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：本文提出一种联合生存与混合效应模型，用于通过纵向数据和高维协变量解释生存时间。纵向数据采用非线性效应模型进行建模，其中回归函数作为连接函数纳入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建立关联。此外，Cox模型还考虑了高维协变量的纳入。本研究的主要目标有两个：首先，识别对解释生存时间有贡献的相关协变量；其次，估计联合模型的所有未知参数。为此，我们考虑对Lasso惩罚似然函数进行最大化处理。针对该优化问题，我们实现了预条件随机梯度算法以处理非线性混合效应模型的潜变量，并结合近端算子处理惩罚项不可微的问题。我们通过相关仿真实验，展示了所提出的变量选择与参数估计方法在Cox模型与逻辑模型联合建模中的性能表现。