Rank tests for clustered data with potentially informative cluster size: Novel st

描述（由申请人提供）：本提案的总体目标是，当聚类大小具有潜在的信息量时，为聚类数据开发适当的基于秩的测试，并使用现有的牙科数据库资源，特别是从皮埃蒙特65 +牙科研究和爱奥华氟化物研究中获得的资源，应用结果方法进行各种边缘比较（例如，治疗前后牙齿的平均状况）。当集群中的单元数量是非恒定/随机的，并且与感兴趣的结果相关时，信息集群大小就会出现。在牙科数据的上下文中，属于一个个体的所有牙齿将形成一个簇。由于牙齿脱落（成人）与我们计划研究的两种疾病相关，即牙周病和龋齿，因此我们在Piedmont数据集中具有潜在的信息聚类大小。这是一个方法上的挑战，使经典的等级检验适应这种情况。例如，即使通过适当的方差估计调整聚类依赖性，两样本Wilcoxon秩和检验也难以在信息聚类下保持正确的大小/显著性水平。本提案的目标是开发适当的基于秩的测试（以及相关的R估计器）类别，并研究它们在具有信息聚类大小的聚类依赖下适应边缘推理的三个经典问题的统计性质。这些是所谓的单样本定位问题（目标1），回归问题（目标2）和关联问题（目标3）。在这些问题中，我们将使用在信息簇大小场景下保持适当渐近大小的一般分数函数获得一类检验统计量。我们还将研究边际参数的相关R估计的性质。前两个问题的多元扩展也将被考虑（目标4）。拟议研究的另一个重要组成部分将是扩展这些程序来处理缺失数据，其中缺失机制可以使用可观察协变量建模（目标5）。最后，当聚类大小不具有信息性时，就像爱荷华研究中只包含儿童的情况一样，我们将能够通过在我们的测试统计构建中纳入聚类特定权重来提高我们的测试的能力（目标6）。

DESCRIPTION (provided by applicant): The overall goal of this proposal is to develop appropriate rank based tests for clustered data when the cluster size is potentially informative and apply the resulting methods for various marginal comparisons (e.g., average condition of teeth before and after treatment) using existing dental database resources, specifically as obtained from the Piedmont 65 + Dental Study and Iowa Fluoride Study. Informative cluster size arises when the number of units in a cluster is non-constant/random and in correlation with the outcome of interest. In the context of dental data, all teeth belonging to an individual will form a cluster. Since tooth loss (in adult) is correlated with two of the diseases we are planning to study, namely, periodontal disease and dental caries, we have potentially informative cluster sizes in the Piedmont data sets. It is a methodological challenge to adapt a classical rank test to such situations. As for example, the two sample Wilcoxon rank sum test has difficulty maintaining the correct size/significance level under informative clustering even if it is adjusted for cluster dependence through appropriate variance estimate. This proposal has a goal of developing proper classes of rank based tests (and related R estimators) and studying their statistical properties for three classical problems adapted to marginal inference under cluster dependence with informative cluster size. These are the so called one sample location problem (Aim 1), the regression problem (Aim 2) and the association problem (Aim 3). In each of these problems, we will obtain a class of test statistics using general score functions that maintain proper asymptotic size under the informative cluster size scenario. We will also study the properties of the related R estimates of marginal parameters. Multivariate extensions of the first two problems will also be considered (Aim 4). Another signification component of the proposed research will be to extend these procedures to handle missing data where the missingness mechanism can be modeled using observable covariates (Aim 5). Finally, when the cluster size is not informative, as in the case of Iowa Study which comprises of children only, we will be able to increase the power of our tests by incorporating cluster specific weights in the construction of our test statistics (Aim 6).