Order restricted statistical inference and its applications

当你去药房配药时，你有没有想过药物的剂量是否适合你？剂量会不会太低，以至于药物不起作用？剂量会不会太高，可能会引起一些副作用？你有没有想过加拿大卫生部是如何决定批准或拒绝一种新药的？在这项研究中，这些问题中的一些可以通过剂量反应和毒性研究来回答。例如，剂量反应研究在第二阶段和第三阶段临床试验中是有用的，以评估药物的疗效和毒性，以确定其有效和安全的范围。零剂量通常包括作为对照，与较高剂量进行比较。这自然会导致多重比较。剂量的有序性质表明使用逐步程序和利用这种排序信息来提高统计程序的效率。由于医学、毒理学、工程学和经济学等领域的问题，有序限制下的统计推断一直是一个非常活跃的研究领域。在这个研究方案中，我们将利用在剂量-反应和毒性研究中自然产生的不同类型的预先排序信息以及定量生物测定来开发几种简单而有效的方法。

When you go to the pharmacy and fill a prescription up, have you ever wondered if the dose of the drug is right for you? Can the dose be too low so that the drug will not work? Can the dose be too high that it may cause some side effects? Have you ever thought about how Health Canada makes a decision to approve or to reject a new drug? Some of these questions can be answered by dose-response and toxicity studies in this research. For example, dose-response studies are useful in Phase II and Phase III clinical trials to evaluate efficacy and toxicity of a drug in order to determine its effective and safe ranges. A zero dose is generally included as a control against which higher doses are compared. This naturally leads to multiple comparisons. The ordered nature of doses suggests the use of stepwise procedures and the utilization of such ordering information to increase the efficiency of statistical procedures. Statistical inference under order restrictions has been a very active area of research motivated by problems in areas such as medicine, toxicology, engineering and economics. In this research proposal we will develop several simple and effective methods by utilizing different types of prior ordering information which arise naturally in dose-response and toxicity studies, and quantal bioassay.