A compound optimality criterion for D-efficient and separation-robust designs for the logistic regression model

The (Formula presented.) -criterion is proposed to generate optimal designs for the logistic regression model with reduced separation probabilities. This compound criterion has two components: (a) the (Formula presented.) -efficiency of the candidate design and (b) a penalty term that captures the average distance of the candidate design's support points from the region of maximum prediction variance (MPV). A (Formula presented.) -optimal design maximizes the (Formula presented.) -criterion. The aim is to obtain compromise experimental designs with high (Formula presented.) -efficiencies that are more robust to separation than a (Formula presented.) -optimal design of equal size. This paper presents the (Formula presented.) -criterion and demonstrates examples of its potential use as a means of mitigating separation in the design phase of a binary response experiment. For the examples presented, the local (Formula presented.) -optimal designs offer a 20-30% reduction in separation probability over the local (Formula presented.) -optimal designs while maintaining (Formula presented.) -efficiencies over 93%. A robust design methodology is also demonstrated, where a robust (Formula presented.) -optimal design is compared to a Bayesian (Formula presented.) -optimal design and shown to have comparable (Formula presented.) -efficiencies across a range of randomly drawn parameter values while offering a mean reduction in separation probability of 23.9%.