Statistical Methods with Applications to Toxicology and Microarray data

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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.