Correcting for nonrandom ascertainment in generalized linear mixed models (GLMMs), fitted using Gibbs sampling

Paul R Burton

Research output: Contribution to journalArticle (Academic Journal)peer-review

21 Citations (Scopus)


Gibbs sampling-based generalized linear mixed models (GLMMs) provide a convenient and flexible way to extend variance components models for multivariate normally distributed continuous traits to other classes of phenotype. This includes binary traits and right-censored failure times such as age-at-onset data. The approach has applications in many areas of genetic epidemiology. However, the required GLMMs are sensitive to nonrandom ascertainment. In the absence of an appropriate correction for ascertainment, they can exhibit marked positive bias in the estimated grand mean and serious shrinkage in the estimated magnitude of variance components. To compound practical difficulties, it is currently difficult to implement a conventional adjustment for ascertainment because of the need to undertake repeated integration across the distribution of random effects. This is prohibitively slow when it must be repeated at every iteration of the Markov chain Monte Carlo (MCMC) procedure. This paper motivates a correction for ascertainment that is based on sampling random effects rather than integrating across them and can therefore be implemented in a general-purpose Gibbs sampling environment such as WinBUGS. The approach has the characteristic that it returns ascertainment-adjusted parameter estimates that pertain to the true distribution of determinants in the ascertained sample rather than in the general population. The implications of this characteristic are investigated and discussed. This paper extends the utility of Gibbs sampling-based GLMMs to a variety of settings in which family data are ascertained nonrandomly.

Original languageEnglish
Pages (from-to)24-35
Number of pages12
JournalGenetic Epidemiology
Issue number1
Publication statusPublished - Jan 2003

Bibliographical note

Copyright 2003 Wiley-Liss, Inc.


  • Age of Onset
  • Analysis of Variance
  • Bias (Epidemiology)
  • Effect Modifier, Epidemiologic
  • Genetic Diseases, Inborn
  • Genetic Variation
  • Genetics, Population
  • Genotype
  • Humans
  • Linear Models
  • Markov Chains
  • Models, Genetic
  • Monte Carlo Method
  • Pedigree
  • Phenotype
  • Predictive Value of Tests
  • Sampling Studies
  • Sensitivity and Specificity

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