Optimal designs for criteria involving log(potency) in comparative binary bioassays

Optimal designs are investigated for bioassays involving two parallel dose–response relationships, where estimating relative potency is the main interest. Local and Bayesian D-optimal designs are considered, as well as Ds-optimal designs where the mean response of one substance (standard) is regarded as of no interest. A range of link functions relating expected response to log(dose) are considered. The range of prior distributions used for the Bayesian optimal designs includes uniform, trivariate normal and a bivariate normal with an independent uniform for log(potency). Because of the lack of closed form solutions for Bayesian optimal designs, much of the investigation is numerical and extends work pertaining to a single binary dose–response.