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A monotone single index model for missing-at-random longitudinal proportion data.

Satwik Acharyya1, Debdeep Pati2, Shumei Sun3

  • 1Department of Biostatistics, University of Michigan, Ann Arbor, MI, USA.

Journal of Applied Statistics
|April 17, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces flexible semi-parametric Beta regression models for longitudinal proportion data. The novel approach effectively models covariate effects using time-varying single index models, improving analysis of obesity research data.

Keywords:
62P10Beta regressionHamiltonian Monte Carlobody fatmonotoneproportion datasingle-index model

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Area of Science:

  • Biostatistics
  • Longitudinal Data Analysis
  • Statistical Modeling

Background:

  • Beta distributions are standard for proportion data in longitudinal studies.
  • Existing models may struggle with complex covariate effects and link function misspecification.

Purpose of the Study:

  • Develop semi-parametric Beta regression models for proportion-valued responses in longitudinal studies.
  • Flexibly model aggregate covariate effects using interpretable time-varying single index transforms.
  • Address missing-at-random data within a Bayesian framework.

Main Methods:

  • Utilized single index models for dimension reduction and accommodating link function misspecification.
  • Employed Bayesian methodology with Hamiltonian Monte Carlo sampling for inference.
  • Incorporated missing-at-random handling for proportion responses.

Main Results:

  • Demonstrated the utility of semi-parametric Beta regression for complex longitudinal proportion data.
  • Validated the methodology through simulation studies assessing frequentist properties and robustness.
  • Successfully applied the model to a longitudinal obesity dataset on body fat proportion.

Conclusions:

  • The proposed semi-parametric Beta regression models offer a flexible and robust approach for analyzing longitudinal proportion data.
  • The single index transform effectively captures aggregate covariate effects.
  • The methodology provides valuable insights for obesity research and similar fields.