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Abstract：
The problem of constructing locally D-optimal designs for two-variable logistic model with no interaction has been studied in many literature. In Kabera, Haines, and Ndlovu (2015), the model is restricted to have positive slopes and negative intercept for the assumptions that the probability of response increases with doses for both drugs and that the probability of response is less than 0.5 at zero dose level of both drugs. The design space mainly discussed is the set [0, ∞) × [0, ∞), while the finite rectangular design space is presented only in scenarios where the results for the unlimited design space are still appropriate. In this paper, we intend to loose these restrictions and discuss the rectangular design spaces for the model where the D-optimal designs can not be obtained. The result can be extended to the models where drugs have negative or opposite effects, or the models with positive intercept, by using translation and reflection in the first quadrant.
摘要：
在许多文献中已经研究了为没有相互作用的两变量逻辑模型构造局部D最优设计的问题。在卡贝拉,Haines,Ndlovu(2015)对于以下假设,即两种药物的应答概率随剂量的增加而增加,并且两种药物在零剂量水平下的应答概率小于0.5,该模型被限制为具有正斜率和负截距.主要讨论的设计空间是集合[0，∞)×[0，∞)，而有限矩形设计空间仅在无限设计空间的结果仍然合适的情况下呈现。在本文中,我们打算放宽这些限制，并讨论无法获得D最优设计的模型的矩形设计空间。结果可以扩展到药物具有负面或相反作用的模型，或者具有正截距的模型，通过在第一象限中使用翻译和反射。
