全基因组关联分析中混合模型的原理、优化与应用

doi:10.3864/j.issn.0578-1752.2023.09.001

Abstract

Abstract:

Genome-wide association study (GWAS) is an effective method to locate genomic loci that are significantly associated with traits. With the accumulated phenotypic data, the continuous development of high-throughput genotyping technology, and the improved statistical methods, it promotes the wide application of GWAS in area of human disease and animal and plant genetics. False positives are one of the important concerns that impair the reliability of genome-wide association results. To control the false positives, in addition to correcting the P-values, GWAS models have been continuously improved from the naive methods like ANOVA (for quantitative trait) or Chi-square test (for quality trait), to general linear model (GLM), which incorporates fixed-effect covariates, to the mixed linear model (MLM), which incorporates random effects. Fitting individual genetic effects into random effects defined by the genomic relationships matrix (GRM) is commonly adapted currently. Since the parameter estimation of MLM consumes a lot of computational resources, researchers have tried to optimize solving models and constructing GRM (which also improves computing efficiency), and the time complexity gradually decreased from O(MN³) to O(MN) for MLM-based methods, achieving a great leap in computational speed and statistical efficacy. For inflations caused by unbalanced case-control data, researchers further correct the generalized mixed linear model (GLMM). This paper comprehensively introduces the basic principles and development of GWAS, with specific emphasis on the model improvement and optimization details. We also list the applications of MLM in GWAS in agriculture, including progress on animals, plants and microbes, as well as the application of haplotype in GWAS. Finally, we give prospects on the future developments of GWAS from the viewpoints of further model optimization and experimental design.

Key words: genome-wide association study, complex traits, random effects, genomic relationships matrix, mixed linear model

TAN LiZhi, ZHAO YiQiang. Principle, Optimization and Application of Mixed Models in Genome- Wide Association Study[J].Scientia Agricultura Sinica, 2023, 56(9): 1617-1632.

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Figures/Tables 4

Fig. 1

Table 1

Optimization model of MLM in GWAS"

计算模型 Computational model	功能与方法要点 Methodological highlights	计算速度 Computational speed	发表时间 Publication time	参考文献 Reference	来源网站 Resource
EMMA	似然估计的优化对象为遗传方差和残差方差之比 Optimize the ratio of genetic variance to residual variance in ML or REML	慢 Low	2008	[18]	https://tassel.bitbucket.io
CMLM	对个体间的亲缘关系进行聚类，通过用组的相似性替代个体的相似性，提高计算速度同时提高检测功效 Cluster the kinship among individuals, replace individual similarity with group similarity to improve both computing speed and statistical power	中 Intermediate	2010	[20]	https://tassel.bitbucket.io
EMMAX	单次估计随机效应方差，转化混合线性模型为普通线性模型 Single estimation of variance of random effects, transform mixed linear model into an ordinary linear model	中 Intermediate	2010	[19]	https://csg.sph.umich.edu/kang/emmax
FaST-LMM	通过对随机效应矩阵的特征分解去掉相关性，将混合线性模型转化为包括目标标记效应的普通线性模型 Transform mixed linear model into an ordinary linear model with by performing spectral decomposition of the random effects matrix to remove correlations	中/快（n<m） Intermediate/fast (n<m)	2011	[5]	https://github.com/fastlmm/FaST-LMM
GEMMA	通过优化矩阵运算和迭代算法，加速标记效应的精确估计 Accelerate the exact estimation of marker effects by optimizing algorithms of matrix operations and iterative algorithm	中 Intermediate	2012	[24]	https://www.xzlab.org/software.html
GRAMMAR -Gamma	对表型残差和GRAMMAR-Gamma因子进行估计并优化。对表型残差和基因型之间的关联进行得分检验并校正统计量 Estimate and optimize phenotypic residuals and GRAMMAR-Gamma factors. Implement score-based association test and corrections for the statistic	快 Fast	2012	[23]	https://github.com/GenABEL-Project
MLMM	将多个相关标记作为固定效应拟合到MLM中，以逐步回归的方式压缩由随机效应解释的方差，实现随机效应的消除 Include significant markers in the MLM as fixed covariates, splitting the variance explained by random effects by forward-backward stepwise approach to eliminate random effects	中 Intermediate	2012	[28]	https://github.com/timflutre/mlmm.gwas
SUPER	使用区间内最显著的标记并剔除与待测标记连锁的标记后，对剩余标记构建性状特异的亲缘矩阵 Use the most significant markers to represent each bin and exclude markers that are in LD to the testing markers, construct a complementary trait specific kinship with remaining markers.	中 Intermediate	2014	[26]	https://www.zzlab.net
BOLT-LMM	计算近似表型残差，使用贝叶斯模型与经典关联方法结合的回顾性得分统计量检验残差与检测标记间的关联 Compute approximate phenotypic residuals and tests the residuals for association with candidate markers via a retrospective score statistic that integrate Bayesian modeling and frequentist association testing	很快 Very fast	2015	[6]	https://alkesgroup.broadinstitute.org/BOLT-LMM
FarmCPU	独立随机效应模型筛选位点，独立的固定效应验证位点，两者交替使用直到没有新的候选标记进入到模型中 Markers are estimated by REM and tested by FEM independently, and both methods are used iteratively until no change on new candidate markers	快 Fast	2016	[14]	https://www.zzlab.net/FarmCPU
BLINK	使用贝叶斯信息标准替代随机效应中的REML估计，使用LD信息挑选候选位点，不再使用混合线性模型 Replace REML with BIC in estimating random effects and select candidate markers by LD, the mixed linear model is no longer used	快 Fast	2018	[29]	https://www.zzlab.net/blink
FastGWA	基于亲缘关系矩阵稀疏化和网格搜索的REML算法的计算优化 Computational optimization of REML algorithm based on sparse GRM and grid search	极快 Extremely fast	2019	[7]	https://yanglab.westlake.edu.cn/software/

Table 1

Fig. 2

Table 2

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Principle, Optimization and Application of Mixed Models in Genome- Wide Association Study

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计算模型 Computational model	功能与方法要点 Methodological highlights	计算速度 Computational speed	发表时间 Publication time	参考文献 Reference	来源网站 Resource
GMMAT	使用PQL与AI-REML对零模型进行参数估计，保留参数并使用得分检验所有标记 Use PQL and AI-REML to estimate parameters of null model, retaining parameters to perform the score test for all markers	中 Intermediate	2016	[32]	https://www.hsph.harvard.edu/xlin/software.html#gmmat
SAIGE	PCG代替矩阵特征分解，使用SPA解决病例对照比失衡 Replace matrix Eigen decomposition with PCG and use SPA to calibrate unbalanced case-control ratio	很快 Very fast	2018	[33]	https://github.com/weizhouUMICH/SAIGE/
FastGWA- GLMM	基于亲缘关系矩阵稀疏化和网格搜索的REML算法的计算优化 Computational optimization of REML algorithm based on sparse GRM and grid search	极快 Extremely fast	2021	[34]	https://yanglab.westlake.edu.cn/software/gcta/
POLMM	可分析有序分类变量,使用PCG或稀疏矩阵加速矩阵运算，通过SPA校准P值 Analyze ordinal categorical data, use PCG or sparse GRM to accelerate matrix operations and P-values adjusted by SPA	很快 Very fast	2021	[35]	https://github.com/WenjianBI/POLMM

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