Cost-Efficient Sequential Designs for Binary Response Models

The efficiency of an experimental design is ultimately measured in terms of time and resources needed for the experiment. This paper studies optimal sequential (multi-stage) designs in the situation where each stage involves a fixed cost. The problem is motivated by switching measurements on superconducting Josephson junctions. In this quantum mechanical experiment, the current is the controlled covariate and a binary response indicating the presence or the absence of a voltage response is measured. The binary response can be modeled by a generalized linear model with the complementary log-log link function. The other models considered in the paper are the logit model and the probit model. For these three models, we determine the approximately optimal sample size for the next stage as a function of the current Fisher information and the stage cost. The cost-efficiency of the proposed designs is demonstrated in simulations based on real data from switching measurements. The results can be directly applied to switching measurements and they may lead to substantial savings in the time needed for the experiment.