Statistical Theory and Methodology with Applications to

NIEHS的科学家通常对研究一种化学物质对组织或细胞或基因表达的影响等感兴趣。因此，他们进行了适当的剂量反应或时间过程实验。基于现有的科学知识，研究人员可以假设关于剂量和/或时间的某些平均反应模式。在某些情况下，研究人员可能还会对检测出现显著效果的最低剂量或时间点感兴趣。通常，零假设是平坦的响应，并且人们可以使用数学上的不等式来表示可选的假设，这种数学不等式被称为顺序限制，在感兴趣的未知参数之间。顺序限制通常可以用一个图来表示，其中每个未知参数用圆圈表示，而两个未知参数之间的不等性用指向较大参数的箭头表示。序受限统计推断是指考虑参数空间上的序约束的统计过程。 国家毒理学计划(NTP)定期进行剂量反应研究，以调查各种化学物质的致癌和毒性效应。利用在每种剂量下获得的反应，研究人员有兴趣确定肿瘤发病率是否随着剂量的增加而增加。 作为另一个例子，在为期90天的慢性毒性前期研究中，NTP收集了关于每种动物的各种变量的数据。对于每个剂量组，NTP感兴趣的是检测与对照组相比，剂量组的平均反应是否增加(或减少)，但对剂量之间的关系没有事先的期望。 在这个研究计划中，我们正在开发统计程序，这些程序可以用于分析具有上述特征的数据，这些数据通常由研究人员生成。新的程序通常比一些常用的统计程序更敏感。我们正在应用新的程序来分析NIEHS的研究人员获得的一些数据。

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.