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

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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.