Shi Haolun, Dong Jianghu, Wang Liangliang, Cao Jiguo
Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, British Columbia, Canada.
Department of Biostatistics & Division of Nephrology, University of Nebraska Medical Center, Nebraska, USA.
Stat Med. 2021 Feb 10;40(3):712-724. doi: 10.1002/sim.8798. Epub 2020 Nov 11.
In longitudinal studies, the values of biomarkers are often informatively missing due to dropout. The conventional functional principal component analysis typically disregards the missing information and simply treats the unobserved data points as missing completely at random. As a result, the estimation of the mean function and the covariance surface might be biased, resulting in a biased estimation of the functional principal components. We propose the informatively missing functional principal component analysis (imFunPCA), which is well suited for cases where the longitudinal trajectories are subject to informative missingness. Computation of the functional principal components in our approach is based on the likelihood of the data, where information of both the observed and missing data points are incorporated. We adopt a regression-based orthogonal approximation method to decompose the latent stochastic process based on a set of orthonormal empirical basis functions. Under the case of informative missingness, we show via simulation studies that the performance of our approach is superior to that of the conventional ones. We apply our method on a longitudinal dataset of kidney glomerular filtration rates for patients post renal transplantation.
在纵向研究中，由于失访，生物标志物的值常常存在信息性缺失。传统的功能主成分分析通常会忽略这些缺失信息，仅仅将未观测到的数据点视为完全随机缺失。因此，均值函数和协方差曲面的估计可能会产生偏差，进而导致功能主成分的估计出现偏差。我们提出了信息性缺失功能主成分分析（imFunPCA），它非常适用于纵向轨迹存在信息性缺失的情况。我们方法中功能主成分的计算基于数据的似然性，其中观测到的数据点和缺失的数据点的信息都被纳入考虑。我们采用基于回归的正交近似方法，基于一组正交的经验基函数来分解潜在的随机过程。在信息性缺失的情况下，我们通过模拟研究表明，我们方法的性能优于传统方法。我们将我们的方法应用于肾移植术后患者肾小球滤过率的纵向数据集。
