Bayesian sequential design for sensitivity experiments with hybrid responses

In experimental design, a common problem seen in practice is when the result includes one binary response and multiple continuous responses. However, this problem receives scant attention. Most studies pertaining to this problem usually consider the situation in which the continuous responses are independent of the stimulus level condition on the binary response. However, in many practical applications, real data show that this conditional independent assumption is not always appropriate. This article considers a new model for the dependent situation and a corresponding sequential design is proposed under the decision-theoretic framework. To deal with the problem of complex computation involved in searching for optimal designs, fast algorithms are presented using two strategies to approximate the optimal criterion, denoted as SI-optimal design and Bayesian D-optimal design, respectively. Simulation studies based on data from a Chinese chemical material factory show that the proposed methods perform well in estimating the interesting quantiles.