In this paper we derive locally Dand ED p-optimal designs for the exponential, log-linear and three parameter EMAX-model. We show that for each model the locally Dand ED p-optimal designs are supported at the same set of points, while the corresponding weights are dierent. This indicates that for a given model, Doptimal designs are ecient for estimating the smallest dose which achieves 100p% of the maximum eect in the observed dose range. Conversely, ED p-optimal designs also yield good D-eciencies. We illustrate the results using several examples and demonstrate that locally Dand ED p-optimal designs for the EMAX-, log-linear and exponential model are relatively robust with respect to misspecication of the model parameters.
Dose finding studies often compare several doses of a new compound with a marketed standard treatment as an active control. In the past, however, research has focused mostly on experimental designs for placebo-controlled dose finding studies. To the best of our knowledge, optimal designs for dose finding studies with an active control have not been considered so far. As the statistical analysis for an active controlled dose finding study can be formulated in terms of a mixture of two regression models, the related design problem is different to what has been investigated before in the literature. We present a rigorous approach to the problem of determining optimal designs for estimating the smallest dose achieving the same treatment effect as the active control. We determine explicitly the locally optimal designs for a broad class of models employed in such studies. We also discuss robust design strategies and determine related Bayesian and standardized minimax optimal designs. We illustrate the results by investigating alternative designs for a clinical trial which has recently appeared in a consulting project of one of the authors.
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