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Bayesian inference in semiparametric mixed models for longitudinal data.

Yisheng Li1, Xihong Lin, Peter Müller

  • 1Department of Biostatistics, Division of Quantitative Sciences, University of Texas M. D. Anderson Cancer Center, Houston, Texas 77030, USA. ysli@mdanderson.org

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|May 13, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a new Bayesian approach for semiparametric mixed models (SPMMs) in longitudinal data analysis. The method improves inference for regression coefficients and nonparametric functions, addressing issues with existing Dirichlet process priors.

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Area of Science:

  • Biostatistics
  • Longitudinal Data Analysis
  • Bayesian Inference

Background:

  • Semiparametric mixed models (SPMMs) are used for longitudinal data.
  • SPMMs incorporate nonparametric functions for time effects and parametric functions for covariates.
  • Within-subject correlation is handled by random effects, which can be parametric or nonparametric.

Purpose of the Study:

  • To develop a robust Bayesian inference framework for SPMMs.
  • To address identifiability issues and potential bias in existing methods, particularly those using Dirichlet process (DP) priors.
  • To propose a novel uniform shrinkage prior (USP) for variance components and smoothing parameters.

Main Methods:

  • Modeling the nonparametric function using Bayesian cubic smoothing splines.
  • Employing normal distributions and Dirichlet process (DP) priors for random effects.
  • Introducing a uniform shrinkage prior (USP) for variance components and DP hyperparameters.
  • Proposing a postprocessing technique to adjust for potential bias in fixed effects.

Main Results:

  • Demonstrated proper posteriors under USP, flat priors for fixed effects, and improper priors for residual variance.
  • Identified potential bias and weak identifiability issues with commonly assumed DP priors.
  • Illustrated the method's application on a longitudinal hormone dataset.

Conclusions:

  • The proposed Bayesian approach with USP offers improved inference for SPMMs.
  • The postprocessing adjustment effectively mitigates bias associated with certain DP prior specifications.
  • Extensive simulations confirm the method's superior finite sample performance compared to existing techniques.