COVARIANCE ESTIMATION FOR LONGITUDINAL CANCER DATA

描述（申请人摘要）：在统计建模中，协方差 建筑物通常被认为是一种讨厌的东西，或者至少是次要的 平均值。然而，当分析的目标包括估计 受试者特异性效应或预测，协方差结构的估计 是非常重要的.该项目将制定方法， 纵向癌症研究中协方差结构的估计。这将 提高了估计固定和随机效应的效率， 作为特定对象的轨迹和预测。具体来说，这个项目 将开发协方差矩阵的估计量，这些估计量对各种 特征结构和/或结构假设，开发方法来计算这些 层次模型中的估计量，并开发模型类来解释 协方差中的异质性（由协变量解释和未解释） 在纵向试验中跨学科的结构。总之，这将提供 更大的建模灵活性，以及进行推断的效率， 纵向癌症数据。 这些方法包括开发合理的先验分布， 可以导出在小样本和/或 更高的维度和层次模型的构建， 受试者之间协变量的异质协方差结构和/或 先验分布共同的主题将是先验分布， 协方差矩阵或函数朝向某个参数形式或朝向某个 “平均”矩阵或函数，收缩量由 数据计算有效的方法来计算估计量和拟合 将探索模型，其中一些模型仅涉及微小的修改， 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.