Functional principal component analysis for longitudinal data with informative dropout

Haolun Shi, Jianghu Dong, Liangliang Wang, Jiguo Cao

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)712-724
Number of pages13
JournalStatistics in Medicine
Issue number3
StatePublished - Feb 10 2021


  • filtration rates
  • functional data analysis
  • informative missing
  • kidney glomerular likelihood
  • orthonormal empirical basis functions

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability


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