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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Published on: July 3, 2020

Efficient estimation for patient-specific rates of disease progression using nonnormal linear mixed models.

Peng Zhang1, Peter X-K Song, Annie Qu

  • 1Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada.

Biometrics
|May 16, 2007
PubMed
Summary

This study introduces nonnormal linear mixed models using a log-gamma distribution for analyzing longitudinal disease progression data. This approach offers more accurate patient-specific progression profiles compared to standard models, especially with skewed data.

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Area of Science:

  • Biostatistics
  • Longitudinal Data Analysis
  • Clinical Trial Analysis

Background:

  • Longitudinal data analysis in clinical trials often assumes normal distributions for random effects.
  • The Modification of Diet in Renal Disease (MDRD) trial data exhibits a negatively skewed distribution for disease progression random effects.
  • Standard normal linear mixed models may not accurately capture subject-specific disease progression in such cases.

Purpose of the Study:

  • To develop and present a novel class of nonnormal linear mixed models for longitudinal data.
  • To efficiently estimate subject-specific disease progression, addressing the negative skewness observed in MDRD trial data.
  • To compare patient-specific progression profiles derived from the new model against traditional normal linear mixed models.

Main Methods:

  • Proposed a nonnormal linear mixed model assuming a log-gamma distribution for random effects.
  • Employed maximum likelihood inference for parameter estimation.
  • Derived predictive distributions for patient-specific disease progression rates and developed a lack-of-fit test for model validation.

Main Results:

  • The log-gamma distribution provided a significantly better fit to the MDRD data compared to the normality assumption.
  • Patient-specific disease progression profiles derived from the nonnormal model differed notably from those obtained using normal models.
  • The proposed maximum likelihood inference effectively handled missing at random (MAR) data.

Conclusions:

  • Nonnormal linear mixed models, specifically with a log-gamma distribution, are superior for analyzing longitudinal data with skewed random effects.
  • The new modeling approach yields more accurate and distinct individual disease progression trajectories.
  • This methodology enhances the analysis of clinical trial data, particularly in the presence of non-normal random effects and missing data.