Center for Statistical Genetics, The Pennsylvania State University, Hershey, PA 17033, U.S.A.
Stat Med. 2013 Feb 10;32(3):509-23. doi: 10.1002/sim.5535. Epub 2012 Aug 17.
Many phenomena of fundamental importance to biology and biomedicine arise as a dynamic curve, such as organ growth and HIV dynamics. The genetic mapping of these traits is challenged by longitudinal variables measured at irregular and possibly subject-specific time points, in which case nonnegative definiteness of the estimated covariance matrix needs to be guaranteed. We present a semiparametric approach for genetic mapping within the mixture-model setting by jointly modeling mean and covariance structures for irregular longitudinal data. Penalized spline is used to model the mean functions of individual quantitative trait locus (QTL) genotypes as latent variables, whereas an extended generalized linear model is used to approximate the covariance matrix. The parameters for modeling the mean-covariances are estimated by MCMC, using the Gibbs sampler and the Metropolis-Hastings algorithm. We derive the full conditional distributions for the mean and covariance parameters and compute Bayes factors to test the hypothesis about the existence of significant QTLs. We used the model to screen the existence of specific QTLs for age-specific change of body mass index with a sparse longitudinal data set. The new model provides powerful means for broadening the application of genetic mapping to reveal the genetic control of dynamic traits.
许多对生物学和生物医学至关重要的现象都是以动态曲线的形式出现的，例如器官生长和 HIV 动力学。这些特征的遗传定位受到在不规则且可能特定于个体的时间点测量的纵向变量的挑战，在这种情况下，需要保证估计协方差矩阵的非负定。我们提出了一种在混合模型设置中进行遗传映射的半参数方法，通过联合建模不规则纵向数据的均值和协方差结构来实现。惩罚样条用于将个体数量性状基因座 (QTL) 基因型的均值函数建模为潜在变量，而扩展的广义线性模型用于逼近协方差矩阵。使用 MCMC 通过 Gibbs 采样器和 Metropolis-Hastings 算法估计用于建模均值协方差的参数。我们推导了均值和协方差参数的完整条件分布，并计算了贝叶斯因子来检验关于存在显著 QTL 的假设。我们使用该模型筛选了稀疏纵向数据集体重指数随年龄变化的特定 QTL 的存在。该新模型为拓宽遗传映射的应用以揭示动态特征的遗传控制提供了有力的手段。
