Optimal designs for mean–covariance models with missing observations

This paper focuses on the optimal design of time point allocation in repeated measurements experiments with applications to longitudinal studies. Most design literature mainly focus on the estimation of the mean responses of each subject whereas we try to find the design that aids the estimation of both the mean and the correlation structures of longitudinal observations. Our design criterion also takes into account the missing data issue, which is very common in practice. Instead of the local optimal design approach, which relies on a good guess of the unknown parameter, we adopt the Bayesian optimal design approach to protect for the parameter uncertainty. To allow for operational errors such as time delays, we discuss the sampling windows which allow flexibility in timing the data collection. In other words, our design is robust against the missingness, parameter uncertainty, and operational errors. Simulation studies and a real data analysis are carried out to demonstrate the proposed criterion as well as the resulting designs.