In dose-finding studies, c-optimal designs provide the most efficient design to study an interesting target dose. However, there is no guarantee that a c-optimal design that works best for estimating one specific target dose still performs well for estimating other target doses. Considering the demand in estimating multiple target dose levels, the robustness of the optimal design becomes important. In this study, the 4-parameter logistic model is adopted to describe dose-response curves. Under nonlinear models, optimal design truly depends on the pre-specified nominal parameter values. If the pre-specified values of the parameters are not close to the true values, optimal designs become far from optimum. In this research, I study an optimal design that works well for estimating multiple EDps and for unknown parameter values. To address this parameter uncertainty, a two-stage design technique is adopted using two different approaches. One approach is to utilize a design augmentation at the second stage, the other one is to apply a Bayesian paradigm to find the optimal design at the second stage. For the Bayesian approach, one challenging task is that it requires heavy computation in the numerical calculation when searching for the Bayesian optimal design. To overcome this problem, a clustering method can be applied. These two-stage design strategies are applied to construct a robust optimal design for estimating multiple EDps. Through a simulation study, the proposed two-stage optimal designs are compared with the traditional uniform design and the enhanced uniform design to see how well they perform in estimating multiple ED ps when the parameter values are mis-specified.
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