Optimal planned missing data design for linear latent growth curve models

Longitudinal data collection is a time-consuming and cost-intensive part of developmental research. Wu et al. (2016) discussed planned missing (PM) designs that are similar in efficiency to complete designs but require fewer observations per person. The authors reported optimal PM designs for linear latent growth curve models based on extensive Monte Carlo simulations. They called for further formal investigation of the question as to how much the proposed PM mechanisms influence study design efficiency to arrive at a better understanding of PM designs. Here, we propose an approximate solution to the design problem by comparing the asymptotic effective errors of PM designs. Effective error was previously used to find optimal longitudinal study designs for complete data designs; here, we extend the approach to planned missing designs. We show how effective error is a metric for comparing the efficiency of study designs with both planned and unplanned missing data, and how earlier simulation-based results for PM designs can be explained by an asymptotic solution. Our approach is computationally more efficient than Wu et al.'s approach and leads to a better understanding of how various design factors, such as the number of measurement occasions, their temporal arrangement, attrition rates, and PM design patterns interact and how they conjointly determine design efficiency. We provide R scripts to calculate effective errors in various scenarios of PM designs.