Order restricted statistical inference and its applications

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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.