Statistical Aspects of Optimal Treatment Assignment

The issue of treatment assignment is ordinarily dealt with within the framework of testing Aptitude Treatment Interaction hypotheses ATI research mostly uses linear regression techniques, and an ATI exist when the AT regression lines cross each other within the relevant interval of the aptitude variable. Consistent with this approach is the use of the points of interaction of AT regression lines as treatment-assignment rule; In this paper, it is proposed to replace such rules by monotone; nonrandomized (Bayes) rules. Both continuous and dichotomous criteria for treatment success are considered. An example of the latter can be found in individualized instruction when learning success is evaluated using a mastery test; The solutions given in this paper are based on linear; normal ogive, and threshold utility functions. Finally; some modifications of these functions are discussed which are believed to be more realistic in the context of individualized instruction but for which no optimal monotone assignment ruleS are available yet.