Simultaneous statistical inference under order restrictions and its application to dose-response studies

在毒理学和生物制药研究中，为了研究化合物的作用，通常将几个增加的剂量水平与对照进行比较。对照可以是中性对照、安慰剂或活性对照、已知有效的标准药物。因此，剂量反应实验通常以单向布局进行，其中所考虑的化合物的剂量被分配给单独的受试者组。在这些研究中有不同的关注点。在毒理学研究中，主要关注的是所考虑的毒素的安全性，目标是估计与对照组无显著差异的最高剂量。该最高剂量通常称为趋势无统计学显著性或未观察到不良事件水平剂量。然而，在药物研究中，主要目标是评估是否确实存在剂量反应效应，这意味着与对照相比，至少一种治疗是有效的。如果发现剂量反应效应，则确定产生优于对照的预期效应的最低剂量水平。该最低剂量水平通常被称为最小有效剂量，该剂量在临床上显著优于中性对照的平均反应;即 MED=min{d（i）：m（i）>m（0）+ c}，其中c定义为实验者预先指定的临床显著差异。对于疗效研究，确定最低有效剂量很重要，因为高剂量往往会产生不良副作用。本研究的目的是为回归曲线的各种先验信息构造最有效的统计推断程序。

SUMMARY OF PROPOSAL FOR PUBLIC RELEASE In toxicological and biopharmaceutical studies, to investigate the effect of a compound several increasing dose levels are usually compared with a control. The control may be a neutral control, a placebo, or an active control, a standard drug known to be effective. Therefore, dose-response experiments are often conducted in a one-way layout in which the doses of the compound under consideration are allocated to separate groups of subjects. There are different concerns in these studies. In toxicological studies, the main concern is the safety of the toxin under consideration and the goal is to estimate the highest dose that shows no significant difference from the control. This highest dose is generally called the no statistical significance for trend or no observed adverse event level dose. In pharmaceutical studies, however, the primary goal is to assess whether there is indeed a dose-response effect which means that at least one treatment is effective in comparison to the control. If a dose response effect is found, then to identify the lowest dose level producing a desirable effect over that of the control. This lowest dose level is commonly referred to as the minimum effective dose, the dose that is clinically significantly better than the mean response of the neutral control; that is         MED=min{d(i):m(i)>m(0) + c} where c is defined as a clinically significant difference preassigned by an experimenter. For efficacy studies, identifying the minimum effective dose is important since high doses often turn out to have undesirable side effects. The aim of this investigation is to construct most efficient statistical inference procedures for various kind of prior information concerning regression curves.