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Regularized continuous‐time Markov Model via elastic net
Author(s) -
Huang Shuang ,
Hu Chengcheng ,
Bell Melanie L.,
Billheimer Dean ,
Guerra Stefano ,
Roe Denise ,
Vasquez Monica M.,
Bedrick Edward J.
Publication year - 2018
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.12868
Subject(s) - overfitting , elastic net regularization , covariate , markov chain , markov model , computer science , mathematical optimization , algorithm , mathematics , coordinate descent , path (computing) , variable order markov model , feature selection , artificial intelligence , machine learning , artificial neural network , programming language
Summary 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.