由系数\(D = pAB - pApB\)归一化定义的连锁不平衡统计量的数学性质。
Mathematical Properties of Linkage Disequilibrium Statistics Defined by Normalization of the Coefficient D = pAB - pApB.
作者信息
Kang Jonathan T L, Rosenberg Noah A
机构信息
Department of Biology, Stanford University, Stanford, California, USA,
Department of Biology, Stanford University, Stanford, California, USA.
出版信息
Hum Hered. 2019;84(3):127-143. doi: 10.1159/000504171. Epub 2020 Feb 11.
Abstract
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.
摘要
背景
许多用于测量连锁不平衡（LD）的统计量采用LD系数D的归一化形式。不同的归一化产生具有不同范围、解释以及支持其使用的论据的统计量。
方法
在此，为了比较这些归一化的数学性质，我们考虑其中5个归一化统计量，描述它们的上界、在可能的等位基因频率对集合上其最大值的均值，以及给定统计量特定值时可及的等位基因频率区域的大小。
结果
我们给出了统计量d和ρ这些性质的详细特征描述，类似于之前对r2所进行的计算。我们研究了这些统计量之间的关系，揭示了其中一些统计量具有紧密联系的条件。
结论
这些结果有助于深入了解LD测量，特别是在对相同数据进行计算时，对不同LD测量特征差异的理解。
相似文献
1
Mathematical Properties of Linkage Disequilibrium Statistics Defined by Normalization of the Coefficient D = pAB - pApB.由系数\(D = pAB - pApB\)归一化定义的连锁不平衡统计量的数学性质。
Hum Hered. 2019;84(3):127-143. doi: 10.1159/000504171. Epub 2020 Feb 11.
2
Bounds and normalization of the composite linkage disequilibrium coefficient.复合连锁不平衡系数的界限与归一化
Genet Epidemiol. 2004 Nov;27(3):252-7. doi: 10.1002/gepi.20015.
3
Mathematical properties of the r2 measure of linkage disequilibrium.连锁不平衡r2测量的数学性质。
Theor Popul Biol. 2008 Aug;74(1):130-7. doi: 10.1016/j.tpb.2008.05.006. Epub 2008 Jun 1.
4
The nonlinear structure of linkage disequilibrium.连锁不平衡的非线性结构。
Theor Popul Biol. 2020 Aug;134:160-170. doi: 10.1016/j.tpb.2020.02.005. Epub 2020 Mar 25.
5
The D' measure of overall gametic disequilibrium between pairs of multiallelic loci.多等位基因座对之间总体配子不平衡的D'度量。
Evolution. 2000 Oct;54(5):1809-12.
6
Linkage detection adaptive to linkage disequilibrium: the disequilibrium maximum-likelihood-binomial test for affected-sibship data.适应连锁不平衡的连锁检测：用于患病同胞对数据的不平衡最大似然二项式检验
Am J Hum Genet. 1999 Dec;65(6):1741-59. doi: 10.1086/302659.
7
Bias of allele-sharing linkage statistics in the presence of intermarker linkage disequilibrium.存在标记间连锁不平衡时等位基因共享连锁统计的偏倚。
BMC Genet. 2005 Dec 30;6 Suppl 1(Suppl 1):S82. doi: 10.1186/1471-2156-6-S1-S82.
8
On the uses and applications of the most commonly used measures of linkage disequilibrium from the comparative analysis of their statistical properties.基于连锁不平衡最常用测度统计特性的比较分析，探讨其用途与应用。
Hum Hered. 2011;71(3):186-95. doi: 10.1159/000327732. Epub 2011 Jul 20.
9
Linkage disequilibrium inflates type I error rates in multipoint linkage analysis when parental genotypes are missing.当亲本基因型缺失时，连锁不平衡会在多点连锁分析中夸大I型错误率。
Hum Hered. 2005;59(4):220-7. doi: 10.1159/000087122. Epub 2005 Jul 26.
10
LDpop: an interactive online tool to calculate and visualize geographic LD patterns.LDpop：一个交互式在线工具，用于计算和可视化地理 LD 模式。
BMC Bioinformatics. 2020 Jan 10;21(1):14. doi: 10.1186/s12859-020-3340-1.
引用本文的文献
1
Accounting for population structure and data quality in demographic inference with linkage disequilibrium methods.在使用连锁不平衡方法进行人口统计学推断时考虑人口结构和数据质量。
Nat Commun. 2025 Jul 1;16(1):6054. doi: 10.1038/s41467-025-61378-w.
2
Mathematical bounds on r and the effect size in case-control genome-wide association studies.病例对照全基因组关联研究中r和效应大小的数学界限。
Theor Popul Biol. 2025 Aug;164:1-11. doi: 10.1016/j.tpb.2025.04.003. Epub 2025 May 15.
3
Are you with me? Co-occurrence tests from community ecology can identify positive and negative epistasis between inversions in Mimulus guttatus.你明白我的意思吗？来自群落生态学的共现测试可以识别出沟酸浆属植物中倒位之间的正上位性和负上位性。
PLoS One. 2025 Apr 28;20(4):e0321253. doi: 10.1371/journal.pone.0321253. eCollection 2025.
4
Mathematical bounds on and the effect size in case-control genome-wide association studies.病例对照全基因组关联研究中 的数学界限及效应大小
bioRxiv. 2024 Dec 17:2024.12.17.628943. doi: 10.1101/2024.12.17.628943.
5
Intragenomic conflicts with plasmids and chromosomal mobile genetic elements drive the evolution of natural transformation within species.基因组内冲突与质粒和染色体移动遗传元件共同推动了物种内自然转化的进化。
PLoS Biol. 2024 Oct 14;22(10):e3002814. doi: 10.1371/journal.pbio.3002814. eCollection 2024 Oct.
6
Single Nucleotide Polymorphisms of CYP3A4 and CYP3A5 in Romanian Kidney Transplant Recipients: Effect on Tacrolimus Pharmacokinetics in a Single-Center Experience.罗马尼亚肾移植受者中CYP3A4和CYP3A5的单核苷酸多态性：单中心经验中其对他克莫司药代动力学的影响
J Clin Med. 2024 Mar 28;13(7):1968. doi: 10.3390/jcm13071968.
7
Genome-Wide SNP and Indel Discovery in Abaca ( Née) and among Other spp. for Abaca Genetic Resources Management.用于麻蕉遗传资源管理的麻蕉（Née）及其他物种全基因组单核苷酸多态性和插入缺失发现
Curr Issues Mol Biol. 2023 Jul 12;45(7):5776-5797. doi: 10.3390/cimb45070365.
8
Genetics of SLE: does this explain susceptibility and severity across racial groups?SLE 的遗传学：这是否可以解释不同种族人群的易感性和严重程度？
Rheumatology (Oxford). 2023 Mar 29;62(Suppl 1):i15-i21. doi: 10.1093/rheumatology/keac695.
9
Linkage disequilibrium between rare mutations.稀有突变之间的连锁不平衡。
Genetics. 2022 Apr 4;220(4). doi: 10.1093/genetics/iyac004.
本文引用的文献
1
Mathematical Constraints on : Biallelic Markers in Arbitrarily Many Populations.任意多个群体中双等位基因标记的数学约束条件
Genetics. 2017 Jul;206(3):1581-1600. doi: 10.1534/genetics.116.199141. Epub 2017 May 5.
2
The impact of rare and low-frequency genetic variants in common disease.罕见和低频基因变异在常见疾病中的影响。
Genome Biol. 2017 Apr 27;18(1):77. doi: 10.1186/s13059-017-1212-4.
3
Are rare variants really independent?罕见变异真的是独立的吗？
Genet Epidemiol. 2017 May;41(4):363-371. doi: 10.1002/gepi.22039. Epub 2017 Mar 16.
4
Modeling Linkage Disequilibrium Increases Accuracy of Polygenic Risk Scores.连锁不平衡建模提高了多基因风险评分的准确性。
Am J Hum Genet. 2015 Oct 1;97(4):576-92. doi: 10.1016/j.ajhg.2015.09.001.
5
Rare variant association studies: considerations, challenges and opportunities.罕见变异关联研究：考量、挑战与机遇
Genome Med. 2015 Feb 23;7(1):16. doi: 10.1186/s13073-015-0138-2. eCollection 2015.
6
Linkage disequilibrium network analysis (LDna) gives a global view of chromosomal inversions, local adaptation and geographic structure.连锁不平衡网络分析（LDna）提供了染色体倒位、局部适应性和地理结构的全局视图。
Mol Ecol Resour. 2015 Sep;15(5):1031-45. doi: 10.1111/1755-0998.12369. Epub 2015 Jan 21.
7
Linkage disequilibrium in finite populations.有限群体中的连锁不平衡。
Theor Appl Genet. 1968 Jun;38(6):226-31. doi: 10.1007/BF01245622.
8
Identifying rare variants associated with complex traits via sequencing.通过测序鉴定与复杂性状相关的罕见变异。
Curr Protoc Hum Genet. 2013 Jul;Chapter 1:Unit 1.26. doi: 10.1002/0471142905.hg0126s78.
9
On the uses and applications of the most commonly used measures of linkage disequilibrium from the comparative analysis of their statistical properties.基于连锁不平衡最常用测度统计特性的比较分析，探讨其用途与应用。
Hum Hered. 2011;71(3):186-95. doi: 10.1159/000327732. Epub 2011 Jul 20.
10
The estimator of the optimal measure of allelic association: mean, variance and probability distribution when the sample size tends to infinity.等位基因关联最优度量的估计量：样本量趋于无穷时的均值、方差和概率分布。
Stat Appl Genet Mol Biol. 2008;7(1):Article 20. doi: 10.2202/1544-6115.1370. Epub 2008 Jun 30.
Zotero 插件