Statistical Theory and Methodology with Applications to

NIEHS的科学家通常对研究某种化学物质对组织、细胞或基因表达等的影响感兴趣。因此，他们进行适当的剂量反应或时间过程实验。根据现有的科学知识，研究人员可以假设有关剂量和/或时间的某些平均反应模式。在某些情况下，研究人员也可能有兴趣检测出现显著效应的最低剂量或时间点。通常，零假设是一个平坦的响应，人们可以使用数学不等式（称为顺序限制）来表示感兴趣的未知参数之间的替代假设。顺序限制通常可以使用图来表示，其中每个未知参数用圆圈表示，两个未知参数之间的不等式用指向较大参数的箭头表示。次序限制统计推理是指考虑参数空间上的次序限制的统计过程。

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. 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. 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. As another example, in the 90-day pre-chronic toxicity studies, the NTP collects data on a wide range of variables on each animal. For each, the NTP is interested in detecting whether the dose groups have an increased (or decreased) mean response compared to the control group, but there is no prior expectation about the relationships among the doses. In this research program we are developing statistical procedures that can be useful for analyzing data, routinely generated by the researchers are NIEHS, that have the above feature. The new procedures are generally more sensitive than some of the commonly used statistical procedures. We are applying the new procedures for analyzing some of the data obtained by the researchers at NIEHS.