On the Equivalence of Constrained and Compound Optimal Designs

Bayesian optimal designs for estimating a set of symmetrical quantiles

“…On the other hand, constrained optimal designs are harder to ÿnd but easier to interpret because of the intuitive formulation of the design problem. Cook and Wong [12] considered linear models when there are two objectives and established that every constrained optimal design is a compound optimal design and vice versa. Clyde and Chaloner [13] extended this equivalence result to non-linear models where there are two or more objectives and Bayesian optimal designs are sought.…”

“…This means that we want a constrained optimal design with e 2 ¿0:90 and e 1 = e 3 : In the Appendix we argued that when 1 = 3 = , the compound optimal design is approximately symmetric about 0 and has the same e ciency for estimating ED25 and ED75, that is, e 1 ≈ e 3 . This implies that the original three-objective design problem can be reduced to a two-objective problem, and the desired constrained optimal design can be found from an e ciency plot [12]. In this case, since e 1 ≈ e 3 , we plot e 1 (or e 3 ) and e 2 versus (Figure 1) where ranges from 0 to 0.5.…”

“…This is a three-objective design problem. It is now harder to ÿnd the constrained optimal design from the compound optimal design because the e ciency plot is three-dimensional and the e ciency curves are no longer monotonic as they were in two-objective design problems [12]. For example, we observe from Table I that the design with [ T = (0:3; 0:4; 0:3) is more e cient for estimating ED50 than the design with [ T = (0; 0:5; 0:5) although the latter has more weight on 2 .…”

Allocating Multiple Patients at a Time in Multiple-Objective Response-Adaptive Repeated Measurement Designs

“…To date, more research has been done to conduct multiple objective designs (Cook & Wong, 1994;Clyde & Chaloner, 1996;Antognini & Giovagnoli, 2010). More recently, we proposed an adaptive allocation strategy to construct multiple-objective RADs, that increase both estimation precision and treatment benefit for trials with continuous outcomes (Liang & Carriere, 2009).…”

Constrained optimal discrimination designs for Fourier regression models

“…The present paper is devoted to the problem of constructing optimal discrimination designs using constrained optimality criteria. Constrained optimal designs have primarily been considered by Stigler (1971), Studden (1982b) and Lee (1988a,b), whereas Cook and Wong (1994), Dette (1995) and Clyde and Chaloner (1996) investigated the relation between this approach and compound optimality criteria.…”