Optimal Next-stage Designs for Sparse Functional/Longitudinal Data

Ming-Hung Kao, Alejandro Vidales Aller, Ping-Han Huang
Arizona State University

Selecting the best time points to collect informative observations for precisely predicting individual curves is an important optimal design issue for studies involving sparse longitudinal/functional data. Tackling this issue requires knowledge of unknown model parameters, and the previous works primarily yield locally optimal designs by replacing these parameters with their estimates from the prior stage. However, except for the parameter estimates, the data collected at the prior stage and the design used to collect them are discarded at the next stage. To avoid this waste of resources, a multi-stage design approach is proposed in this work. The primary design goal is to develop optimal designs for future subjects in the next stage, by adapting to the prior-stage design and by considering the trajectory recovery of all the curves in both the prior and next stages. An optimlaity criterion, relevant theoretical results, and an efficient computational approach are developed for finding such an optimal next-stage design. Numerical studies, including a real case, are conducted to compare the obtained design with other designs.