Modeling energy balance while correcting for measurement error via free knot splines

PLoS One. 2018 Aug 30;13(8):e0201892. doi: 10.1371/journal.pone.0201892. eCollection 2018.

Abstract

Measurements of energy balance components (energy intake, energy expenditure, changes in energy stores) are often plagued with measurement error. Doubly-labeled water can measure energy intake (EI) with negligible error, but is expensive and cumbersome. An alternative approach that is gaining popularity is to use the energy balance principle, by measuring energy expenditure (EE) and change in energy stores (ES) and then back-calculate EI. Gold standard methods for EE and ES exist and are known to give accurate measurements, albeit at a high cost. We propose a joint statistical model to assess the measurement error in cheaper, non-intrusive measures of EE and ES. We let the unknown true EE and ES for individuals be latent variables, and model them using a bivariate distribution. We try both a bivariate Normal as well as a Dirichlet Process Mixture Model, and compare the results via simulation. Our approach, is the first to account for the dependencies that exist in individuals' daily EE and ES. We employ semiparametric regression with free knot splines for measurements with error, and linear components for error free covariates. We adopt a Bayesian approach to estimation and inference and use Reversible Jump Markov Chain Monte Carlo to generate draws from the posterior distribution. Based on the semiparameteric regression, we develop a calibration equation that adjusts a cheaper, less reliable estimate, closer to the true value. Along with this calibrated value, our method also gives credible intervals to assess uncertainty. A simulation study shows our calibration helps produce a more accurate estimate. Our approach compares favorably in terms of prediction to other commonly used models.

Publication types

  • Research Support, N.I.H., Extramural

MeSH terms

  • Bayes Theorem
  • Body Mass Index
  • Calibration
  • Computer Simulation
  • Energy Intake
  • Energy Metabolism*
  • Female
  • Homeostasis*
  • Humans
  • Male
  • Markov Chains
  • Models, Biological*
  • Monte Carlo Method
  • Uncertainty

Grants and funding

This work was funded by NIH grant HL091024. There was no additional external funding received for this study. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.