A Bayesian multiple imputation approach to bivariate functional data with missing components

Jeong Hoon Jang, Amita K. Manatunga, Changgee Chang, Qi Long

Research output: Contribution to journalArticlepeer-review

Abstract

Existing missing data methods for functional data mainly focus on reconstructing missing measurements along a single function—a univariate functional data setting. Motivated by a renal study, we focus on a bivariate functional data setting, where each sampling unit is a collection of two distinct component functions, one of which may be missing. Specifically, we propose a Bayesian multiple imputation approach based on a bivariate functional latent factor model that exploits the joint changing patterns of the component functions to allow accurate and stable imputation of one component given the other. We further extend the framework to address multilevel bivariate functional data with missing components by modeling and exploiting inter-component and intra-subject correlations. We develop a Gibbs sampling algorithm that simultaneously generates multiple imputations of missing component functions and posterior samples of model parameters. For multilevel bivariate functional data, a partially collapsed Gibbs sampler is implemented to improve computational efficiency. Our simulation study demonstrates that our methods outperform other competing methods for imputing missing components of bivariate functional data under various designs and missingness rates. The motivating renal study aims to investigate the distribution and pharmacokinetic properties of baseline and post-furosemide renogram curves that provide further insights into the underlying mechanism of renal obstruction, with post-furosemide renogram curves missing for some subjects. We apply the proposed methods to impute missing post-furosemide renogram curves and obtain more refined insights.

Original languageEnglish
Pages (from-to)4772-4793
Number of pages22
JournalStatistics in Medicine
Volume40
Issue number22
DOIs
Publication statusPublished - 2021 Sep 30

Bibliographical note

Funding Information:
This research was supported by the grant R01DK108070 from the National Institute of Diabetes and Digestive and Kidney Diseases.

Publisher Copyright:
© 2021 John Wiley & Sons Ltd.

All Science Journal Classification (ASJC) codes

  • Epidemiology
  • Statistics and Probability

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