{"title":"由系数D = pAB - pApB归一化定义的连杆不平衡统计量的数学性质。","authors":"Jonathan T L Kang, Noah A Rosenberg","doi":"10.1159/000504171","DOIUrl":null,"url":null,"abstract":"<p><strong>Background: </strong>Many statistics for measuring linkage disequilibrium (LD) take the form of a normalization of the LD coefficient D. Different normalizations produce statistics with different ranges, interpretations, and arguments favoring their use.</p><p><strong>Methods: </strong>Here, to compare the mathematical properties of these normalizations, we consider 5 of these normalized statistics, describing their upper bounds, the mean values of their maxima over the set of possible allele frequency pairs, and the size of the allele frequency regions accessible given specified values of the statistics.</p><p><strong>Results: </strong>We produce detailed characterizations of these properties for the statistics d and ρ, analogous to computations previously performed for r2. We examine the relationships among the statistics, uncovering conditions under which some of them have close connections.</p><p><strong>Conclusion: </strong>The results contribute insight into LD measurement, particularly the understanding of differences in the features of different LD measures when computed on the same data.</p>","PeriodicalId":13226,"journal":{"name":"Human Heredity","volume":"84 3","pages":"127-143"},"PeriodicalIF":1.1000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1159/000504171","citationCount":"6","resultStr":"{\"title\":\"Mathematical Properties of Linkage Disequilibrium Statistics Defined by Normalization of the Coefficient D = pAB - pApB.\",\"authors\":\"Jonathan T L Kang, Noah A Rosenberg\",\"doi\":\"10.1159/000504171\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><strong>Background: </strong>Many statistics for measuring linkage disequilibrium (LD) take the form of a normalization of the LD coefficient D. Different normalizations produce statistics with different ranges, interpretations, and arguments favoring their use.</p><p><strong>Methods: </strong>Here, to compare the mathematical properties of these normalizations, we consider 5 of these normalized statistics, describing their upper bounds, the mean values of their maxima over the set of possible allele frequency pairs, and the size of the allele frequency regions accessible given specified values of the statistics.</p><p><strong>Results: </strong>We produce detailed characterizations of these properties for the statistics d and ρ, analogous to computations previously performed for r2. We examine the relationships among the statistics, uncovering conditions under which some of them have close connections.</p><p><strong>Conclusion: </strong>The results contribute insight into LD measurement, particularly the understanding of differences in the features of different LD measures when computed on the same data.</p>\",\"PeriodicalId\":13226,\"journal\":{\"name\":\"Human Heredity\",\"volume\":\"84 3\",\"pages\":\"127-143\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1159/000504171\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Human Heredity\",\"FirstCategoryId\":\"99\",\"ListUrlMain\":\"https://doi.org/10.1159/000504171\",\"RegionNum\":4,\"RegionCategory\":\"生物学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2020/2/11 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q4\",\"JCRName\":\"GENETICS & HEREDITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Human Heredity","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1159/000504171","RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2020/2/11 0:00:00","PubModel":"Epub","JCR":"Q4","JCRName":"GENETICS & HEREDITY","Score":null,"Total":0}
Mathematical Properties of Linkage Disequilibrium Statistics Defined by Normalization of the Coefficient D = pAB - pApB.
Background: Many statistics for measuring linkage disequilibrium (LD) take the form of a normalization of the LD coefficient D. Different normalizations produce statistics with different ranges, interpretations, and arguments favoring their use.
Methods: Here, to compare the mathematical properties of these normalizations, we consider 5 of these normalized statistics, describing their upper bounds, the mean values of their maxima over the set of possible allele frequency pairs, and the size of the allele frequency regions accessible given specified values of the statistics.
Results: We produce detailed characterizations of these properties for the statistics d and ρ, analogous to computations previously performed for r2. We examine the relationships among the statistics, uncovering conditions under which some of them have close connections.
Conclusion: The results contribute insight into LD measurement, particularly the understanding of differences in the features of different LD measures when computed on the same data.
期刊介绍：
Gathering original research reports and short communications from all over the world, ''Human Heredity'' is devoted to methodological and applied research on the genetics of human populations, association and linkage analysis, genetic mechanisms of disease, and new methods for statistical genetics, for example, analysis of rare variants and results from next generation sequencing. The value of this information to many branches of medicine is shown by the number of citations the journal receives in fields ranging from immunology and hematology to epidemiology and public health planning, and the fact that at least 50% of all ''Human Heredity'' papers are still cited more than 8 years after publication (according to ISI Journal Citation Reports). Special issues on methodological topics (such as ‘Consanguinity and Genomics’ in 2014; ‘Analyzing Rare Variants in Complex Diseases’ in 2012) or reviews of advances in particular fields (‘Genetic Diversity in European Populations: Evolutionary Evidence and Medical Implications’ in 2014; ‘Genes and the Environment in Obesity’ in 2013) are published every year. Renowned experts in the field are invited to contribute to these special issues.
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