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Mixed-effects models for conditional quantiles with longitudinal data.

Yuan Liu1, Matteo Bottai

  • 1Medical University of South Carolina, USA.

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This study introduces a new quantile mixed-effects regression model for dependent data. It accurately models longitudinal data and efficiently estimates effects, offering a comprehensive understanding of distributions.

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Area of Science:

  • Biostatistics
  • Statistical Modeling
  • Longitudinal Data Analysis

Background:

  • Dependent data, such as longitudinal measurements, present unique statistical challenges.
  • Estimating conditional quantiles is crucial for a comprehensive understanding of response variables.
  • Existing methods may not fully capture data dependence or provide efficient estimates for over-dispersed errors.

Purpose of the Study:

  • To propose a novel regression method for estimating conditional quantiles of continuous response variables with dependent data.
  • To incorporate random coefficients following a multivariate Laplace distribution to model data dependence.
  • To assess the performance of the proposed method through simulation studies and application to clinical data.

Main Methods:

  • Development of a quantile mixed-effects regression model.
  • Inclusion of random coefficients modeled by a multivariate Laplace distribution.
  • Simulation studies to evaluate model performance against existing methods.
  • Application to bounded outcome clinical data.

Main Results:

  • The proposed method accurately models dependence in longitudinal data.
  • Efficient estimation of fixed effects is achieved, especially with over-dispersed errors.
  • Performance is comparable to linear mixed models for symmetric errors but superior for over-dispersed errors.
  • The model allows for estimation across different conditional distribution locations.

Conclusions:

  • The quantile mixed-effects regression model provides a robust approach for analyzing dependent data.
  • It offers a more comprehensive understanding of the data by estimating quantiles beyond the mean.
  • The method is particularly advantageous when dealing with over-dispersed errors and bounded outcome variables.