Simultaneous variable selection for joint models of longitudinal and survival outcomes

Zangdong He, Wanzhu Tu, Sijian Wang, Haoda Fu, Zhangsheng Yu

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


Joint models of longitudinal and survival outcomes have been used with increasing frequency in clinical investigations. Correct specification of fixed and random effects is essential for practical data analysis. Simultaneous selection of variables in both longitudinal and survival components functions as a necessary safeguard against model misspecification. However, variable selection in such models has not been studied. No existing computational tools, to the best of our knowledge, have been made available to practitioners. In this article, we describe a penalized likelihood method with adaptive least absolute shrinkage and selection operator (ALASSO) penalty functions for simultaneous selection of fixed and random effects in joint models. To perform selection in variance components of random effects, we reparameterize the variance components using a Cholesky decomposition; in doing so, a penalty function of group shrinkage is introduced. To reduce the estimation bias resulted from penalization, we propose a two-stage selection procedure in which the magnitude of the bias is ameliorated in the second stage. The penalized likelihood is approximated by Gaussian quadrature and optimized by an EM algorithm. Simulation study showed excellent selection results in the first stage and small estimation biases in the second stage. To illustrate, we analyzed a longitudinally observed clinical marker and patient survival in a cohort of patients with heart failure.

Original languageEnglish (US)
Pages (from-to)178-187
Number of pages10
Issue number1
StatePublished - Mar 1 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


  • Cholesky decomposition
  • EM algorithm
  • Gaussian quadrature
  • Joint models
  • Mixed effect selection


Dive into the research topics of 'Simultaneous variable selection for joint models of longitudinal and survival outcomes'. Together they form a unique fingerprint.

Cite this