Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York

FGF receptor genes and breast cancer susceptibility: results from the Breast Cancer Association Consortium

Background:Breast cancer is one of the most common malignancies in women. Genome-wide association studies have identified FGFR2 as a breast cancer susceptibility gene. Common variation in other fibroblast growth factor (FGF) receptors might also modify risk. We tested this hypothesis by studying genotyped single-nucleotide polymorphisms (SNPs) and imputed SNPs in FGFR1, FGFR3, FGFR4 and FGFRL1 in the Breast Cancer Association Consortium. Methods:Data were combined from 49 studies, including 53 835 cases and 50 156 controls, of which 89 050 (46 450 cases and 42 600 controls) were of European ancestry, 12 893 (6269 cases and 6624 controls) of Asian and 2048 (1116 cases and 932 controls) of African ancestry. Associations with risk of breast cancer, overall and by disease sub-type, were assessed using unconditional logistic regression. Results:Little evidence of association with breast cancer risk was observed for SNPs in the FGF receptor genes. The strongest evidence in European women was for rs743682 in FGFR3; the estimated per-allele odds ratio was 1.05 (95 confidence interval=1.02-1.09, P=0.0020), which is substantially lower than that observed for SNPs in FGFR2. Conclusion:Our results suggest that common variants in the other FGF receptors are not associated with risk of breast cancer to the degree observed for FGFR2. © 2014 Cancer Research UK

Inequalities in the use of secondary prevention of cardiovascular disease by socioeconomic status: evidence from the PURE observational study

Background: There is little evidence on the use of secondary prevention medicines for cardiovascular disease by socioeconomic groups in countries at different levels of economic development. Methods: We assessed use of antiplatelet, cholesterol, and blood-pressure-lowering drugs in 8492 individuals with self-reported cardiovascular disease from 21 countries enrolled in the Prospective Urban Rural Epidemiology (PURE) study. Defining one or more drugs as a minimal level of secondary prevention, wealth-related inequality was measured using the Wagstaff concentration index, scaled from −1 (pro-poor) to 1 (pro-rich), standardised by age and sex. Correlations between inequalities and national health-related indicators were estimated. Findings: The proportion of patients with cardiovascular disease on three medications ranged from 0% in South Africa (95% CI 0–1·7), Tanzania (0–3·6), and Zimbabwe (0–5·1), to 49·3% in Canada (44·4–54·3). Proportions receiving at least one drug varied from 2·0% (95% CI 0·5–6·9) in Tanzania to 91·4% (86·6–94·6) in Sweden. There was significant (p<0·05) pro-rich inequality in Saudi Arabia, China, Colombia, India, Pakistan, and Zimbabwe. Pro-poor distributions were observed in Sweden, Brazil, Chile, Poland, and the occupied Palestinian territory. The strongest predictors of inequality were public expenditure on health and overall use of secondary prevention medicines. Interpretation: Use of medication for secondary prevention of cardiovascular disease is alarmingly low. In many countries with the lowest use, pro-rich inequality is greatest. Policies associated with an equal or pro-poor distribution include free medications and community health programmes to support adherence to medications. Funding: Full funding sources listed at the end of the paper (see Acknowledgments)

Insights into malaria susceptibility using genome-wide data on 17,000 individuals from Africa, Asia and Oceania

The human genetic factors that affect resistance to infectious disease are poorly understood. Here we report a genome-wide association study in 17,000 severe malaria cases and population controls from 11 countries, informed by sequencing of family trios and by direct typing of candidate loci in an additional 15,000 samples. We identify five replicable associations with genome-wide levels of evidence including a newly implicated variant on chromosome 6. Jointly, these variants account for around one-tenth of the heritability of severe malaria, which we estimate as -23% using genome-wide genotypes. We interrogate available functional data and discover an erythroid-specific transcription start site underlying the known association in ATP2B4, but are unable to identify a likely causal mechanism at the chromosome 6 locus. Previously reported HLA associations do not replicate in these samples. This large dataset will provide a foundation for further research on thegenetic determinants of malaria resistance in diverse populations.Peer reviewe

The BRCA2 c.68-7T > A variant is not pathogenic : A model for clinical calibration of spliceogenicity

Although the spliceogenic nature of the BRCA2 c.68-7T > A variant has been demonstrated, its association with cancer risk remains controversial. In this study, we accurately quantified by real-time PCR and digital PCR (dPCR), the BRCA2 isoforms retaining or missing exon 3. In addition, the combined odds ratio for causality of the variant was estimated using genetic and clinical data, and its associated cancer risk was estimated by case-control analysis in 83,636 individuals. Co-occurrence in trans with pathogenic BRCA2 variants was assessed in 5,382 families. Exon 3 exclusion rate was 4.5-fold higher in variant carriers (13%) than controls (3%), indicating an exclusion rate for the c.68-7T > A allele of approximately 20%. The posterior probability of pathogenicity was 7.44x10(-115). There was neither evidence for increased risk of breast cancer (OR 1.03; 95% CI 0.86-1.24) nor for a deleterious effect of the variant when co-occurring with pathogenic variants. Our data provide for the first time robust evidence of the nonpathogenicity of the BRCA2 c.68-7T > A. Genetic and quantitative transcript analyses together inform the threshold for the ratio between functional and altered BRCA2 isoforms compatible with normal cell function. These findings might be exploited to assess the relevance for cancer risk of other BRCA2 spliceogenic variants.Peer reviewe

Inheritance of deleterious mutations at both BRCA1 and BRCA2 in an international sample of 32,295 women

Background: Most BRCA1 or BRCA2 mutation carriers have inherited a single (heterozygous) mutation. Transheterozygotes (TH) who have inherited deleterious mutations in both BRCA1 and BRCA2 are rare, and the consequences of transheterozygosity are poorly understood. Methods: From 32,295 female BRCA1/2 mutation carriers, we identified 93 TH (0.3 %). "Cases" were defined as TH, and "controls" were single mutations at BRCA1 (SH1) or BRCA2 (SH2). Matched SH1 "controls" carried a BRCA1 mutation found in the TH "case". Matched SH2 "controls" carried a BRCA2 mutation found in the TH "case". After matching the TH carriers with SH1 or SH2, 91 TH were matched to 9316 SH1, and 89 TH were matched to 3370 SH2. Results: The majority of TH (45.2 %) involved the three common Jewish mutations. TH were more likely than SH1 and SH2 women to have been ever diagnosed with breast cancer (BC; p = 0.002). TH were more likely to be diagnosed with ovarian cancer (OC) than SH2 (p = 0.017), but not SH1. Age at BC diagnosis was the same in TH vs. SH1 (p = 0.231), but was on average 4.5 years younger in TH than in SH2 (p < 0.001). BC in TH was more likely to be estrogen receptor (ER) positive (p = 0.010) or progesterone receptor (PR) positive (p = 0.013) than in SH1, but less likely to be ER positive (p < 0.001) or PR positive (p = 0.012) than SH2. Among 15 tumors from TH patients, there was no clear pattern of loss of heterozygosity (LOH) for BRCA1 or BRCA2 in either BC or OC. Conclusions: Our observations suggest that clinical TH phenotypes resemble SH1. However, TH breast tumor marker characteristics are phenotypically intermediate to SH1 and SH2

A new strategy for enhancing imputation quality of rare variants from next-generation sequencing data via combining SNP and exome chip data

Background: Rare variants have gathered increasing attention as a possible alternative source of missing heritability. Since next generation sequencing technology is not yet cost-effective for large-scale genomic studies, a widely used alternative approach is imputation. However, the imputation approach may be limited by the low accuracy of the imputed rare variants. To improve imputation accuracy of rare variants, various approaches have been suggested, including increasing the sample size of the reference panel, using sequencing data from study-specific samples (i.e., specific populations), and using local reference panels by genotyping or sequencing a subset of study samples. While these approaches mainly utilize reference panels, imputation accuracy of rare variants can also be increased by using exome chips containing rare variants. The exome chip contains 250 K rare variants selected from the discovered variants of about 12,000 sequenced samples. If exome chip data are available for previously genotyped samples, the combined approach using a genotype panel of merged data, including exome chips and SNP chips, should increase the imputation accuracy of rare variants. Results: In this study, we describe a combined imputation which uses both exome chip and SNP chip data simultaneously as a genotype panel. The effectiveness and performance of the combined approach was demonstrated using a reference panel of 848 samples constructed using exome sequencing data from the T2D-GENES consortium and 5,349 sample genotype panels consisting of an exome chip and SNP chip. As a result, the combined approach increased imputation quality up to 11 %, and genomic coverage for rare variants up to 117.7 % (MAF < 1 %), compared to imputation using the SNP chip alone. Also, we investigated the systematic effect of reference panels on imputation quality using five reference panels and three genotype panels. The best performing approach was the combination of the study specific reference panel and the genotype panel of combined data. Conclusions: Our study demonstrates that combined datasets, including SNP chips and exome chips, enhances both the imputation quality and genomic coverage of rare variants

Fine-Scale Mapping of the 5q11.2 Breast Cancer Locus Reveals at Least Three Independent Risk Variants Regulating MAP3K1

Peer reviewe

Identification of independent association signals and putative functional variants for breast cancer risk through fine-scale mapping of the 12p11 locus.

BACKGROUND: Multiple recent genome-wide association studies (GWAS) have identified a single nucleotide polymorphism (SNP), rs10771399, at 12p11 that is associated with breast cancer risk. METHOD: We performed a fine-scale mapping study of a 700 kb region including 441 genotyped and more than 1300 imputed genetic variants in 48,155 cases and 43,612 controls of European descent, 6269 cases and 6624 controls of East Asian descent and 1116 cases and 932 controls of African descent in the Breast Cancer Association Consortium (BCAC; http://bcac.ccge.medschl.cam.ac.uk/ ), and in 15,252 BRCA1 mutation carriers in the Consortium of Investigators of Modifiers of BRCA1/2 (CIMBA). Stepwise regression analyses were performed to identify independent association signals. Data from the Encyclopedia of DNA Elements project (ENCODE) and the Cancer Genome Atlas (TCGA) were used for functional annotation. RESULTS: Analysis of data from European descendants found evidence for four independent association signals at 12p11, represented by rs7297051 (odds ratio (OR) = 1.09, 95 % confidence interval (CI) = 1.06-1.12; P = 3 × 10(-9)), rs805510 (OR = 1.08, 95 % CI = 1.04-1.12, P = 2 × 10(-5)), and rs1871152 (OR = 1.04, 95 % CI = 1.02-1.06; P = 2 × 10(-4)) identified in the general populations, and rs113824616 (P = 7 × 10(-5)) identified in the meta-analysis of BCAC ER-negative cases and BRCA1 mutation carriers. SNPs rs7297051, rs805510 and rs113824616 were also associated with breast cancer risk at P < 0.05 in East Asians, but none of the associations were statistically significant in African descendants. Multiple candidate functional variants are located in putative enhancer sequences. Chromatin interaction data suggested that PTHLH was the likely target gene of these enhancers. Of the six variants with the strongest evidence of potential functionality, rs11049453 was statistically significantly associated with the expression of PTHLH and its nearby gene CCDC91 at P < 0.05. CONCLUSION: This study identified four independent association signals at 12p11 and revealed potentially functional variants, providing additional insights into the underlying biological mechanism(s) for the association observed between variants at 12p11 and breast cancer risk.UK funding includes Cancer Research UK and NIH.This is the final version of the article. It first appeared from BioMed Central via http://dx.doi.org/10.1186/s13058-016-0718-

Refined histopathological predictors of BRCA1 and BRCA2 mutation status: A large-scale analysis of breast cancer characteristics from the BCAC, CIMBA, and ENIGMA consortia

Introduction: The distribution of histopathological features of invasive breast tumors in BRCA1 or BRCA2 germline mutation carriers differs from that of individuals with no known mutation. Histopathological features thus have utility for mutation prediction, including statistical modeling to assess pathogenicity of BRCA1 or BRCA2 variants of uncertain clinical significance. We analyzed large pathology datasets accrued by the Consortium of Investigators of Modifiers of BRCA1/2 (CIMBA) and the Breast Cancer Association Consortium (BCAC) to reassess histopathological predictors of BRCA1 and BRCA2 mutation status, and provide robust likelihood ratio (LR) estimates for statistical modeling. Methods: Selection criteria for study/center inclusion were estrogen receptor (ER) status or grade data available for invasive breast cancer diagnosed younger than 70 years. The dataset included 4,477 BRCA1 mutation carriers, 2,565 BRCA2 mutation carriers, and 47,565 BCAC breast cancer cases. Country-stratified estimates of the