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.

翻译：本文考虑一种联合生存与混合效应模型，用于解释纵向数据和高维协变量下的生存时间。纵向数据采用非线性效应模型进行建模，其中回归函数作为链接函数纳入Cox模型作为协变量。通过这种方式，纵向数据与特定时间点的生存时间相关联。此外，Cox模型还考虑了高维协变量的包含。本研究的主要目标有两个：第一，识别有助于解释生存时间的相关协变量；第二，估计联合模型中所有未知参数。为此，我们考虑最大化Lasso惩罚似然函数。为了解决优化问题，我们实现了一种预处理随机梯度方法，用于处理非线性混合效应模型中的潜在变量，并结合近端算子来管理惩罚项的非可微性。我们提供了相关模拟，展示了所提出的变量选择和参数估计方法在Cox与logistic模型联合建模中的性能。