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.

中文翻译：

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纵向数据的功能主成分分析，提供有意义的辍学信息

在纵向研究中，由于辍学，生物标志物的值通常会翔实地缺失。常规功能主成分分析通常会忽略丢失的信息，而只是将未观察到的数据点视为完全随机丢失。结果，平均函数和协方差表面的估计可能会出现偏差，从而导致功能主成分的估计出现偏差。我们提出了信息缺失的功能主成分分析（imFunPCA），它非常适合于纵向轨迹易受信息缺失影响的情况。在我们的方法中，功能主成分的计算是基于数据的可能性，其中结合了观察到的数据点和缺失的数据点的信息。我们采用基于回归的正交逼近方法，基于一组正交的经验基础函数来分解潜在的随机过程。在信息缺失的情况下，我们通过仿真研究表明，我们的方法的性能优于传统方法。我们将我们的方法应用于肾脏移植后患者肾小球滤过率的纵向数据集。