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This paper considers a joint survival and mixed-effects model to explain thesurvival time from longitudinal data and high-dimensional covariates. Thelongitudinal data is modeled using a nonlinear effects model, where theregression function serves as a link function incorporated into a Cox model asa covariate. In that way, the longitudinal data is related to the survival timeat a given time. Additionally, the Cox model takes into account the inclusionof high-dimensional covariates. The main objectives of this research aretwo-fold: first, to identify the relevant covariates that contribute toexplaining survival time, and second, to estimate all unknown parameters of thejoint model. For that purpose, we consider the maximization of a Lassopenalized likelihood. To tackle the optimization problem, we implement apre-conditioned stochastic gradient to handle the latent variables of thenonlinear mixed-effects model associated with a proximal operator to manage thenon-differentiability of the penalty. We provide relevant simulations thatshowcase the performance of the proposed variable selection and parameters'estimation method in the joint modeling of a Cox and logistic model.

Estimation and variable selection in a joint model of survival times and longitudinal outcomes with random effects