Optimal Designs for Bivariate Logistic Regression

SUMMARY In drug-testing experiments the primary responses of interest are efficacy and toxicity. These can be modeled as a bivariate quantal response using the Gumbel model for bivariate logistic regression. D-optimal and Q-optimal experimental designs are developed for this model. The Q-optimal design minimizes the average asymptotic prediction variance of p(l, 0; d), the probability of efficacy without toxicity at dose d, over a desired range of doses. The robustness of these designs to parameter misspecification is discussed. In addition, D-efficiencies of Q-optimal designs and Q-efficiencies of Doptimal designs are presented. An extension of the general equivalence theorem to the multivariate case is applied to these designs.