Time-Varying Latent Effect Model for Longitudinal Data with Informative Observation Times

Na Cai, Wenbin Lu, Hao Helen Zhang

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


In analysis of longitudinal data, it is not uncommon that observation times of repeated measurements are subject-specific and correlated with underlying longitudinal outcomes. Taking account of the dependence between observation times and longitudinal outcomes is critical under these situations to assure the validity of statistical inference. In this article, we propose a flexible joint model for longitudinal data analysis in the presence of informative observation times. In particular, the new procedure considers the shared random-effect model and assumes a time-varying coefficient for the latent variable, allowing a flexible way of modeling longitudinal outcomes while adjusting their association with observation times. Estimating equations are developed for parameter estimation. We show that the resulting estimators are consistent and asymptotically normal, with variance-covariance matrix that has a closed form and can be consistently estimated by the usual plug-in method. One additional advantage of the procedure is that it provides a unified framework to test whether the effect of the latent variable is zero, constant, or time-varying. Simulation studies show that the proposed approach is appropriate for practical use. An application to a bladder cancer data is also given to illustrate the methodology.

Original languageEnglish (US)
Pages (from-to)1093-1102
Number of pages10
Issue number4
StatePublished - Dec 2012


  • Estimating equation method
  • Informative observation times
  • Longitudinal data analysis
  • Time-varying effect

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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