School of Mathematics and Statistics - Research Publications
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ItemPopulation Structure and Cryptic Relatedness in Genetic Association Studies(INST MATHEMATICAL STATISTICS, 2009-11)We review the problem of confounding in genetic association studies, which arises principally because of population structure and cryptic relatedness. Many treatments of the problem consider only a simple ``island'' model of population structure. We take a broader approach, which views population structure and cryptic relatedness as different aspects of a single confounder: the unobserved pedigree defining the (often distant) relationships among the study subjects. Kinship is therefore a central concept, and we review methods of defining and estimating kinship coefficients, both pedigree-based and marker-based. In this unified framework we review solutions to the problem of population structure, including family-based study designs, genomic control, structured association, regression control, principal components adjustment and linear mixed models. The last solution makes the most explicit use of the kinships among the study subjects, and has an established role in the analysis of animal and plant breeding studies. Recent computational developments mean that analyses of human genetic association data are beginning to benefit from its powerful tests for association, which protect against population structure and cryptic kinship, as well as intermediate levels of confounding by the pedigree.
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ItemLimit theorems for sequences of random trees(SPRINGER, 2009-08)We consider a random tree and introduce a metric in the space of trees to define the ``mean tree'' as the tree minimizing the average distance to the random tree. When the resulting metric space is compact we have laws of large numbers and central limit theorems for sequence of independent identically distributed random trees. As application we propose tests to check if two samples of random trees have the same law.
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ItemCommon Genetic Variation Near Melatonin Receptor MTNR1B Contributes to Raised Plasma Glucose and Increased Risk of Type 2 Diabetes Among Indian Asians and European Caucasians(AMER DIABETES ASSOC, 2009-11)OBJECTIVE: Fasting plasma glucose and risk of type 2 diabetes are higher among Indian Asians than among European and North American Caucasians. Few studies have investigated genetic factors influencing glucose metabolism among Indian Asians. RESEARCH DESIGN AND METHODS: We carried out genome-wide association studies for fasting glucose in 5,089 nondiabetic Indian Asians genotyped with the Illumina Hap610 BeadChip and 2,385 Indian Asians (698 with type 2 diabetes) genotyped with the Illumina 300 BeadChip. Results were compared with findings in 4,462 European Caucasians. RESULTS: We identified three single nucleotide polymorphisms (SNPs) associated with glucose among Indian Asians at P < 5 x 10(-8), all near melatonin receptor MTNR1B. The most closely associated was rs2166706 (combined P = 2.1 x 10(-9)), which is in moderate linkage disequilibrium with rs1387153 (r(2) = 0.60) and rs10830963 (r(2) = 0.45), both previously associated with glucose in European Caucasians. Risk allele frequency and effect sizes for rs2166706 were similar among Indian Asians and European Caucasians: frequency 46.2 versus 45.0%, respectively (P = 0.44); effect 0.05 (95% CI 0.01-0.08) versus 0.05 (0.03-0.07 mmol/l), respectively, higher glucose per allele copy (P = 0.84). SNP rs2166706 was associated with type 2 diabetes in Indian Asians (odds ratio 1.21 [95% CI 1.06-1.38] per copy of risk allele; P = 0.006). SNPs at the GCK, GCKR, and G6PC2 loci were also associated with glucose among Indian Asians. Risk allele frequencies of rs1260326 (GCKR) and rs560887 (G6PC2) were higher among Indian Asians compared with European Caucasians. CONCLUSIONS: Common genetic variation near MTNR1B influences blood glucose and risk of type 2 diabetes in Indian Asians. Genetic variation at the MTNR1B, GCK, GCKR, and G6PC2 loci may contribute to abnormal glucose metabolism and related metabolic disturbances among Indian Asians.
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ItemPathway Analysis of GWAS Provides New Insights into Genetic Susceptibility to 3 Inflammatory Diseases(PUBLIC LIBRARY SCIENCE, 2009-11-30)Although the introduction of genome-wide association studies (GWAS) have greatly increased the number of genes associated with common diseases, only a small proportion of the predicted genetic contribution has so far been elucidated. Studying the cumulative variation of polymorphisms in multiple genes acting in functional pathways may provide a complementary approach to the more common single SNP association approach in understanding genetic determinants of common disease. We developed a novel pathway-based method to assess the combined contribution of multiple genetic variants acting within canonical biological pathways and applied it to data from 14,000 UK individuals with 7 common diseases. We tested inflammatory pathways for association with Crohn's disease (CD), rheumatoid arthritis (RA) and type 1 diabetes (T1D) with 4 non-inflammatory diseases as controls. Using a variable selection algorithm, we identified variants responsible for the pathway association and evaluated their use for disease prediction using a 10 fold cross-validation framework in order to calculate out-of-sample area under the Receiver Operating Curve (AUC). The generalisability of these predictive models was tested on an independent birth cohort from Northern Finland. Multiple canonical inflammatory pathways showed highly significant associations (p 10(-3)-10(-20)) with CD, T1D and RA. Variable selection identified on average a set of 205 SNPs (149 genes) for T1D, 350 SNPs (189 genes) for RA and 493 SNPs (277 genes) for CD. The pattern of polymorphisms at these SNPS were found to be highly predictive of T1D (91% AUC) and RA (85% AUC), and weakly predictive of CD (60% AUC). The predictive ability of the T1D model (without any parameter refitting) had good predictive ability (79% AUC) in the Finnish cohort. Our analysis suggests that genetic contribution to common inflammatory diseases operates through multiple genes interacting in functional pathways.