Estimation and variable selection in a joint model of survival times and longitudinal outcomes with random effects.
Résumé
This paper considers a joint survival and mixed-effects model to explain the survival time from longitudinal data and high-dimensional covariates. The longitudinal data is modeled using a nonlinear effects model, where the regression function serves as a link function incorporated into a Cox model as a covariate. In that way, the longitudinal data is related to the survival time at a given time. Additionally, the Cox model takes into account the inclusion of high-dimensional covariates. The main objectives of this research are two-fold: first, to identify the relevant covariates that contribute to explaining survival time, and second, to estimate all unknown parameters of the joint model. For that purpose, we consider the maximization of a Lasso penalized likelihood. To tackle the optimization problem, we implement a pre-conditioned stochastic gradient to handle the latent variables of the nonlinear mixed-effects model associated with a proximal operator to manage the non-differentiability of the penalty. We provide relevant simulations that showcase the performance of the proposed variable selection and parameters' estimation method in the joint modeling of a Cox and logistic model.
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main.pdf (797.49 Ko)
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beta.png (42.94 Ko)
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beta_penalized.png (54.48 Ko)
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beta_unpenalized.png (52.43 Ko)
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grad_example_run.png (131.97 Ko)
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regularization_path.png (154.31 Ko)
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theta_example_run.png (139.66 Ko)
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violin_penalized_plot.png (232.21 Ko)
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violin_unpenalized_plot.png (233.18 Ko)
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