Optimal Study Design for Reducing Variances of Coefficient Estimators in Change-Point Models

In longitudinal studies, we measure the same variables at multiple time-points to track their change over time. The exact data collection schedules (i.e., time of participants' visits) are often pre-determined to accommodate the ease of project management and compliance. Therefore, it is common to schedule those visits at equally spaced time intervals. However, recent publications based on simulated experiments indicate that the power of studies and the precision of model parameter estimators is related to the participants' visiting scheme. So, in this work, we investigate how to schedule participants' visits to better study the accelerated cognitive decline of senior adults, where a broken-stick model is often applied. We formulate this optimal design problem on scheduling participants' visiting into a high- dimensional optimization problem and derive its approximate solution by adding reasonable constraints. Based on this approximation, we propose a novel design of the visiting scheme that aims to maximize the power (i.e. reduce the variance of estimators) in identifying the onset of accelerated decline. Using both simulation studies and evidence from real data, we demonstrate that our design outperforms the standard equally-spaced one when we have strong prior knowledge on the change-points. This novel design helps researchers plan their longitudinal studies with improved power in detecting pattern change without collecting extra data. Also, this individual-level scheduling system helps monitor seniors' cognitive function and, therefore, benefits the development of personal level treatment for cognitive decline, which agrees with the trend of the health care system.