Yao Fang, Müller Hans-Georg, Clifford Andrew J, Dueker Steven R, Follett Jennifer, Lin Yumei, Buchholz Bruce A, Vogel John S
Department of Statistics, University of California, One Shields Ave., Davis, California 95616, USA.
Biometrics. 2003 Sep;59(3):676-85. doi: 10.1111/1541-0420.00078.
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.
我们展示了一种非参数方法在对功能曲线数据进行功能主成分分析中的应用，这些功能曲线数据由一组受试者随机轨迹的测量值组成。这种设计通常由一个不规则的时间点网格组成，在该网格上对多个受试者进行重复测量。我们引入了功能主成分得分的收缩估计，其作为模型中的随机效应。散点图平滑方法用于估计该模型的均值函数和协方差曲面。我们提出在协方差曲面的邻域和对角线上进行改进估计，测量误差在那里有所反映。加性测量误差的存在促使对功能主成分得分进行收缩估计。收缩估计是通过最佳线性预测以及在广义版本中开发的，旨在最小化一次曲线留出预测误差。个体轨迹的估计结合了从该个体以及所有其他个体获得的数据。我们将我们的方法应用于关于健康成年人以小剂量示踪剂(^{14}C) - 叶酸给药后血浆中(^{14}C) - 叶酸水平随时间变化分析的新数据。引入了时间变换来处理关于测量时间点的设计不规则性。所提出的方法结合了收缩和数据自适应特征，被认为非常适合描述(^{14}C) - 叶酸比活性的群体动力学和随机效应，并且也可应用于其他功能数据分析问题。
