Min-Max Solutions for Parametric Continuous Static Game under Roughness (Parameters in the Cost Function and Feasible Region Is a Rough Set)

Any simple perturbation in a part of the game whether in the cost function and/or conditions is a big problem because it will require a game re-solution to obtain the perturbed optimal solution. This is a waste of time because there are methods required several steps to obtain the optimal solution, then at the end we may find that there is no solution. Therefore, it was necessary to find a method to ensure that the game optimal solution exists in the case of a change in the game data. This is the aim of this paper. We first provided a continuous static game rough treatment with Min-Max solutions, then a parametric study for the processing game and called a parametric rough continuous static game (PRCSG). In a Parametric study, a solution approach is provided based on the parameter existence in the cost function that reflects the perturbation that may occur to it to determine the parameter range in which the optimal solution point keeps in the surely region that is called the stability set of the 1st kind. Also the sets of possible upper and lower stability to which the optimal solution belongs are characterized. Finally, numerical examples are given to clarify the solution algorithm

Association of Type and Location of BRCA1 and BRCA2 Mutations With Risk of Breast and Ovarian Cancer (vol 313, pg 1347, 2015)

Heli Nevanlinna ja Kristiina Aittomäki ovat CIMBA Consortium -työryhmän jäseniä.IMPORTANCE Limited information about the relationship between specific mutations in BRCA1 or BRCA2 (BRCA1/2) and cancer risk exists. OBJECTIVE To identify mutation-specific cancer risks for carriers of BRCA1/2. DESIGN, SETTING, AND PARTICIPANTS Observational study of women who were ascertained between 1937 and 2011 (median, 1999) and found to carry disease-associated BRCA1 or BRCA2 mutations. The international sample comprised 19 581 carriers of BRCA1 mutations and 11 900 carriers of BRCA2 mutations from 55 centers in 33 countries on 6 continents. We estimated hazard ratios for breast and ovarian cancer based on mutation type, function, and nucleotide position. We also estimated RHR, the ratio of breast vs ovarian cancer hazard ratios. A value of RHR greater than 1 indicated elevated breast cancer risk; a value of RHR less than 1 indicated elevated ovarian cancer risk. EXPOSURES Mutations of BRCA1 or BRCA2. MAIN OUTCOMES AND MEASURES Breast and ovarian cancer risks. RESULTS Among BRCA1 mutation carriers, 9052 women (46%) were diagnosed with breast cancer, 2317(12%) with ovarian cancer, 1041 (5%) with breast and ovarian cancer, and 7171 (37%) without cancer. Among BRCA2 mutation carriers, 6180 women (52%) were diagnosed with breast cancer, 682(6%) with ovarian cancer, 272(2%) with breast and ovarian cancer, and 4766 (40%) without cancer. In BRCA1, we identified 3 breast cancer cluster regions (BCCRs) located at c.179 to c.505 (BCCR1; RHR = 1.46; 95% Cl, 1.22-1.74; P = 2 x 10(-6)), c.4328 to c.4945 (BCCR2; RH R = 1.34; 95% Cl, 1.01-1.78; P =.04), and c. 5261 to c.5563 (BCCR2', RHR = 1.38; 95% Cl, 1.22-1.55; P = 6 x 10(-9)). We also identified an ovarian cancer cluster region (OCCR) from c.1380 to c.4062 (approximately exon 11) with RHR = 0.62 (95% Cl, 0.56-0.70; P = 9 x 10(-17)). In BRCA2, we observed multiple BCCRs spanning c.1 to c.596 (BCCR1; RHR = 1.71; 95% Cl, 1.06-2.78; P =.03), c.772 to c.1806 (BCCRI; RHR = 1.63; 95% Cl, 1.10-2.40; P =.01), and c.7394 to c.8904 (BCCR2; RHR = 2.31; 95% Cl, 1.69-3.16; P =.00002). We also identified 3 OCCRs: the first (OCCR1) spanned c.3249 to c.5681 that was adjacent to c.5946delT (6174delT; RHR = 0.51; 95% Cl, 0.44-0.60; P = 6 x 10(-17)). The second OCCR spanned c.6645 to c.7471 (OCCR2; RHR = 0.57; 95% Cl, 0.41-0.80; P =.001). Mutations conferring nonsense-mediated decay were associated with differential breast or ovarian cancer risks and an earlier age of breast cancer diagnosis for both BRCA1 and BRCA2 mutation carriers. CONCLUSIONS AND RELEVANCE Breast and ovarian cancer risks varied by type and location of BRCA1/2 mutations. With appropriate validation, these data may have implications for risk assessment and cancer prevention decision making for carriers of BRCA1 and BRCA2 mutations.Peer reviewe

Identification of six new susceptibility loci for invasive epithelial ovarian cancer.

Genome-wide association studies (GWAS) have identified 12 epithelial ovarian cancer (EOC) susceptibility alleles. The pattern of association at these loci is consistent in BRCA1 and BRCA2 mutation carriers who are at high risk of EOC. After imputation to 1000 Genomes Project data, we assessed associations of 11 million genetic variants with EOC risk from 15,437 cases unselected for family history and 30,845 controls and from 15,252 BRCA1 mutation carriers and 8,211 BRCA2 mutation carriers (3,096 with ovarian cancer), and we combined the results in a meta-analysis. This new study design yielded increased statistical power, leading to the discovery of six new EOC susceptibility loci. Variants at 1p36 (nearest gene, WNT4), 4q26 (SYNPO2), 9q34.2 (ABO) and 17q11.2 (ATAD5) were associated with EOC risk, and at 1p34.3 (RSPO1) and 6p22.1 (GPX6) variants were specifically associated with the serous EOC subtype, all with P < 5 × 10(-8). Incorporating these variants into risk assessment tools will improve clinical risk predictions for BRCA1 and BRCA2 mutation carriers.COGS project is funded through a European Commission's Seventh Framework Programme grant (agreement number 223175 ] HEALTH ]F2 ]2009 ]223175). The CIMBA data management and data analysis were supported by Cancer Research.UK grants 12292/A11174 and C1287/A10118. The Ovarian Cancer Association Consortium is supported by a grant from the Ovarian Cancer Research Fund thanks to donations by the family and friends of Kathryn Sladek Smith (PPD/RPCI.07). The scientific development and funding for this project were in part supported by the US National Cancer Institute GAME ]ON Post ]GWAS Initiative (U19 ]CA148112). This study made use of data generated by the Wellcome Trust Case Control consortium. Funding for the project was provided by the Wellcome Trust under award 076113. The results published here are in part based upon data generated by The Cancer Genome Atlas Pilot Project established by the National Cancer Institute and National Human Genome Research Institute (dbGap accession number phs000178.v8.p7). The cBio portal is developed and maintained by the Computational Biology Center at Memorial Sloan ] Kettering Cancer Center. SH is supported by an NHMRC Program Grant to GCT. Details of the funding of individual investigators and studies are provided in the Supplementary Note. This study made use of data generated by the Wellcome Trust Case Control consortium, funding for which was provided by the Wellcome Trust under award 076113. The results published here are, in part, based upon data generated by The Cancer Genome Atlas Pilot Project established by the National Cancerhttp://dx.doi.org/10.1038/ng.3185This is the Author Accepted Manuscript of 'Identification of six new susceptibility loci for invasive epithelial ovarian cancer' which was published in Nature Genetics 47, 164–171 (2015) © Nature Publishing Group - content may only be used for academic research

An original phylogenetic approach identified mitochondrial haplogroup T1a1 as inversely associated with breast cancer risk in BRCA2 mutation carriers

Introduction: Individuals carrying pathogenic mutations in the BRCA1 and BRCA2 genes have a high lifetime risk of breast cancer. BRCA1 and BRCA2 are involved in DNA double-strand break repair, DNA alterations that can be caused by exposure to reactive oxygen species, a main source of which are mitochondria. Mitochondrial genome variations affect electron transport chain efficiency and reactive oxygen species production. Individuals with different mitochondrial haplogroups differ in their metabolism and sensitivity to oxidative stress. Variability in mitochondrial genetic background can alter reactive oxygen species production, leading to cancer risk. In the present study, we tested the hypothesis that mitochondrial haplogroups modify breast cancer risk in BRCA1/2 mutation carriers. Methods: We genotyped 22,214 (11,421 affected, 10,793 unaffected) mutation carriers belonging to the Consortium of Investigators of Modifiers of BRCA1/2 for 129 mitochondrial polymorphisms using the iCOGS array. Haplogroup inference and association detection were performed using a phylogenetic approach. ALTree was applied to explore the reference mitochondrial evolutionary tree and detect subclades enriched in affected or unaffected individuals. Results: We discovered that subclade T1a1 was depleted in affected BRCA2 mutation carriers compared with the rest of clade T (hazard ratio (HR) = 0.55; 95% confidence interval (CI), 0.34 to 0.88; P = 0.01). Compared with the most frequent haplogroup in the general population (that is, H and T clades), the T1a1 haplogroup has a HR of 0.62 (95% CI, 0.40 to 0.95; P = 0.03). We also identified three potential susceptibility loci, including G13708A/rs28359178, which has demonstrated an inverse association with familial breast cancer risk. Conclusions: This study illustrates how original approaches such as the phylogeny-based method we used can empower classical molecular epidemiological studies aimed at identifying association or risk modification effects.Peer reviewe

An original phylogenetic approach identified mitochondrial haplogroup T1a1 as inversely associated with breast cancer risk in BRCA2 mutation carriers

Abstract Introduction Individuals carrying pathogenic mutations in the BRCA1 and BRCA2 genes have a high lifetime risk of breast cancer. BRCA1 and BRCA2 are involved in DNA double-strand break repair, DNA alterations that can be caused by exposure to reactive oxygen species, a main source of which are mitochondria. Mitochondrial genome variations affect electron transport chain efficiency and reactive oxygen species production. Individuals with different mitochondrial haplogroups differ in their metabolism and sensitivity to oxidative stress. Variability in mitochondrial genetic background can alter reactive oxygen species production, leading to cancer risk. In the present study, we tested the hypothesis that mitochondrial haplogroups modify breast cancer risk in BRCA1/2 mutation carriers. Methods We genotyped 22,214 (11,421 affected, 10,793 unaffected) mutation carriers belonging to the Consortium of Investigators of Modifiers of BRCA1/2 for 129 mitochondrial polymorphisms using the iCOGS array. Haplogroup inference and association detection were performed using a phylogenetic approach. ALTree was applied to explore the reference mitochondrial evolutionary tree and detect subclades enriched in affected or unaffected individuals. Results We discovered that subclade T1a1 was depleted in affected BRCA2 mutation carriers compared with the rest of clade T (hazard ratio (HR) = 0.55; 95% confidence interval (CI), 0.34 to 0.88; P = 0.01). Compared with the most frequent haplogroup in the general population (that is, H and T clades), the T1a1 haplogroup has a HR of 0.62 (95% CI, 0.40 to 0.95; P = 0.03). We also identified three potential susceptibility loci, including G13708A/rs28359178, which has demonstrated an inverse association with familial breast cancer risk. Conclusions This study illustrates how original approaches such as the phylogeny-based method we used can empower classical molecular epidemiological studies aimed at identifying association or risk modification effects

An original phylogenetic approach identified mitochondrial haplogroup T1a1 as inversely associated with breast cancer risk in BRCA2 mutation carriers.

INTRODUCTION: Individuals carrying pathogenic mutations in the BRCA1 and BRCA2 genes have a high lifetime risk of breast cancer. BRCA1 and BRCA2 are involved in DNA double-strand break repair, DNA alterations that can be caused by exposure to reactive oxygen species, a main source of which are mitochondria. Mitochondrial genome variations affect electron transport chain efficiency and reactive oxygen species production. Individuals with different mitochondrial haplogroups differ in their metabolism and sensitivity to oxidative stress. Variability in mitochondrial genetic background can alter reactive oxygen species production, leading to cancer risk. In the present study, we tested the hypothesis that mitochondrial haplogroups modify breast cancer risk in BRCA1/2 mutation carriers. METHODS: We genotyped 22,214 (11,421 affected, 10,793 unaffected) mutation carriers belonging to the Consortium of Investigators of Modifiers of BRCA1/2 for 129 mitochondrial polymorphisms using the iCOGS array. Haplogroup inference and association detection were performed using a phylogenetic approach. ALTree was applied to explore the reference mitochondrial evolutionary tree and detect subclades enriched in affected or unaffected individuals. RESULTS: We discovered that subclade T1a1 was depleted in affected BRCA2 mutation carriers compared with the rest of clade T (hazard ratio (HR) = 0.55; 95% confidence interval (CI), 0.34 to 0.88; P = 0.01). Compared with the most frequent haplogroup in the general population (that is, H and T clades), the T1a1 haplogroup has a HR of 0.62 (95% CI, 0.40 to 0.95; P = 0.03). We also identified three potential susceptibility loci, including G13708A/rs28359178, which has demonstrated an inverse association with familial breast cancer risk. CONCLUSIONS: This study illustrates how original approaches such as the phylogeny-based method we used can empower classical molecular epidemiological studies aimed at identifying association or risk modification effects

Identification of six new susceptibility loci for invasive epithelial ovarian cancer

Genome Instability and Cance