FPCA-based Method to Select Optimal Sampling Schedules That Capture Between-subject Variability in Longitudinal Studies

Abstract

Summary A critical component of longitudinal study design involves determining the sampling schedule. Criteria for optimal design often focus on accurate estimation of the mean profile, although capturing the between-subject variance of the longitudinal process is also important since variance patterns may be associated with covariates of interest or predict future outcomes. Existing design approaches have limited applicability when one wishes to optimize sampling schedules to capture between-individual variability. We propose an approach to derive optimal sampling schedules based on functional principal component analysis (FPCA), which separately characterizes the mean and the variability of longitudinal profiles and leads to a parsimonious representation of the temporal pattern of the variability. Simulation studies show that the new design approach performs equally well compared to an existing approach based on parametric mixed model (PMM) when a PMM is adequate for the data, and outperforms the PMM-based approach otherwise. We use the methods to design studies aiming to characterize daily salivary cortisol profiles and identify the optimal days within the menstrual cycle when urinary progesterone should be measured.

Optimal design for classification of functional data

“…(), Ji & Müller () and Berrendero et al . () used a greedy search algorithm, and Wu et al () proposed a Metropolis sampling method. Here, we propose a computationally efficient approach for finding optimal sampling points, which does not require the specification of candidate sampling points.…”

“…; Ji & Müller, ; Wu et al . ; Park et al . ) has been proposed to predict either individual curves and/or a scalar outcome.…”

A joint design for functional data with application to scheduling ultrasound scans

“…If the number of selected design points is small, then we use a full search algorithm (i.e., we evaluate for every combination of points from ). If the number of selected design points is large, a full search becomes computationally difficult and one may use a Monte Carlo sampling method in Wu et al (2017) or a sequential search method in Ji and Müller (2017) . In this paper we focus on the full search algorithm.…”

“… Ji and Müller (2017) proposed prediction-based criteria for sampling functional data with the target of either recovering individual functions or predicting a scalar outcome. Wu et al (2017) exploited the mixed effects model representation of functional data and proposed a design criterion based on Fisher’s information matrix of eigenvalues of the covariance function. There are several limitations with these approaches.…”

“…There are several limitations with these approaches. Wu et al (2017) focused on recovering individual functions, while Ji and Müller (2017) were limited to the study of design separately and did not consider a joint design, which is the focus of our data application. In addition, in these works the number of design points was pre-fixed and no data-driven method was developed.…”