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Model Selection for Cox Models with Time-Varying Coefficients

Authors

  • Jun Yan,

    Corresponding author
    1. Department of Statistics, University of Connecticut, Storrs, Connecticut 06269, U.S.A.
    2. Institute for Public Health Research, University of Connecticut Health Center, East Hartford, Connecticut 06108, U.S.A.
    3. Center for Environmental Sciences and Engineering, University of Connecticut, Storrs, Connecticut 06269, U.S.A.
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  • Jian Huang

    1. Department of Statistics and Actuarial Science, University of Iowa, Iowa City, Iowa 52242, U.S.A.
    2. Department of Biostatistics, School of Public Health, University of Iowa, Iowa City, Iowa 52242, U.S.A.
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email: jun.yan@uconn.edu

Abstract

Summary Cox models with time-varying coefficients offer great flexibility in capturing the temporal dynamics of covariate effects on right-censored failure times. Because not all covariate coefficients are time varying, model selection for such models presents an additional challenge, which is to distinguish covariates with time-varying coefficient from those with time-independent coefficient. We propose an adaptive group lasso method that not only selects important variables but also selects between time-independent and time-varying specifications of their presence in the model. Each covariate effect is partitioned into a time-independent part and a time-varying part, the latter of which is characterized by a group of coefficients of basis splines without intercept. Model selection and estimation are carried out through a fast, iterative group shooting algorithm. Our approach is shown to have good properties in a simulation study that mimics realistic situations with up to 20 variables. A real example illustrates the utility of the method.

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