Theory & Methods: Selecting Closest to Control

Abstract

Consider the usual one-way fixed effect analysis of variance model where the populations i (i = 0, 1, . . . , k) have independent normal distributions with unknown means and common unknown variance. Let 0 be a control population with which the other (treatment) populations are to be compared. The basic problem is to select the treatment that is closest to the control mean. This situation occurs when one of the i must be chosen, regardless of how many are equivalent to the control in the sense of having means sufficiently close. This paper follows the approach of Hsu (1996) and is based on a set of simultaneous confidence intervals. It provides a table of critical values which allows direct implementation of the new inference procedure. The applications given are of the balanced cross-over design type with negligible carry-over effects, for which the results of this paper may be used. One of the applications refers to the selection of a drug, which may not be bioequivalent to a reference formulation but is the closest of those drugs that are readily available to the group of patients considered.