Often NIEHS scientists are interested in studying the effect of a chemical on a tissue or a cell or a gene expression, etc. Accordingly, they conduct suitable dose-response or time-course experiments. Based on the available scientific knowledge, a researcher may hypothesize certain patterns of mean response with respect to dose and/or time. In some instances a researcher may also be interested in detecting the lowest dose or time point at which a significant effect is seen. For example, the National Toxicology Program (NTP) routinely conducts dose-response studies to investigate the carcinogenic and toxic effects of various chemicals. Using the responses obtained at each dose, the researchers are interested in determining if tumor incidence increases with dose. Similarly, researchers in the National Center for Toxicogenomics (NCT) and in the NTP are also interested in understanding the changes in gene expression in a tissue or cell line when an animal or a cell line is exposed to a compound at various doses and for various duration of times. Accordingly, a variety of dose-response and time-course microarray experiments are conducted to understand the gene expression profiles over duration of exposure and/or dose of exposure. Usually, the null hypothesis is a flat response and one can express the alternative hypotheses using mathematical inequalities, known as order restrictions, between the unknown parameters of interest. Order restrictions can often be expressed using a graph where each unknown parameter is denoted by a circle, and the inequality, between two unknown parameters, is denoted by an arrow that points towards the larger parameter. Order-restricted statistical inference refers to statistical procedures that take into consideration the order restrictions on the parameter space. In this research program we are developing statistical procedures that can be useful for analyzing data, routinely generated by NIEHS researchers, with the above feature. The new procedures are generally more sensitive than some of the commonly used statistical procedures.
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