panel of 34 genes [7]. Of these five (ATM, BRCA1, BRCA2, CHEK2, PALB2) were chosen for further analysis and presented here. These five genes, where the evidence for association with breast cancer risk is strongest, are most relevant to risk prediction and included in the current version of the BOADICEA/CanRisk risk prediction tool [8]. Details of library preparation, sequencing, variant calling, quality control procedures, and variant classification has been documented previously [7]. Missense variants in the entire gene were identified using the Ensembl Variant Effect Predictor (VEP; version 101.0) [9]. Rare variants for in silico analysis were defined as those with allele frequency < 0.1% (calculated as previously described [7]); in addition, variants with frequency < 5% were retained for a frequency-based analysis. Carriers of missense variants predicted to affect RNA splicing, according to the MaxEntScan tool [10] and SpliceAI scores [11], were removed (see Additional File 2: Table S3). Variants were annotated for functional protein domain location, defined according to published literature, the UniProt Knowledgebase [12], and for BRCA1 and BRCA2, the ENIGMA BRCA1/2 expert panel guidelines [13] (see Additional File 1: Table S4). Variants were also classified for disease pathogenicity assertion in ClinVar [14] with a filter for no conflicting interpretations; for BRCA1 and BRCA2, variants were also reviewed against the ENIGMA BRCA1/2 expert panel guidelines. The ENIGMA terminology report [15] reserves use of the word "pathogenic" to describe variants associated with at least a twofold cancer risk; however, for the purpose of this article, we describe any variant associated with risk as pathogenic.
Align-GVGD classifies variants according to the level of cross-species conservation observed for a single missense substitution while considering the biophysical characteristics of the amino acids. CADD, BayesDel, and REVEL are ensemble methods that integrate several different annotations, including conservation metrics, regulatory information, transcript information, and protein-level scores, into a single score of deleteriousness. Helix combines structural, alignment, and gene data with a strict training regime where circularity is actively avoided to produce a variant score and certainty estimate. All variants were scored using default software settings. For Align-GVGD, the sequence alignment with the deepest phylogeny level was used. Variants in BRCA1 and BRCA2 were also annotated with the predictions of Hart et al. [21], who developed two BRCA-specific in silico algorithms (Random Forest (RF) and Naïve Voting Method (NVM)) to classify missense variants as functionally damaging or neutral. In addition, BRCA1 variants were annotated using the prediction of loss-of-function made by the Saturation Genome Editing (SGE) experiments of Findlay et al. [22], which involved a comprehensive functional assessment of missense variants lying within the functional domain coding regions of BRCA1. BRCA2 variants were annotated using homology-directed DNA repair (HDR) assay scores and predictions of pathogenicity from Richardson et al. [23]. For PALB2, variants were annotated with five different assay scores measuring HDR activity, PARPi sensitivity, and homologous recombination (HR) efficiency from the functional screening studies of Boonen et al. [24], Rodrigue et al. [25] and Wiltshire et al. [26].

Statistical analysis
The dataset was split into a training (80% of individuals) and a validation (20%) set. Samples for the validation set were selected randomly from population studies of cases unselected for family history of breast cancer and controls, in countries contributing a total of > 5000 samples (Denmark, Germany, Singapore (Chinese), Sweden, UK, USA). All remaining samples were included in the training set. The training set included 37,211 cases from population studies, 11,409 cases from familial studies, and 42,334 controls. Of these, 3818 individuals were carriers of PTVs in one or more of the five genes under consideration and were excluded from all analyses except the mixture models (see below). The validation set included 11,019 cases and 10,831 controls from population studies and did not include any carriers of PTVs. Oversampling of cases with a family history increases power but leads to biased effect sizes, so we chose this approach to maximize the power to discriminate between models in the training set, which could then be refit and tested on a dataset unselected for family history. All analyses were adjusted for country as a covariate; in addition, for Malaysia and Singapore, the three distinct ethnic groups (Chinese, Indian, Malay) were treated as different strata, and the UK was treated as three strata (SEARCH from East Anglia, GENSCOT from Scotland, and PROCAS and FHRISK from north-west England).

Training dataset analysis
An analysis flow diagram is presented in Fig. S1 (see Additional File 1). Analyses were performed in R version 4.0.3 (R: A Language and Environment for Statistical Computing; http:// www.r-proje ct. org). We first used logistic regression (LR) to explore which of the five in silico scores (Align-GVGD, BayesDel, CADD, Helix, and REVEL-all analyzed as continuous variables) were most strongly associated with risk of breast cancer. In addition, to assess the utility of gene-specific in silico tools, we analyzed the Hart et al. RF and NVM in silico predictions for BRCA1 and BRCA2. To evaluate the usefulness of functional predictions, we also analyzed the BRCA1 SGE score; the Richardson et al. BRCA2 HDR score; and, for PALB2, five functional assay scores. These analyses were restricted to carriers of a rare (frequency < 0.1%) missense variant in the training set, with an endpoint of breast cancer occurrence (yes/no). The strongest predictors were used to test the association of different categories of the score(s) compared to a baseline category, in conjunction with functional protein domains, and hence create a set of risk categories. LR was then used in the training set (carriers and non-carriers) to estimate the odds ratios (OR) associated with different risk categories. As an alternative approach, we fitted mixture models in which only a proportion of variants (α) was assumed to be risk associated in the given gene; the OR was assumed to be the same for all risk associated variants, but the proportion of risk associated variants varied by risk category (as defined in the LR models). This model is motivated by the binary variant classification approach used in clinical genetics, where all variants are assumed to be either associated with moderate-high risk (likely pathogenic) or not (likely benign) [27]. We considered two types of mixture model: a constrained model in which the missense OR was equal to that of PTVs, and an unconstrained model in which the missense OR could differ from the PTV OR. Carriers of PTVs in the gene under consideration were re-included in the mixture models (to allow the risk associated missense OR to be constrained to the PTV OR). The mixture models were fitted using an expectation-maximization (EM) algorithm [28]. In the expectation step, the (posterior) probability that each variant was risk associated, given the case control data on that variant in the training set and the current parameter values was calculated. These probabilities were then used as weights in a logistic regression analysis in the maximization step. In a case-control dataset, the naïve proportions, α, will be biased because risk associated variants are more likely to be found in cases. For the final models, therefore, we also computed the proportions based only on variants reported in controls. To evaluate the overall fit of the models, we compared log-likelihoods.
The initial model selection was based on all samples, but final parameter estimates were obtained from population studies only. In the results, the ORs, P-values, and α presented are from population studies, unless indicated by the suffix "ALL".
Case-only analyses of age at diagnosis, with risk category as the outcome variable, were performed to evaluate trends in the ORs for variant risk category by age. We evaluated individual risk variants previously reported in literature and, in aggregate, those classified as "pathogenic" or "likely pathogenic" (hereafter, all termed: (likely) pathogenic) according to clinical guidelines. To examine whether rare variant frequency is associated with risk, we used a carrier-only LR analysis to test frequency up to 0.5% on a continuous scale and a log scale, and to compare rare variants in two groups: frequency < 0.1% versus frequency 0.1-0.5%. We also performed burden analyses within each gene comparing the risk for non-carriers to the risk for carriers of variants in one of four frequency groups: < 0.1%; 0.1-0.5%; 0.5-1%; and 1-5%. Variants with frequency between 0.1 and 5% were also evaluated individually.

Validation dataset analysis
To evaluate the calibration of the in silico training models, we performed case-control analyses using the validation dataset. In these analyses, OR estimates were fixed according to the population estimates from the training models (Table 1), but the other parameters (intercept and country covariates) were reestimated, since the case-control proportions might differ between the training and validation datasets. From the validation model, we extracted the predicted probability that each individual was a case and hence derived expected numbers of cases and controls in each risk group. These were used to plot observed versus expected OR estimates and perform a goodness of fit chi-squared test.
The mixture models were assessed similarly, with the exception that both the OR parameter and the proportion of risk associated variants, α, were fixed. However, an adjustment to α was incorporated to allow for the different distribution of cases and controls within the validation set compared to the training set. To do this, the proportions of cases and controls that were carrying a risk associated variant in the training set were estimated separately and α in the validation set was then computed as a weighted average of these two estimates. As an alternative approach, the predicted ORs in the validation set were computed using the posterior probabilities (PP) of each variant being risk associated (from the training set) as weights. This analysis was restricted to the subset of individuals carrying variants found in the training set or carrying no variant. As a final analysis, a single unconstrained logistic regression model comprising all the defined risk groups across the five genes, with non-carriers of any missense variant as the baseline group, was fitted, and the risks in the validation set were evaluated.
The estimated familial relative risk j due to deleterious missenses in each gene j was estimated using the where p j is the estimated total frequency of deleterious missense variants, q j = 1 = p j and r j is the estimated relative risk conferred by deleterious variants. The total contribution of deleterious missense variants was estimated by assuming that the contribution of variants in the different genes is additive, i.e., mis = 1 + ( j − 1) . The proportion of the overall familial relative risk due to missense variants was then calculated as log( mis )/log(2) , that is assuming an overall familial relative risk of 2 and that variant combine multiplicatively with other genetic/familial factors, consistent with previous observations.

ATM
The analysis of ATM missense variants included 4522 carriers of 1146 unique variants. In the carrier only analysis, BayesDel (p ALL = 0.024), CADD (p ALL = 0.0022), Helix (p ALL = 0.0045), and REVEL (p ALL = 0.024) scores were all predictive of risk (see Additional File 2: Table S5). For the most strongly associated score, CADD, the risk appeared to be restricted to the fifth quintile (Q5; CADD > 3.736542; p = 0.033 compared with third quintile). Functional protein domain was also predictive, with increased risks associated with the FRAP-ATM-TRRAP (FAT; p ALL = 9.5 × 10 −4 ) and phosphatidylinositol 3-kinase and 4-kinase (PIK; p ALL = 0.0016) domains compared with variants outside a known domain. Including CADD and protein domain, only variants in the category that included CADD Q5 variants in the FAT or PIK domains (FAT/PIK + CADD5) were associated with risk relative to non-carriers (OR 1.64 (1.33-2.02), p = 3.1 × 10 −6 ; Table 1, Figs. 1a and 2a). In the most parsimonious mixture model, risk associated variants conferred an equivalent risk to PTVs (OR 2.16 (1.78-2.63)); an estimated 54% (95% CI (41-68%)) of variants in the FAT/PIK + CADD5 risk group were risk associated, compared to less than 6% of variants in other risk categories (Table 1, Figs. 1a and 2a). There was no evidence that missense variants were associated with a different risk compared with PTVs (p = 0.48). The mixture model was a slightly better fit to the data than the LR model (2 × log-likelihood difference = 0.67). There was no association between age-at-diagnosis and risk category (see Additional File 1: Table S6).
Thirteen ATM missense variants were classified as (likely) pathogenic on the ClinVar database (see Additional File 1: Table S7). These variants, in aggregate, were associated with an increased risk (OR 1.85 (0.98-3.50, p = 0.060; p ALL = 0.00053)). However, the association of (likely) pathogenic variants was not present when the analysis was restricted to the five variants not in the FAT or PIK domains (OR = 0.97 (0.19-5.08)), though the carrier numbers were small and the confidence interval wide. Conversely, variants in the FAT/PIK + CADD5 risk group, in aggregate, remained risk associated, even when Odds ratios for breast cancer risk from logistic regression models. Alpha is the estimated proportion of risk associated variants from mixture models, based on variants in control samples. ATM risk categories: variants lying within the FAT or PI3K/PI4K protein domains with CADD score in the fifth quintile (FAT/PIK + CADD5); variants lying within the FAT or PI3K/PI4K protein domains with CADD score in any of the first four quintiles (FAT/PIK + CADD1-4); variants lying outside the FAT and PI3K/PI4K protein domains (Outside FAT/PIK). B BRCA1. Odds ratios for breast cancer risk from logistic regression models. Alpha is the estimated proportion of risk associated variants from mixture models, based on variants in control samples. BRCA1 risk categories: variants lying within the RING or BRCT domains with a high Helix score (RING/BRCT + Helix-high); variants lying with the RING or BRCT domains with a low Helix score (RING/ BRCT + Helix-low); variants lying outside the RING and BRCT domains (Outside RING/BRCT). C BRCA2. Odds ratios for breast cancer risk from logistic regression models. Alpha is the estimated proportion of risk associated variants from mixture models, based on variants in control samples. BRCA2 risk categories: variants with a high Helix score (Helix-high); variants with a low Helix score (Helix-low). D CHEK2. Odds ratios for breast cancer risk from logistic regression models. Alpha is the estimated proportion of risk associated variants from mixture models, based on variants in control samples. CHEK2 risk categories: variants with a high Helix score (Helix-high); variants with a low Helix score (Helix-low). E PALB2. Odds ratios for breast cancer risk from logistic regression models. Alpha is the estimated proportion of risk associated variants from mixture models, based on variants in control samples.   Table S7). One of these (c.8546G > C) is located in the PIK domain, the other (c.3848 T > C) is not within any domain; however, both have a Q5 CADD score. The pathogenic variants listed on ClinVar include c.7271 T > G (p.Val2424Gly), previously reported as associated with high risk of breast cancer [29,30]. In the training dataset, c.7271 T > G was identified in 12 cases (6 population-based) and 6 controls and was not associated with risk (p = 0.37, p ALL = 0.081); its population-based OR estimate of 1.63 (0.56-4.73) was lower than previous estimates (for example [31]). Another variant previously reported as risk associated, c.6919C > T (p.Leu2307Phe) [32], was associated with an increased population risk (OR = 3.71 (1.87-7.38), p = 0.00018). Both variants are located in the FAT domain and have a CADD score in Q5, but after excluding them from the model, there remained a significantly increased risk for carriers in the FAT/PIK + CADD5 risk group (OR 1.48 (1.18-1.85), p = 0.00064).

BRCA1
The analysis of BRCA1 missense variants included 2288 carriers of 644 unique variants. For missense variant carriers, all five continuous in silico scores were associated with risk (Align-GVGD p ALL = 1.3 × 10 −8 , BayesDel p ALL = 0.0013, CADD p ALL = 0.011, Helix p ALL = 2.1 × 10 −9 , REVEL p ALL = 1.5 × 10 −5 ). Variants in two protein domains were also significantly associated with risk compared with variants outside these domains (RING finger domain p ALL = 3.5 × 10 −4 ; BRCA1 C-terminal domains (BRCT I-II) p ALL = 0.0030; see Additional File 2: Table S5). The Helix tool categorizes variants with a high score (> 0.5) as "deleterious" and variants with a low score (< 0.5) as "benign"; hereafter, we refer to these categories as Helix-high and Helix-low, respectively. Including Helix category and protein domain, we found that only variants that were inside the RING or BRCT I-II domains and also in the Helix-high category (RING/ BRCT + Helix-high) were associated with risk (OR compared with non-carriers 4.94 (2.83-8.61), p = 1.9 × 10 −8 ; p ALL = 2.5 × 10 −9 ; Table 1, Figs. 1b and 2b). In a mixture model in which the OR for risk associated missense variants was constrained to that for PTVs (OR 10.61 (7.92-14.21)), the estimated proportions of risk associated variants in the RING/BRCT + Helix-high risk category was 48% (19-78%) and close to 0% for all other variants (Table 1, Figs. 1b and 2b). There was no evidence that the risk associated missense OR differed from the PTV OR (p = 0.98). The LR and mixture models were similarly good fits to the data (2 × log-likelihood difference = 0.30).
In a case-only analysis, the OR associated with variants in the RING/BRCT + Helix-high risk category reduced as age increased (per year OR 0.98 (0.96-1.00), p = 0.036; see Additional File 1: Table S6).
According to the ENIGMA guidelines and/or ClinVar classifications [13,14], 13 of the BRCA1 missense variants in the dataset (four in the RING domain and nine in the BRCT domains) would be classified as (likely) pathogenic (see Additional File 1: Table S7). In total, the 13 variants were carried by 60 cases and 6 controls and were strongly associated with risk in the subset of population samples (OR 16.68 (5.16-53.94), p = 2.6 × 10 −6 ). In our dataset, the most frequent of these variants was c.181 T > G (p.Cys61Gly), carried by 29 cases and 2 controls (OR 15.06 (3.58-63.36)). After excluding all (likely) pathogenic variants, there also remained an increased risk associated with variants in the RING/BRCT + Helixhigh category (OR 2.39 (1.19-4.78), p = 0.014)).
BRCA1 Saturation Genome Editing (SGE) score [22] was available for 100 unique variants and was strongly associated with risk (p ALL = 1.5 × 10 −4 ; see Additional File 2: Table S5). Carriers of variants with an SGE loss of function (LOF SGE ) consequence had a higher risk than carriers of variants with a functional (FUNC SGE ) consequence (OR ALL 10.79 (3.31-35.16)). Carriers of variants with an intermediate function (INT SGE ) consequence also had, on average, a higher risk than carriers of FUNC SGE variants (OR ALL 3.17 (0.32-31.15)) though the number of INT SGE carriers was small (total n = 6). Since the BRCA1 SGE experiment specifically targeted the domain-coding regions of the gene, only four variants outside of the domains were scored. Thus, all BRCA1 missense variants were assigned to one of four potential risk levels, with SGE score prioritized where available: INT SGE /LOF SGE ; RING/BRCT + Helix-high (SGE score missing); RING/ BRCT + Helix-low (SGE score missing); or FUNC SGE or carriers of variants outside of the domains. Compared with non-carriers, there was increased risk for carriers of variants in the INT SGE /LOF SGE category (OR 7.22 (2.48-21.01), p = 2.9 × 10 −4 ) and in the RING/BRCT + Helixhigh category (OR 5.35 (2.48-11.57), p = 2.0 × 10 −5 ; see Additional File 1: Table S8). In a mixture model in which the OR for risk associated missense variants was constrained to that for PTVs (OR 10.69 (7.97-14.33)), the estimated proportions of risk associated variants in the INT SGE /LOF SGE and the RING/BRCT + Helix-high risk categories were 75% (24-97%) and 51% (6-94%), respectively (Additional File 1: Table S8). The SGE LR model and SGE mixture model were similarly good fits to the data (2 × log-likelihood difference = 0.12) and both were better fits to the data compared to the Helix-only models (LR models 2 × log-likelihood difference = 3.40, mixture models 2 × log-likelihood difference = 3.58).

BRCA2
The analysis of BRCA2 missense variants included 5467 carriers of 1425 unique variants. Align-GVGD (p ALL = 0.0072), BayesDel (p ALL = 0.059), CADD (p ALL = 0.036), and Helix (p ALL = 0.0016) scores were associated with risk for carriers of BRCA2 missense variants (see Additional File 2: Table S5). Risks did not differ by protein domain (p ALL = 0.91). Compared with noncarriers, carriers of Helix-high variants had a modestly increased risk of breast cancer (OR 1.28 (0.96-1.70), p = 0.087; p ALL = 0.020) whereas carriers of a Helixlow variant had no increased risk (OR 0.98 (0.92-1.04), p = 0.47; p ALL = 0.40; Table 1, Figs. 1c and 2c). Under a mixture model in which risk associated missense variants conferred the same risk as PTVs (OR 5.87 (4.75-7.24)), an estimated 11% (4-25%) of the Helix-high variants were associated with risk, compared with < 0.1% of Helix-low variants ( Table 1, Figs. 1c and 2c). A model that allowed the OR for missense variants to differ from that of PTVs did not converge. The constrained mixture model was a better fit to the data than the logistic regression model (2 × log-likelihood difference = 6.38). There was no association between age-at-diagnosis and risk category (see Additional File 1: Table S6).
Twelve BRCA2 variants would be classified as (likely) pathogenic according to ENIGMA guidelines or ClinVar (see Additional File 1: Table S7). In aggregate, the relative risk estimate for these variants was similar to that for PTVs (OR 8.91 (2.61-30.42), p = 4.8 × 10 −4 ). Ten of these variants were categorized as Helix-high and two as Helixlow. Two of the variants categorized as (likely) pathogenic and Helix-high were observed in controls only (see Additional File 1: Table S7). After excluding the (likely) pathogenic variants from the LR model, there remained no increased risk associated with variants classified as Helix-high (OR 0.60 (0.27-1.34)).
RF and NVM predictions were available for 1338 and 1339 unique BRCA2 missense variants, respectively. There was no association with risk for variants predicted to be damaging by either the RF model (p = 0.16) or the NVM model (p = 0.32; see Additional File 2: Table S5).
BRCA2 HDR assay score was available for 82 unique variants and was strongly associated with risk (p ALL = 6.7 × 10 −4 ; see Additional File 2: Table S5).
Carriers of variants with a prediction of likely pathogenic or pathogenic (LP/P) had a higher risk than carriers of variants with a prediction of likely benign or benign (LB/B) (OR ALL 5.57 (2.36-13.17)). Since the BRCA2 HDR experiment specifically targeted the DNA binding domain-coding region of the gene, no variants outside of the domains were scored. Thus, all BRCA2 missense variants were assigned to one of four potential risk levels, with functional classification prioritized where available: LP/P; Helix-high (no functional classification); Helixlow (no functional classification); or LB/B. Compared with non-carriers, there was increased risk for carriers of variants in the LP/P category only (OR 4.72 (1.88-11.84), p = 9.3 × 10 −4 ); see Additional File 1: Table S9). In a mixture model in which the OR for risk associated missense variants was constrained to that for PTVs (OR 5.86 (4.75-7.24)), the estimated proportions of risk associated variants in LP/P risk category was 43% (11-82%) (see Additional File 1: Table S9). The functional LR model was a slightly better fit to the data than the mixture model (2 × log-likelihood difference = 1.85) but both were better fits to the data compared to the Helix-only models (LR models 2 × log-likelihood difference = 13.88, mixture models 2 × log-likelihood difference = 5.65).
In the mixture model analysis, the constrained model in which risk associated missense variants conferred the same risk as PTVs could be rejected (p = 0.027). Under the best fitting model, the OR for missense variants was 1.75 (1.47-2.08), with 95% (86-98%) of Helix-high variants and 33% (25-43%) of Helix-low variants being risk associated (see Table 1, Figs. 1d and 2d). The mixture model was a similar fit to the LR model (2 × log-likelihood difference = 0.52). We also explored mixture models with two levels of risk variant: one with an OR equal to that of PTVs and another conferring a lower risk compared to that of PTVs. The two-level model fitted slightly better in the full training dataset (2 × log-likelihood difference = 1.10) but not in the population-based studies (two-level model converged to the one-level model). The OR associated with Helix-high variants decreased as age increased (per year OR 0.99 (0.98-1.00), p = 0.017; see Additional File 1: Table S6).
Two variants, c.470 T > G (p.Ile157Ser) and c.433C > T (p.Arg145Trp), were listed as (likely) pathogenic on ClinVar; both variants have high Helix scores but the number of carriers in our population-based sample was too small to evaluate their association with risk (see Additional File 1: Table S7). One rare variant, c.349A > G (p.Arg117Gly), was previously identified as risk associated in BCAC samples, as part of the OncoArray genome-wide association study (GWAS) project [31]. In the current dataset, this variant, which is in the Helix-high category, had an OR 2.69 (1.46-4.94). After excluding the BCAC GWAS samples from the current dataset, the OR was 3.40 (1.52-7.61). Excluding c.349A > G from the LR model did not change the overall relative risk associated with the Helix-high category (OR 1.64 (1.33-2.02)).

PALB2
The analysis of PALB2 missense variants included 1659 carriers of 472 unique variants. We found no overall evidence of risk associated with missense variants in PALB2 (OR 0.95 (0.85-1.06), p = 0.34; p ALL = 0.98). In the carrier-only analysis, CADD was the only score associated with risk (p ALL = 0.020; see Additional File 2: Table S5); however, there was no significant difference in risk between CADD quintiles (p ALL = 0.16). There was no evidence for a difference in risk for carriers of variants inside any protein domain versus those outside (p ALL = 0.25). In a mixture model in which the missense variant risk was constrained to that for PTVs (OR 4.87 (3.50-6.77)), the estimated proportion of risk associated variants was 0.011% (95% CI 0-88%; Table 1, Figs. 1e and 2e). The log-likelihoods for the mixture model and logistic regression model were similar (2 × log-likelihood difference = 1.01).
Three (likely) pathogenic variants were listed on Clin-Var but none of these were present in our samples. Another variant, c.104 T > C (p.Leu35Pro), has been suggested to be pathogenic based on evidence from one family and tumor genomic analysis [33], but this variant was also not found in our samples.
A subset of the variants from the functional screening studies were available in the training data set: 26 of the 48 assayed by Boonen et al. [24], 34 of the 84 assayed by Wiltshire et al. [26] and 18 of the 44 assayed by Rodrigue et al. [25]. None of the functional assay scores or the authors' corresponding classifications of pathogenicity were associated with risk in the BRIDGES samples (see Additional File 2: Table S5).

Frequency analysis
In burden analyses of variants with frequencies up to 5%, variants in ATM with frequency < 0.1% were associated, in aggregate, with risk (p = 0.0024) but no group of variants of greater frequency was associated (see Additional File 1: Table S10). For CHEK2, variants with frequency < 0.1% (p = 1.1 × 10 −14 ) and those with frequency 0.1-0.5% (p = 3.6 × 10 −5 ) were associated with risk; there were no variants with frequency 0.5-5%. None of the other genes showed an association between any variant frequency group and risk (see Additional File 1: Table S10).
When analyses were restricted to frequencies up to 0.5%, there was no association between risk and frequency, either on a continuous scale or as the difference in risk between the two frequency groups < 0.1% and 0.1-0.5%, for BRCA2, CHEK2, or PALB2 (see Additional File 1: Table S11). For ATM, we found frequency inversely associated with risk (continuous p ALL = 0.0098) and a higher risk for variants with frequency < 0.1% compared with variants of frequency 0.1-0.5% (p ALL = 0.031). After adjusting for the CADD and domain risk groups, the associations remained statistically significant (p ALL = 0.0097 and p ALL = 0.012, respectively). For BRCA1, we found frequency inversely associated with risk (continuous p ALL = 0.022) and a significantly higher risk for variants with frequency < 0.1% compared with variants of frequency 0.1-0.5% (p ALL = 0.0066). However, after adjusting for the Helix and domain risk groups, neither of these associations remained statistically significant (p ALL = 0.36 and p ALL = 0.39, respectively).

Model validation
We evaluated the calibration of the best fitting models from the training set, for each gene, in the validation set: these included the LR models, the mixture model using the estimated proportions (α) from the training set, and the mixture model using the posterior probabilities derived from the training set. For each gene and each model, carriers of variants in the predicted risk groups were associated with an increased risk, and there were no differences between the observed and predicted ORs (see Additional File 1: Table S13 and Figs. S2-S6). In silico scores, likelihood ratios and posterior probabilities for every variant included in the population training dataset are given in Additional File 2: Tables S14-18.
Using a composite five gene model, we estimated ORs for eleven risk categories (Fig. 3). In total, 184 samples carried a missense variant in more than one of the five genes and were excluded from this analysis. Four categories were significantly associated with an increased risk relative to non-carriers, consistent with the estimates derived from the training set: ATM FAT/PIK + CADD5 ( Helix-high variant carriers was higher than that in the training dataset, but the confidence interval was considerably wider (OR 1.54 (0.88-2.68)). As predicted, variants in the remaining categories were not associated with risk.

Discussion
To date, the risks associated with missense variants in breast cancer predisposition genes have been largely unclear. In this study of over 112,000 women, we were able to use a range of in silico scores produced by ATM FAT/PIK + CADD1-4: ATM variants lying within the FAT or PI3K/PI4K protein domains with CADD score in any of first four quintiles; ATM outside FAT/PIK: variants lying outside the FAT and PI3K/PI4K protein domains; BRCA1 RING/BRCT + Helix-high: BRCA1 variants lying within the RING or BRCT domains with a high Helix score; BRCA1 RING/BRCT + Helix-low: BRCA1 variants lying with the RING or BRCT domains with a low Helix score; BRCA1 outside RING/BRCT: BRCA1 variants lying outside the RING and BRCT domains; BRCA2 Helix-high: BRCA2 variants with a high Helix score; BRCA2 Helix-low: BRCA2 variants with a low Helix score; CHEK2 Helix-high: CHEK2 variants with a high Helix score; CHEK2 Helix-low: CHEK2 variants with a low Helix score; PALB2 carriers: carriers of any missense variant in PALB2 statistical algorithms and knowledge of functional protein domains to determine the risks associated with subsets of rare missense variants. We identified groups of missense variants conferring increased risks of breast cancer in ATM, BRCA1, BRCA2, and CHEK2, but not in PALB2. The ORs for BRCA1 and CHEK2 decreased with age at diagnosis, consistent with previous observations for PTVs [7]. Previous analysis of the full BRIDGES dataset showed that protein domains in ATM and BRCA1 were predictive of risk [7]; the analysis presented here showed that in silico scores improved these predictions, in a formal model evaluation that allowed the models to be tested in an independent validation set. Under the best fitting mixture models, for ATM, BRCA1, and BRCA2, a small proportion of rare missense variants were associated with risks comparable to those for PTVs. In contrast, for CHEK2, a high proportion of CHEK2 missense variants were risk associated and the estimated risk was markedly lower than that associated with PTVs. In PALB2, the evidence for association was weak; the mixture model analysis indicated that the proportion of missense variants associated with a high risk is likely to be very small. However, we cannot rule out the possibility that some variants are risk-associated since the power for detecting an association with risk for PALB2 is lower than, for example, BRCA1 and BRCA2. One variant in BRCA1 (p.Arg841Trp) was individually associated with a reduced risk of breast cancer (0.67 (0.52-0.87)). Given that this finding is inconsistent with all the other associations and that the variant is not in any of the key functional domains, it seems quite likely that this is a chance association; further replication in other datasets will be required to confirm or refute the association.
We used five in silico scores to predict the pathogenicity of individual variants. Helix, BayesDel, and CADD were all predictive for the four genes for which we were able to identify subsets of risk-associated variants; Helix was most predictive for BRCA1, BRCA2, and CHEK2 while CADD outperformed all the other scores for ATM. In addition to the in silico scores, we also tested the BRCA1 SGE functional assay score. We found that the SGE score slightly improved the performance of the model for predicting risk for BRCA1 missense variant carriers, compared with the Helix-only model. Consistent with this, we observed two variants that were classified as loss-of-function variants by SGE but appeared in our low-risk group; these were present in three cases and no controls. Conversely, another four variants that were classified as normal function by SGE but appeared in our high-risk group were present in eight cases and five controls. Overall, variants categorized by SGE as disruptive to function, or lying within a protein domain and scored high by Helix, were strongly associated with increased risk. Under the mixture model, the proportions of riskassociated variants were also high, although the confidence intervals for the proportion of associated variants were wide. It is notable that 11 of the 31 variants in these categories have previously been identified as (likely) pathogenic by ClinVar and/or ENIGMA.
Similarly, for BRCA2, we also tested the HDR functional assay score and found it improved the performance of the model for predicting risk for BRCA2 variant carriers, compared to the Helix-only model. Consistent with this, four variants in the Helix-high category were classified as benign by the functional study and observed in 22 cases and 35 controls. Conversely, one variant in the Helix-low category was classified as pathogenic by the functional study and observed in two cases and no controls. After accounting for variants predicted to be pathogenic by the functional assay, there remained no significant increase in risk for carriers of variants in the Helix-high variant category, compared to non-carriers, although the OR of 1.37 for the Helix-high category was higher than the ORs of 0.97 and 0.96 for the Helix-low and predicted benign categories, respectively. We note that the variants tested using the HDR assay were subsequently classified using a combination of the assay result and American College of Medical Genetics and Genomics/Association for Molecular Pathology (ACMG/AMP) guidelines; ACMG guidelines also used by the ENIGMA BRCA1/2 expert panel and in evidence for pathogenicity in ClinVar. Consequently, there is considerable overlap between classifications; nine of the 14 variants classified as (likely) pathogenic by the functional study have been previously identified as (likely) pathogenic by ClinVar and/or ENIGMA.
The BRCA2 HDR functional assay included only variants lying in the DNA binding domain of BRCA2. The majority of high-Helix variants were also in the DNA binding domain (37/62) and fewer [21] in the "coldspot" regions of exons 10 and 11 as described by Dines et al. [35] (by definition, none of the BRCA1 variants in the high-risk category fall in the corresponding exon 11 coldspot).
In ATM, the risk conferred by missense variants was confined to specific protein-coding domains, namely the FAT and PIK domains, consistent with previous studies [5] and as shown previously in BRIDGES [7]. Variants within these domains could be further distinguished using the CADD score; variants in the top quintile were associated with risk whereas variants in the first four quintiles were not. In a mixture model, 54% of variants in the top CADD quintile were estimated to be associated with risk. One variant in this group, c.7271 T > G (p.Val2424Gly), has been previously reported as a breast cancer risk variant but the OR estimate for this variant, 1.63 (0.56-4.73), was markedly lower than previously estimated (relative risks ranging from 8.0 to 12.7) [29][30][31]. The reasons for this difference are unclear but might be due, in part, to previous studies oversampling for cases with a family history of breast cancer.
The results for CHEK2 were in marked contrast to those for BRCA1, BRCA2, and ATM. In the best fitting mixture model, the proportion of associated variants was high, and the estimated risk was clearly lower than for PTVs. A model in which there were two levels of risk, with the higher level equal to the PTV risk, fitted slightly better in the full training dataset but not in the population-based training studies. In addition, however, three individual CHEK2 variants were associated with differing levels of risk: c.470 T > C (p.Ile157Thr) OR 1.24 (1.09-1.42); c.538C > T (p.Arg180Cys) OR 1.44 (1.12-1.84); and c.349A > G (p.Arg117Gly) OR 2.69 (1.46-4.94). The c.470 T > C variant was too common to be included in the main analyses, possibly explaining why the heterogeneity in risk was not readily detectable by the mixture models; however, the confidence interval for c.470 T > C from the individual-level analysis did not include the LR and mixture model OR estimates of 1.73 and 1.75, respectively, for the risk-associated variants. Taken together, these observations suggest that there is substantial variation in risk associated with CHEK2 missense variants.
The relative performances of the in silico prediction algorithms are perhaps less marked than might appear; for example, Helix, which was the most predictive algorithm for three of the genes, was also predictive for ATM. Some of the differences in the associations may be due to chance. Align-GVGD was initially developed for BRCA1/2 so it is perhaps not surprising that the algorithm does relatively well for BRCA1 but less well for CHEK2, for example. Helix was not developed for a specific gene so may be a more useful tool in general.
We controlled for the potential effects of population stratification by stratifying analyses by country and by excluding individuals with the minority ancestry for that country. Thus, European studies excluded individuals of non-European ancestry and Asian studies excluded individuals of non-Asian ancestry. In addition, for the studies in Malaysia and Singapore, we further stratified into the three ethnic groups (Chinese, Malay, Indian). In previous analysis of PTVs, we found no differences in effect sizes when additionally correcting for ancestry informative principal components, suggesting that this correction was adequate, particularly since most of the associations were based on many variants [7]. Nevertheless, it remains possible that some estimates may be biased due to residual population stratification [36,37].
Under the best fitting mixture model, approximately 7% of all rare missense variants in ATM were associated with similar risk to that of PTVs. The estimated carrier frequency of pathogenic missense variants in ATM was 0.0030, or approximately 89% of the PTV frequency. The corresponding proportion of associated rare missense variants for BRCA1 and BRCA2 was 2% and 0.6%, with an estimated carrier frequency of 0.00026 (~ 18%) and 0.00028 (~ 9%), respectively. Thus, missense variants add modestly to the contribution of BRCA1 and BRCA2 variants to breast cancer incidence, but make a relatively more substantial contribution for ATM. The differences between genes in the relative contributions of missense variants to risk presumably reflect the relative proportion of residues within functional domains in which disrupted function is associated with cancer risk, and the size of those domains. For CHEK2, approximately 60% of rare missense variants were risk associated and the estimated carrier frequency of pathogenic missense variants in CHEK2 was comparable to the frequency of PTVs. The predicted proportion of breast cancer cases possessing pathogenic germline missense variants in these genes is approximately 0.6%, 0.3%, 0.2%, and 1.3% for ATM, BRCA1, BRCA2, and CHEK2, respectively. The estimated additional contribution to the familial relative risk of breast cancer made by pathogenic missense variants in these five genes is approximately 2.7%.
The task of identifying which specific individual missense variants are risk associated is a complex one and is difficult to resolve fully even with a large dataset, since most variants are rare and there are many possible models to consider. Despite the size of our study, it was difficult to distinguish, for any gene, between the LR models (in which all variants in a given category confer a given risk) and the mixture models (in which all risk-associated variants confer the same risk, but the proportion that are associated varies by category). This difficulty arises because the number of carriers for individual variants is small, and as a result, the estimated risk of pathogenic missense variants and probability of pathogenicity (α) are strongly confounded. Further, selecting the best models and estimating the risks based on these models is likely to result in overfitting and biased risk estimates. In order to strengthen the validity of our findings, we used a training-validation study design. We were able to replicate the predicted OR estimates in the validation dataset, suggesting that any bias due to overfitting was small. Nevertheless, the validation dataset was relatively small, so further validation of the best models reported here in large independent datasets is critical.
Ultimately, high-throughput functional assays that can evaluate all possible missense substitutions may provide more precise definitions of risk categories. The analyses of the BRCA1 SGE scores and the BRCA2 HDR assay scores suggest that this approach should be useful, although the scores for BRCA1 were highly concordant with the best in silico score in this case. The available PALB2 functional assays did not predict risk, but this may just reflect the low power of these analyses when the proportion of risk-associated variants is very low. As further prediction algorithms based on in silico and/or in vitro data are developed, large population-based epidemiological datasets such as BRIDGES can be used to validate their predictions. However, further large studies are likely to be required to provide more precise variantspecific risk estimates.

Conclusions
This study confirms that subsets of missense variants in established breast cancer susceptibility genes are associated with increased risks of the disease and provides estimates of relative risks for those subsets, as well as probabilities for association with risk at the variant level. The pattern of risk varies substantially by gene. Accurately and precisely defining these risks is critical to the counselling and management of women in whom these variants are identified.