  In longitudinal studies, we observe measurements of the same variables at
different time points to track the changes in their pattern over time. In such
studies, scheduling of the data collection waves (i.e. time of participants'
visits) is often pre-determined to accommodate ease of project management and
compliance. Hence, 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 schemes.
  In this paper, we consider the longitudinal studies that investigate the
changing pattern of a disease outcome, (e.g. the accelerated cognitive decline
of senior adults). Such studies are often analyzed by the broken-stick model,
consisting of two segments of linear models connected at an unknown
change-point. We formulate this design problem into a high-dimensional
optimization problem and derive its analytical solution. Based on this
solution, we propose an optimal design of the visiting scheme that maximizes
the power (i.e. reduce the variance of estimators) to identify the onset of
accelerated decline. Using both simulation studies and evidence from real data,
we demonstrate our optimal design outperforms the standard equally-spaced
design.
  Applying our novel design to plan the longitudinal studies, researchers can
improve the power of detecting pattern change without collecting extra data.
