Optimal designs for multivariate logistic mixed models with longitudinal data

This paper considers the optimal design problem for multivariate mixed-effects logistic models with longitudinal data. A decomposition method of the binary outcome and the penalized quasi-likelihood are used to obtain the information matrix. The D-optimality criterion based on the approximate information matrix is minimized under different cost constraints. The results show that the autocorrelation coefficient plays a significant role in the design. To overcome the dependence of the D-optimal designs on the unknown fixed-effects parameters, the Bayesian D-optimality criterion is proposed. The relative efficiencies of designs reveal that both the cost ratio and autocorrelation coefficient play an important role in the optimal designs.