QTL作图的自适应惩罚最大似然方法
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摘要
许多人类疾病和动植物的重要性状都是数量性状,而数量性状大多是由少数的主基因、多数的微效基因及其相互作用所控制。为了对动植物数量性状遗传改良和人类疾病的预防与控制,首先需要检测这些基因及其相互作用。
随着生物技术的进步,海量SNP标记的出现和数量性状的上位性检测,使得遗传模型中变量的个数远大于样本容量,致使常用的QTL定位方法不敷应用。为此,Zhang和Xu(2005)将贝叶斯压缩估计思想与最大似然方法结合,提出了惩罚最大似然方法。由于方法可行性强和运算速度快,得到广泛使用。然而,实际数据分析时发现：该方法检测紧密连锁QTL和微效QTL时功效偏低,且位置和效应的估计值具有一定的偏性。为克服该缺点,本研究在QTL效应估计时引入了偏性矫正系数；为了自动化实现参数估计过程,将偏性矫正系数改进为偏性矫正函数,这称为自适应惩罚最大似然方法。通过Monte Carlo模拟数据(500次重复)、145个大麦DH系粒重数据集和277个玉米自交系开花期数据集验证了新方法。主要研究结果如下：
1、在惩罚函数中引入偏性矫正系数,并将每个QTL效应方差的先验分布由均匀分布改为逆卡方分布,改变了QTL效应及其先验分布方差的估计量。Monte Carlo模拟研究表明：新方法在检测效应相同符号相反两紧密连锁QTL的功效从25%增加到88%；对于小效应QTL检测功效从60%增加到80%；位置与效应估计值标准差变小偏性降低；假阳性率保持较低水平；计算速度较快。通过145个大麦DH群体粒重的QTL定位与交互验证试验证实了新方法的可靠性。
2、为自动化地实现上述参数估计过程,将偏性矫正系数改为偏性矫正分段函数,称为自适应惩罚最大似然方法。Monte Carlo模拟研究表明：QTL检测功效进一步提高,紧密连锁基因的检测功效大约为98%；对于表型方差的贡献率小于1%的QTL检测功效均高于95%；QTL效应的标准差和均方误差进一步减少,假阳性率为1.2%。大麦数据集交互验证试验表明：新方法优于LASSO方法；玉米数据集的分析结果表明：新方法比混合线性模型和压缩混合线性模型两方法的模型适合性更好。
在海量数据分析、上位性检测、新基因挖掘和全基因组标记辅助育种中,新方法提供了新途径。
Most diseases in human and important traits in plants and animals are quantitative traits, controlled by several major genes, many minor genes and their interactions. To improve these important traits in animals and plants and control these diseases in human, the prerequisite for the improvement and control is to detect the above genes and their interactions.
With the rapid development of biological techniques, the applications of large scale SNP markers and the detection of epistasis result in the situation that the number of variables in the genetic model is much larger than sample size. The case makes the traditional QTL mapping methods infeasible. Therefore, Zhang and Xu (2005) incorporated the idea of Bayesian sgrinkage estimation approach into maximum likelihood framework in order to develop penalized maximum likelihood method. The method with simple algorithm and quick speed may be widely adopted. However, lower power in the detection of linked QTL with effects in opposite directions and minor QTL, along with biased estimates for QTL effects and posittions, is observed in real data analysis. To overcome the issues, biasedness correction coefficient for QTL effect is incorporated into the estimation of QTL effect. To carry out the correction automatically, the above coefficient is further changed into a founction about QTL effect. This method is called adaptive penalized maximum likelihood method. A Monte Carlo simulation experiment, along with a Barley kernel weight dataset of145doubled lines and maize flowering time dataset of277inbred lines, was used to validate the proposed methods in this study. The main results were as follows.
1. Biasedness correction coefficients are incorporated into penalized function, and uniform distribution for prior variance of QTL effect is replaced by inverse chi-square prior distribution. Thus, various estimations for QTL effect and its prior variance are obtained in this study. Results from Monte Carlo simulation experiment show that the power is increased from25%to88%in the detection of linked QTL with effects in opposite directions and from60%to80%in the detection of minor QTL; the biasedness and standard deviation of position and effects of QTL are decreased; lower false positive rate and quick speed remain. The proposed approach is validated by mapping QTL for kernel weight in145barley doubled lines and its cross validation experiment.
2. To perform the above method automatically, the above coefficient should be replaced by a function of QTL effect. This method calls adaptive penalized maximum likelihood method. Results from Monte Carlo simulation experiments show that the power for detection of the above QTL is further increased to more than95%; standard deviation and mean squared error of QTL effect is further decreased; and false positive rate is1.2%. Results from cross-validation experiment of145doubled lines in barley show that the new method is better than the LASSO method; and ones from real data analysis of maize dataset show that the new method has better model goodness-of-fit than mixed linear model and compression mixed linear model approaches.
In high-throughout data analysis, epistatic detection, novel gene mining and genome-wide marker assisted selection, new method provides a new approach.
随着生物技术的进步,海量SNP标记的出现和数量性状的上位性检测,使得遗传模型中变量的个数远大于样本容量,致使常用的QTL定位方法不敷应用。为此,Zhang和Xu(2005)将贝叶斯压缩估计思想与最大似然方法结合,提出了惩罚最大似然方法。由于方法可行性强和运算速度快,得到广泛使用。然而,实际数据分析时发现：该方法检测紧密连锁QTL和微效QTL时功效偏低,且位置和效应的估计值具有一定的偏性。为克服该缺点,本研究在QTL效应估计时引入了偏性矫正系数；为了自动化实现参数估计过程,将偏性矫正系数改进为偏性矫正函数,这称为自适应惩罚最大似然方法。通过Monte Carlo模拟数据(500次重复)、145个大麦DH系粒重数据集和277个玉米自交系开花期数据集验证了新方法。主要研究结果如下：
1、在惩罚函数中引入偏性矫正系数,并将每个QTL效应方差的先验分布由均匀分布改为逆卡方分布,改变了QTL效应及其先验分布方差的估计量。Monte Carlo模拟研究表明：新方法在检测效应相同符号相反两紧密连锁QTL的功效从25%增加到88%；对于小效应QTL检测功效从60%增加到80%；位置与效应估计值标准差变小偏性降低；假阳性率保持较低水平；计算速度较快。通过145个大麦DH群体粒重的QTL定位与交互验证试验证实了新方法的可靠性。
2、为自动化地实现上述参数估计过程,将偏性矫正系数改为偏性矫正分段函数,称为自适应惩罚最大似然方法。Monte Carlo模拟研究表明：QTL检测功效进一步提高,紧密连锁基因的检测功效大约为98%；对于表型方差的贡献率小于1%的QTL检测功效均高于95%；QTL效应的标准差和均方误差进一步减少,假阳性率为1.2%。大麦数据集交互验证试验表明：新方法优于LASSO方法；玉米数据集的分析结果表明：新方法比混合线性模型和压缩混合线性模型两方法的模型适合性更好。
在海量数据分析、上位性检测、新基因挖掘和全基因组标记辅助育种中,新方法提供了新途径。
Most diseases in human and important traits in plants and animals are quantitative traits, controlled by several major genes, many minor genes and their interactions. To improve these important traits in animals and plants and control these diseases in human, the prerequisite for the improvement and control is to detect the above genes and their interactions.
With the rapid development of biological techniques, the applications of large scale SNP markers and the detection of epistasis result in the situation that the number of variables in the genetic model is much larger than sample size. The case makes the traditional QTL mapping methods infeasible. Therefore, Zhang and Xu (2005) incorporated the idea of Bayesian sgrinkage estimation approach into maximum likelihood framework in order to develop penalized maximum likelihood method. The method with simple algorithm and quick speed may be widely adopted. However, lower power in the detection of linked QTL with effects in opposite directions and minor QTL, along with biased estimates for QTL effects and posittions, is observed in real data analysis. To overcome the issues, biasedness correction coefficient for QTL effect is incorporated into the estimation of QTL effect. To carry out the correction automatically, the above coefficient is further changed into a founction about QTL effect. This method is called adaptive penalized maximum likelihood method. A Monte Carlo simulation experiment, along with a Barley kernel weight dataset of145doubled lines and maize flowering time dataset of277inbred lines, was used to validate the proposed methods in this study. The main results were as follows.
1. Biasedness correction coefficients are incorporated into penalized function, and uniform distribution for prior variance of QTL effect is replaced by inverse chi-square prior distribution. Thus, various estimations for QTL effect and its prior variance are obtained in this study. Results from Monte Carlo simulation experiment show that the power is increased from25%to88%in the detection of linked QTL with effects in opposite directions and from60%to80%in the detection of minor QTL; the biasedness and standard deviation of position and effects of QTL are decreased; lower false positive rate and quick speed remain. The proposed approach is validated by mapping QTL for kernel weight in145barley doubled lines and its cross validation experiment.
2. To perform the above method automatically, the above coefficient should be replaced by a function of QTL effect. This method calls adaptive penalized maximum likelihood method. Results from Monte Carlo simulation experiments show that the power for detection of the above QTL is further increased to more than95%; standard deviation and mean squared error of QTL effect is further decreased; and false positive rate is1.2%. Results from cross-validation experiment of145doubled lines in barley show that the new method is better than the LASSO method; and ones from real data analysis of maize dataset show that the new method has better model goodness-of-fit than mixed linear model and compression mixed linear model approaches.
In high-throughout data analysis, epistatic detection, novel gene mining and genome-wide marker assisted selection, new method provides a new approach.
引文
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