Maximin D-optimal designs for binary longitudinal responses

Optimal design problems for logistic mixed effects models for binary longitudinal responses are considered. A function of the approximate information matrix under the framework of the Penalized Quasi Likelihood (PQL) and a generalized linear mixed model with autocorrelation is optimized. Locally D-optimal designs are computed. Maximin D-optimal designs are considered to overcome the problem of parameter value dependency of the D-optimal designs. The results show that the optimal number of repeated measurements depends on the number of regression parameters in the model. The performance of the maximin D-optimal designs in terms of the maximin efficiency (MME) is high for a range of parameter values that is common in practice. The design locations for mixed-effects logistic models generally shift to the left as compared to the design locations for general linear mixed-effects models known in the literature.