COVARIANCE ESTIMATION FOR LONGITUDINAL CANCER DATA

描述(申请人摘要)：在统计建模中的协方差 结构通常被认为是一种麻烦，或者至少是次要的。 中庸之道。然而，当分析的目标包括估计 特定于对象的效应或预测、协方差结构的估计 是非常重要的。该项目将制定改进的方法学 纵向癌症研究中协方差结构的估计。这将是 结果提高了固定和随机影响的估计效率，例如 作为特定于受试者的轨迹和预测。具体地说，这个项目 将开发协方差矩阵的估计器，该估计器对各种 特征结构和/或结构假设，开发计算这些的方法 分层模型中的估计器，并开发要说明的模型类别 协方差中的异质性，既可以用协变量解释，也可以用协变量解释 纵向试验中受试者的结构。总而言之，这将提供 更高的建模灵活性，以及更高的推理效率， 纵向癌症数据。 这些方法包括开发合理的先验分布，根据先验分布 可以推导出在小样本和/或在 高维和分层模型的构建以说明 通过协变量和/或在受试者之间形成异质协方差结构 先前的分发。共同的主题将是sh6nk之前的发行版。 协方差矩阵或函数指向某个参数形式或某个参数形式 ‘Average’矩阵或函数，其收缩程度由 数据。计算高效的方法来计算估计量和拟合出 我们将探索一些模型，其中一些模型将仅涉及对 标准软件。

DESCRIPTION (Applicant's abstract): In statistical modeling the covariance structure is often considered a nuisance, or at least of secondary importance to the mean. However, when the goals of an analysis include estimation of subject-specific effects or prediction, estimation of the covariance structure is very important. This project will develop methodology for improving estimation of covariance structure in longitudinal cancer studies. This will result in increased efficiency in estimation of fixed and random effects, such as subject-specific trajectories, and predictions. Specifically, this project will develop estimators of covariance matrices that are robust to a variety of eigenstructures and/or structural assumptions, develop methods to compute these estimators in hierarchical models, and develop classes of models to account for heterogeneity, both explained and unexplained by covariates, in covariance structures across subjects in longitudinal trials. In sum, this will provide greater flexibility in modeling, and efficiency in making inferences from, longitudinal cancer data. The methods include development of sensible prior distribution from which estimators can be derived that have good properties in small samples and/or in high dimensions and construction of hierarchical models to account for heterogeneous covariance structures across subjects through covariates and/or prior distributions. The common theme will be prior distributions which sh6nk the cova6ance matrix or function toward some parametric form or to some 'average' matrix or function, with the amount of shrinkage determined by the data. Computationally efficient ways to compute the estimators and fit the models will be explored, some of which will involve only minor modifications to standard software.