Bayesian D-optimal designs for the two parameter logistic mixed effects model

Bayesian optimal designs for binary longitudinal responses analyzed with mixed logistic regression describing a linear time effect are considered. In order to find the optimal number and allocations of time points, for different priors, cost constraints and covariance structures of the random effects, a scalar function of the approximate information matrix based on the first order penalized quasi likelihood (PQL1) is optimized. To overcome the problem of dependence of Bayesian designs on the choice of prior distributions, maximin Bayesian D-optimal designs are proposed. The results show that the optimal number of time points depends on the subject-to-measurement cost ratio and increases with the cost ratio. Furthermore, maximin Bayesian D-optimal designs are highly efficient and robust under changes in priors. Locally D-optimal designs are also investigated and maximin locally D-optimal designs are found to have much lower minimum relative efficiency and fewer time points than maximin Bayesian D-optimal designs. When comparing the efficiencies of designs with equidistant time points with the Bayesian D-optimal designs, it was found that three or four equidistant time points are advisable for small cost ratios and five or six equidistant time points for large cost ratios.