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

Peng Zhang, Peter X.K. Song, Annie Qu, Tom Greene

Research output: Contribution to journalArticlepeer-review


This article presents a new class of nonnormal linear mixed models that provide an efficient estimation of subject-specific disease progression in the analysis of longitudinal data from the Modification of Diet in Renal Disease (MDRD) trial. This new analysis addresses the previously reported finding that the distribution of the random effect characterizing disease progression is negatively skewed. We assume a log-gamma distribution for the random effects and provide the maximum likelihood inference for the proposed nonnormal linear mixed model. We derive the predictive distribution of patient-specific disease progression rates, which demonstrates rather different individual progression profiles from those obtained from the normal linear mixed model analysis. To validate the adequacy of the log-gamma assumption versus the usual normality assumption for the random effects, we propose a lack-of-fit test that clearly indicates a better fit for the log-gamma modeling in the analysis of the MDRD data. The full maximum likelihood inference is also advantageous in dealing with the missing at random (MAR) type of dropouts encountered in the MDRD data.

Original languageEnglish (US)
Pages (from-to)29-38
Number of pages10
Issue number1
StatePublished - Mar 2008
Externally publishedYes


  • Disease progression
  • Dropouts
  • Gauss-Newton algorithm
  • Lack-of-fit test
  • Log-gamma distribution
  • Predictive distribution

ASJC Scopus subject areas

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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