Statistical Methods with Applications to Toxicology and Microarray data

以下是过去一年中该研究项目取得的成果： 研究人员经常收集多元二进制响应数据来比较自然有序的实验条件。 有序实验条件的一些实例包括剂量-反应研究中的剂量、临床肿瘤学中的癌症阶段和时程实验中的时间点。 例如，国家毒理学计划定期进行剂量反应研究，以评估化学品的毒性和致癌性。 通常，对于研究中每只动物的每个器官，他们记录肿瘤的存在和不存在。因此，在每只动物上，他们获得了多变量二元响应向量，其中一些组分是潜在依赖的。 例如，已知乳腺肿瘤和脑垂体肿瘤是相关的。 在这种情况下，忽略底层依赖结构并一次分析一个二进制响应的统计方法可能会被低估。 在这个研究项目中，我们正在开发多变量统计方法，在比较实验条件时考虑到潜在的依赖结构。 具体来说，我们正在开发的方法，用于测试有序的实验条件之间的多元随机秩序。 新方法不仅比现有的一些方法更强大，而且还提供了生物学上可解释的结果。 越来越多的研究人员对比较两个或更多实验条件之间的大量变量感兴趣。 例如，毒理学家可能对比较正常组织和肿瘤组织之间数千个基因的表达感兴趣，这导致进行数千次统计测试（称为多重测试）。 进行多重检测时的一个主要问题是控制总体假阳性率。 通常情况下，所有原假设中真原假设的比例是一个未知参数，它在开发多个测试问题的统计测试时起着重要作用。 在文献中已经提出了自适应程序（Hochberg和Benjamini（1990）），其估计真空的比例，并使用这些估计来导出强大的多重测试程序。到目前为止，还没有一个数学证明来证明这些程序控制一般的家庭错误率（FWER）。 在这个项目中，我们引入了新的自适应霍尔姆和Hochberg程序，并证明了他们控制下的正回归依赖的FWER。

Here are a sample of results obtained in this research program during the past year: Researchers often collect multivariate binary response data to compare naturally ordered experimental conditions. Some examples of ordered experimental conditions include doses in a dose-response study, cancer stages in clinical oncology, and time points in a time-course experiment. For example, the National Toxicology Program routinely conducts dose response studies to evaluate toxicity and carcinogenicity of chemicals. Typically, for each organ within each animal in the study, they record the presence and absence of tumor. Thus on each animal they obtain multivariate binary response vector where some of the components are potentially dependent. For example, mammary gland and pituitary gland tumors are known to be correlated. In such situations statistical methods that ignore the underlying dependence structure, and analyze one binary response at a time, can potentially be underpowered. In this research program we are developing multivariate statistical methods that take into account the underlying dependence structure when comparing experimental conditions. Specifically, we are developing methods for testing multivariate stochastic order among ordered experimental conditions. The new methods are not only more powerful than some of the existing methods, but they also provide biologically interpretable results. Increasingly researchers are interested in comparing a large number of variables between two or more experimental conditions. For example, a toxicologist may be interested in comparing the expressions of several thousands of genes between a normal and a tumor tissue, which results in performing thousands of statistical tests (known as multiple testing). A major concern when performing multiple tests is the control of overall false positive rate. Typically, the proportion of true null hypotheses among all null hypotheses is an unknown parameter and it plays an important role when developing statistical tests for multiple testing problems. Adaptive procedures have been proposed in the literature (Hochberg and Benjamini (1990)) that estimate the proportion of true nulls and use those estimates to derive powerful multiple testing procedures. Until now there did not exist a mathematical proof to demonstrate that these procedures control the familywise error rate (FWER) in general. In this project we introduced new adaptive Holm and Hochberg procedures and prove that they control the FWER under positive regression dependence.