Shrinkage estimation for functional principal component scores with application to the population kinetics of plasma folate

We present the application of a nonparametric method to performing functional principal component analysis for functional curve data that consist of measurements of a random trajectory for a sample of subjects. This design typically consists of an irregular grid of time points on which repeated measurements are taken for a number of subjects. We introduce shrinkage estimates for the functional principal component scores that serve as the random effects in the model. Scatterplot smoothing methods are used to estimate the mean function and covariance surface of this model. We propose improved estimation in the neighborhood of and at the diagonal of the covariance surface, where the measurement errors are reflected. The presence of additive measurement errors motivates shrinkage estimates for the functional principal component scores. Shrinkage estimates are developed through best linear prediction and in a generalized version, aiming at minimizing one-curve-leave-out prediction error. The estimation of individual trajectories combines data obtained from that individual as well as all other individuals. We apply our methods to new data regarding the analysis of the level of 14C-folate in plasma as a function of time since dosing of healthy adults with a small tracer dose of 14C-folic acid. A time transformation was incorporated to handle design irregularity concerning the time points on which the measurements were taken. The proposed methodology, incorporating shrinkage and data-adaptive features, is seen to be well suited for describing population kinetics of 14C-folate-specific activity and random effects, and can also be applied to other functional data analysis problems.