  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.
