POWRE: Methods for the Analysis of Data with Multiple Levels of Correlation and a Comparison of Several Fundamental Statistical Approaches

我们将开发改进的统计方法，用于分析具有多个相关级别的潜在非高斯数据，当对家庭内兄弟姐妹的重复观察由于对象内或家庭内的相似而相关时，可能会遇到这种情况。我们的第一个目标是通过扩展准最小二乘法(QLS)[Chaganty(1997)，Shults and Chaganty(1998)，Chaganty and Shults(1999)]来满足文献中对多水平相关数据分析的相对直接方法的需求。我们将使用Shults(2000)中讨论的相关模型来实现QLS，该模型是Lefkopolou，Moore和Ryan(1989)提出的结构的推广。我们研究的激励例子包括一项促进纯母乳喂养的国际试验(Morrow，Guerrero，Shults等)。1999年)和宾夕法尼亚大学正在进行的间质性膀胱炎研究(Mazurick，Landis等。我们的下一个目标是探索与使用模式化相关矩阵来模拟结果之间的关联的方法的好处和实施有关的问题。我们将通过考虑几个研究设计，并检查当关联结构被错误指定时的效率损失，来检查未能为我们的数据的关联结构指定适当的模型的影响。尤其值得关注的是，对于具有多个关联级别的数据，忽略一个或多个关联级别的影响。还将进行模拟，以探索错误指定对小样本回归和相关参数估计的均方误差的影响。我们的最终目标是探索QLS的理论基础，并将QLS与伪似然(PL，Carroll和Ruppert，1998)以及统计文献中描述的其他几种基本方法进行比较。然后，我们将描述一个与QLS密切相关的改进的PL方法，并将为我们的数据的相关结构的几个模型探索这种方法的发展。这个POWRE项目由MPS多学科活动办公室(OMA)和数学科学部(DMS)联合支持。

We will develop improved statistical approaches for the analysis of potentially non-Gaussian data with multiple levels of correlation, as might be encountered when repeated observations collected on siblings within families are correlated due to within subject, or within family, similarities. Our first objective is to fulfill the need in the literature for a relatively straightforward approach for analysis of multi-levelcorrelated data by extending the method of quasi-least squares (QLS) [Chaganty (1997), Shults and Chaganty (1998), and Chaganty and Shults (1999)]. We will implement QLS using a correlation model discussed in Shults (2000) that is a generalization of a structure proposed by Lefkopolou, Moore, and Ryan (1989). Motivational examples for our research include an international trial to promote exclusive breast-feeding (Morrow, Guerrero, Shults, et. al., 1999) and an ongoing study of Interstitial Cystitis at the University ofPennsylvania (Mazurick, Landis, et. al., 2000).Our next objective is to explore issues related to the benefits and implementation of approaches that use patterned correlation matrices to model association among outcomes. We will examine the impact of failure to specify an appropriate model for the correlation structure of our data, by considering several study designs and examining the loss of efficiency when the correlation structure has been incorrectly specified. Of particular interest will be the effect of ignoring one or more levels of correlation for data with multiple levels of association. Simulations will also be conducted to explore the effect of misspecification on the mean square error of the estimates of the regression and correlation parameters for small samples. We will then explore the development of improved guidelines for selection of an appropriate correlation structure when several plausible models are available.Our final objective is to explore the theoretical underpinnings of QLS and contrast QLS with pseudo-likelihood (PL, Carroll and Ruppert, 1998) and several other fundamental approaches that have been described in the statistical literature. We will then describe a modified PL approach that is closely related to QLS and will explore the development of this approach for several models for the correlation structure of our data.This POWRE project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).