Regularized continuous-time Markov Model via elastic net

Shuang Huang, Chengcheng Hu, Melanie L. Bell, Dean Billheimer, Stefano Guerra, Denise Roe, Monica M Vasquez, Edward J Bedrick

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Continuous-time Markov models are commonly used to analyze longitudinal transitions between multiple disease states in panel data, where participants’ disease states are only observed at multiple time points, and the exact state paths between observations are unknown. However, when covariate effects are incorporated and allowed to vary for different transitions, the number of potential parameters to estimate can become large even when the number of covariates is moderate, and traditional maximum likelihood estimation and subset model selection procedures can easily become unstable due to overfitting. We propose a novel regularized continuous-time Markov model with the elastic net penalty, which is capable of simultaneous variable selection and estimation for large number of parameters. We derive an efficient coordinate descent algorithm to solve the penalized optimization problem, which is fully automatic and data driven. We further consider an extension where one of the states is death, and time of death is exactly known but the state path leading to death is unknown. The proposed method is extensively evaluated in a simulation study, and demonstrated in an application to real-world data on airflow limitation state transitions.

Original languageEnglish (US)
Pages (from-to)1045-1054
Number of pages10
Issue number3
StatePublished - Sep 2018


  • Continuous-time Markov model
  • Elastic net penalty
  • Panel data
  • Regularization

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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