Functional principal component analysis for longitudinal data with informative dropout

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.

Automated summary

This study introduces a method for informatively missing longitudinal data called informatively missing functional principal component analysis (imFunPCA), which incorporates information from both observed and missing data points based on the likelihood of the data. The approach uses a regression-based orthogonal approximation method for computing the functional principal components. Simulation studies demonstrate the superior performance of the proposed method compared to conventional approaches in the presence of informative missingness.