formation about the MTD is frequently more ambiguous. Such priorignorance can be reﬂected through the use of vague or non-informativepriors. Thus, for example, the marginal prior distribution of the MTDmight scheme in which the toxicity probabilities are modeled directly asan unknownk-dimensional parameter vector. That is, the dose-toxicitymodel is given byProb DLTjDose¼xifg¼uii¼1;2;...;kð5ÞwithN=[u1u2...,uk] unknown. The authors maintain that byremoving the assumption that the dose-toxicity relationship follows aspeciﬁc parametric curve, such as the logistic model in (3), this modelpermits a more eﬃcient use of prior information. A similar approach isbased on what has variously been referred to as an empiric discrete model(Chevret, 1993), a power function (Kramar et al., 1999; Gasparini andEisele, 2000) or a power model (Heyd and Carlin, 1999). The model isgiven byProb DLTjDose¼xi¼ˆuyið6Þwherey>0 is unknown andˆui(i=1, 2, ...,k
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Bayesian probability, prior distribution, empiric discrete model