Browsing by Author "Zhang, Anqing"

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    Adaptive Two-Stage Optimal Design for Estimating Multiple EDps under the 4-Parameter Logistic Model
    (North Dakota State University, 2018) Zhang, Anqing
    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 s 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 s. 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 s when the parameter values are mis-specified.
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    Robust c-Optimal Design for Estimating the Edp
    (North Dakota State University, 2014) Zhang, Anqing
    Optimal design provides the most efficient design to study dose-response functions. It is often observed to adopt the four-parameter logistic model to describe the dose-response relationships in many dose finding trials. Under the four-parameter logistic model, optimal design to estimate the EDp accurately is presented. The EDp is the dose achieving 100p% of the maximum treatment effect. C-optimal design works the best to estimate the EDp, but the value of p must be predetermined in order to obtain the c-optimal design. Here we investigate the efficiency of c-optimal design to estimate the EDp for different values of p and present robust c-optimal design that works well for the changes in the value of p. Five different values of p are considered in this study: ED10, ED30, ED50, ED70, and ED90. The performance of the robust c-optimal design is obtained and compared to the c-optimal designs and traditional uniform designs.