Individual and Population Penalized Regression Splines for Accelerated Longitudinal Designs

In an accelerated longitudinal design (ALD), individuals enter the study at different points of their growth trajectory and are observed over a short time span relative to the entire time span of interest. ALD data are combined across independent units to provide an estimate of an overall population curve and predictions of individual patterns of change. As a modest extension of the work of Ruppert et al. (2003, Semiparametric Regression, Cambridge University Press), we develop a computationally efficient procedure for the application of longitudinal semiparametric methods under ALD sampling schemes. We compare balanced and complete longitudinal designs to ALDs using the Berkeley Growth Study data and apply our method to longitudinal magnetic resonance imaging (MRI) brain structure size (volume) measurements from an ongoing developmental study. Potential applications extend beyond growth studies to many other fields in which cost and feasibility constraints impose restrictions on sample size and on the numbers and timings of repeated measurements across subjects.