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

Jeong Hoon Jang1, Amita K Manatunga2, Changgee Chang3

  • 1Department of Biostatistics and Health Data Science, Indiana University School of Medicine, Indianapolis, Indiana, USA.

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|June 8, 2021
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Summary
This summary is machine-generated.

This study introduces a new Bayesian imputation method for missing bivariate functional data, improving accuracy in complex datasets. The approach enhances analysis for studies like renal function, where data is often incomplete.

Keywords:
Bayesian latent factor modelbivariate functional datacurvesmissing datamultiple imputation

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Area of Science:

  • Statistics
  • Biostatistics
  • Functional Data Analysis

Background:

  • Current methods for missing functional data primarily address univariate settings.
  • Bivariate functional data, common in medical studies like renal function analysis, presents unique challenges with missing components.
  • Accurate imputation is crucial for understanding complex biological processes and disease mechanisms.

Purpose of the Study:

  • To develop a robust method for imputing missing component functions in bivariate functional data.
  • To extend the imputation framework for multilevel bivariate functional data, accounting for correlations.
  • To apply the novel method to a renal study investigating renogram curves.

Main Methods:

  • Proposed a Bayesian multiple imputation approach utilizing a bivariate functional latent factor model.
  • Developed a Gibbs sampling algorithm for simultaneous imputation and parameter estimation.
  • Implemented a partially collapsed Gibbs sampler for improved computational efficiency in multilevel data.

Main Results:

  • Simulation studies confirmed the proposed methods outperform existing techniques for imputing missing bivariate functional data.
  • The method demonstrated accuracy and stability by exploiting joint patterns in component functions.
  • Application to renal data successfully imputed missing post-furosemide renogram curves.

Conclusions:

  • The novel Bayesian imputation method effectively handles missing components in bivariate and multilevel functional data.
  • The approach provides more accurate and stable imputations compared to competing methods.
  • This work offers refined insights into renal obstruction mechanisms through improved analysis of renogram data.