Multiple testing methods for random fields and high-dimensional dependent data

描述（由申请人提供）：大规模多重检测在使用高通量技术搜索疾病和健康风险标志物方面已经变得无处不在。虽然用于多个测试的统计方法通常假定测试之间是独立的，但许多实际情况显示出依赖性和潜在的结构。在蛋白质组学数据中，空间结构的例子是一维的（1D）；在环境数据的情况下为2D；脑成像数据则是3D的。在分析中忽略相关性可能会导致发现的特征的不同集合和顺序，从而导致错误率增加和潜在的重要特征缺失。有必要描述多重检验中相关性的影响，并将其纳入分析。本提案的目标是开发多种测试方法，将数据中的相关性纳入其中，以提高统计能力，控制错误率并获得适当的可解释结果。这有两种不同的方法。(1)在目标1和目标2中，我们假设空间结构和平稳遍历相关，其中感兴趣的信号由相对少量的单峰组成。我们使用随机场理论计算p值来测试观测数据平滑后的局部最大值的高度。我们从一维到三维域，从等宽峰到不等宽峰的复杂度来发展这些方法。然后，我们将这些方法应用于高通量技术获得的各种类型的数据，特别是：用于识别癌症蛋白质生物标志物的质谱数据；用于识别因气候变化而面临热应激风险的地理区域的气候模式输出数据；以及用于识别与异常认知发展有关的解剖区域的脑成像数据。(2)在目标3中，我们假设了一个一般的相关结构，不一定是平稳的或遍历的，并提出了一个条件边际分析，其中通过对观察到的可能为零的情况的边际分布进行条件反射，将相关性纳入其中。虽然不是唯一的，但重点始终放在错误发现率推断上。这一建议提供了一个统一的随机场信号检测的观点，广泛应用于从蛋白质组学到医学成像到环境监测等一系列问题。从统计的角度出发，为随机场中FDR的控制问题提供了一个新的答案。通过利用依赖结构，本文开发的方法在寻找标记时提供了更高的统计能力，从而在后续研究中检测到的错误标记数量较少。

DESCRIPTION (provided by applicant): Large-scale multiple testing has become ubiquitous in the search for disease and health risk markers using high-throughput technologies. While statistical methods for multiple testing often assume independence between the tests, many real situations exhibit dependence and an underlying structure. Examples of spatial structure are one-dimensional (1D) in the case of proteomic data; 2D in the case of environmental data; and 3D in the case of brain imaging data. Ignoring correlation in the analysis may lead to a different set and ordering of discovered features, resulting in increased error rates and potential missing of important features. There is a need to characterize the effect of correlation in multiple testing and incorporate it into the analysis. The goal of this proposal is to develop multiple testing methods that incorporate the correlation in the data in order to increase statistical power, control error rates and obtain appropriately interpretable results. This is done in two different ways. (1) In Aims 1 and 2, we assume a spatial structure and stationary ergodic correlation, where the signal of interest consists of a relatively small number of unimodal peaks. We use random field theory to compute p-values for testing the heights of local maxima of the observed data after smoothing. We develop these methods in complexity from 1D to 3D domains, and from peaks of equal width to peaks of unequal width. We then adapt and apply these methods to various types of data obtained from high-throughput technologies, specifically: mass- spectrometry data for identifying protein biomarkers of cancer; climate model output data for identification of geographical regions at risk for heat stress as a result of climate change; and brain imaging data for identification of anatomical regions involved in abnormal cognitive development. (2) In Aim 3, we assume a general correlation structure, not necessarily stationary or ergodic, and propose a conditional marginal analysis, where correlation is incorporated through conditioning on the observed marginal distribution of likely null cases. Although not exclusively, emphasis throughout is placed on false discovery rate inference. This proposal provides a unified view of signal detection for random fields that applies broadly to a large class of problems ranging from proteomics to medical imaging to environmental monitoring. From a statistical point of view, it provides a new answer to the problem of controlling FDR in random fields. By taking advantage of the dependence structure, the methods developed in this proposal offer higher statistical power in the search for markers, so that a smaller number of false markers will be tested in follow-up studies.