Recently, a design was proposed for the Simultaneous Global Drug Development Program (SGDDP) to assess the impact of ethnic factors on the effect of a new treatment for a targeted ethnic (TE) population. It used weighted Z tests to combine the information collected from the TE and non-TE (NTE) subgroups in the SGDDP based on the fundamental assumption on their shared biological commonality. In this article, we mathematically formulated this assumption as the quantitative interaction between treatment effect and subgroup. We used it to more rigorously describe the hypotheses, and showed the unbiasedness of the weighted Z test. Moreover, to study the loss of efficiency from down weighting the NTE information in this SGDDP design, we compared the power of their test with that of the uniformly most powerful (UMP) test, which we showed was also a weighted Z test. We discussed that the choice of weight should balance the maximization of power when the assumption holds and the minimization of bias otherwise.
Keywords: Power; Quantitative interaction assumption; SGDDP; Unbiased; Weighted Z test.