Graves' disease is a common autoimmune disorder characterized by thyroid stimulating hormone receptor autoantibodies (TRAb) and hyperthyroidism. To investigate the genetic architecture of Graves' disease, we conducted a genome-wide association study in 1,536 individuals with Graves' disease (cases) and 1,516 controls. We further evaluated a group of associated SNPs in a second set of 3,994 cases and 3,510 controls. We confirmed four previously reported loci (in the major histocompatibility complex, TSHR, CTLA4 and FCRL3) and identified two new susceptibility loci (the RNASET2-FGFR1OP-CCR6 region at 6q27 (P(combined) = 6.85 × 10(-10) for rs9355610) and an intergenic region at 4p14 (P(combined) = 1.08 × 10(-13) for rs6832151)). These newly associated SNPs were correlated with the expression levels of RNASET2 at 6q27, of CHRNA9 and of a previously uncharacterized gene at 4p14, respectively. Moreover, we identified strong associations of TSHR and major histocompatibility complex class II variants with persistently TRAb-positive Graves' disease.

The generalized orthopair fuzzy set inherits the virtues of intuitionistic fuzzy set and Pythagorean fuzzy set in relaxing the restriction on the support for and support against.The very lax requirement provides decision makers great freedom in expressing their beliefs about membership grades, which makes generalized orthopair fuzzy sets having a wide scope of application in practice. In this paper, we present the Minkowski-type distance measures, including Hamming, Euclidean, and Chebyshev distances, for -rung orthopair fuzzy sets. First, we introduce the Minkowski-type distances of -rung orthopair membership grades, based on which we can rank orthopairs. Second, we propose several distances over -rung orthopair fuzzy sets on a finite discrete universe and subsequently discuss their applications to multiattribute decision-making problems.Then we extend these results to a continuous universe, both bounded and unbounded cases are considered. Some illustrative examples are employed to substantiate the conceptual arguments. K E Y W O R D SMinkowski distance, multiattribute decision making, q-rung orthopair fuzzy set, q-rung orthopair membership grade 802

Graves' disease (GD), characterized by autoantibodies targeting antigens specifically expressed in thyroid tissues causing hyperthyroidism, is triggered by a combination of genetic and environmental factors. However, only a few loci for GD risk were confirmed in the various ethnic groups, and additional genetic determinants have to be detected. In this study, we carried out a three-stage study in 9529 patients with GD and 9984 controls to identify new risk loci for GD and found genome-wide significant associations in the overall populations for five novel susceptibility loci: the GPR174-ITM2A at Xq21.1, C1QTNF6-RAC2 at 22q12.3-13.1, SLAMF6 at 1q23.2, ABO at 9q34.2 and an intergenic region harboring two non-coding RNAs at 14q32.2 and one previous indefinite locus, TG at 8q24.22 (Pcombined < 5 × 10(-8)). The genotypes of corresponding variants at 14q32.2 and 8q24.22 were correlated with the expression levels of C14orf64 and a TG transcript skipping exon 46, respectively. This study increased the number of GD loci with compelling evidence and indicated that non-coding RNAs might be potentially involved in the pathogenesis of GD.

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Generalized orthopair fuzzy sets are extensions of ordinary fuzzy sets by relaxing restrictions on the degrees of support for and support against. Correlation analysis is to measure the statistical relationships between two samples or variables. In this paper, we propose a function measuring the interrelation of two q‐rung orthopair fuzzy sets, whose range is the unit interval [ 0 , 1 ]. First, the correlation and correlation coefficient of q‐rung orthopair membership grades are presented, and their basic properties are investigated. Second, these concepts are extended to q‐rung orthopair fuzzy sets on discrete universes. Then, we discuss their applications in cluster analysis under generalized orthopair fuzzy environments. And, a real‐world problem involving the evaluation of companies is used to illustrate the detailed processes of the clustering algorithm. Finally, we introduce the correlation and correlation coefficient of q‐rung orthopair fuzzy sets on both bounded and unbounded continuous universes and provide some numerical examples to substantiate such arguments.

In our previous studies, we presumed subtypes of Graves’ disease (GD) may be caused by different major susceptibility genes or different variants of a single susceptibility gene. However, more evidence is needed to support this hypothesis. Single-nucleotide polymorphism (SNP) rs2476601 in PTPN22 is the susceptibility loci of GD in the European population. However, this polymorphism has not been found in Asian populations. Here, we investigate whether PTPN22 is the susceptibility gene for GD in Chinese population and further determine the susceptibility variant of PTPN22 in GD. We conducted an imputation analysis based on the results of our genome-wide association study (GWAS) in 1,536 GD patients and 1,516 control subjects. Imputation revealed that 255 common SNPs on a linkage disequilibrium (LD) block containing PTPN22 were associated with GD (P<0.05). Nine tagSNPs that captured the 255 common variants were selected to be further genotyped in a large cohort including 4,368 GD patients and 4,350 matched controls. There was no significant difference between the nine tagSNPs (P>0.05) in either the genotype distribution or allelic frequencies between patients and controls in the replication study. Although the combined analysis exhibited a weak association signal (P combined = 0.003263 for rs3811021), the false positive report probability (FPRP) analysis indicated it was most likely a false positive finding. Our study did not support an association of common SNPs in PTPN22 LD block with GD in Chinese Han population. This suggests that GD in different ethnic population is probably caused by distinct susceptibility genes.

The BACH2 gene regulates B cell differentiation and function and has been reported to be a shared susceptibility gene for several autoimmune diseases. Our previous genome-wide association study (GWAS) indicated that several single nucleotide polymorphisms (SNPs) in the BACH2 gene are associated with Graves' disease (GD) in the Chinese Han population; however, the association did not achieve genome-wide significance levels. Recently, this association of BACH2 with GD was confirmed in Caucasians in the UK population, but fine mapping in this region has not yet been reported. Here, we provide a refined analysis of a 331-kb region in the BACH2 gene, which harbors 359 SNPs, using GWAS data from 1,442 GD patients and 1,468 controls. The SNPs rs2474619 and rs9344996 were implied as the independent variants associated with GD by forward and two-locus logistic regression analysis. We genotyped eight out of 10 tagSNPs with P < 1 × 10(-3) in 3,508 GD patients and 3,209 controls, the results also showed that rs2474619 was independently associated with GD in the combined population from GWAS and the second stage (P = 1.81 × 10(-5)). The rs2474619 and rs9344996 were further genotyped in the third stage cohorts, and rs2474619 showed evidence of association with GD at genome-wide significance levels in the combined population (P = 3.28 × 10(-8), odds ratio = 1.13). The association of rs9344996 with GD can be explained by its linkage to rs2474619 in the combined population. Our study clearly demonstrated that BACH2 is a susceptibility gene for GD in the Chinese Han population and further supported rs2474619, in intron 2 of BACH2, is the best association signal with GD. However, the mechanism by which BACH2 confers increased risk of GD requires further study.

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