27 Optimal and efficient treatment-control designs

Abstract

Publisher Summary This chapter discusses several designs for comparing treatments with a control for various experimental settings, models and inference methods. Bechhofer and Tamhane rediscovered designs with supplemented balance when they were considering the problem of constructing simultaneous confidence intervals for the treatment–control contrasts. They called their designs “Balanced Treatment Incomplete Block (BTIB) designs,” a terminology which has been adopted by many authors. It has long been known that one way to obtain an optimal block design is to construct, if possible, an orthogonal block design, such that within each block the replication of treatments are optimal for a zero-way elimination of heterogeneity model. There are two methods for deriving inferences on the treatment-control contrasts. One is estimation, and the other is simultaneous confidence intervals. The approximate, or continuous, block design theory is wide in its scope. As the theorems in this approach specify proportions of units, which are assigned to each treatment, they give an overall idea of the nature of optimal designs. Also, one rule applies to (almost) all block sizes, and requires only minor computations when the block sizes are altered. These are very desirable properties. On the other hand, application of these designs is possible only after rounding off the treatment-block incidences to nearby integers, and this could result in loss of efficiency.