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

TL;DR

This paper introduces a joint modeling approach for survival times and longitudinal data with high-dimensional covariates, employing regularization and stochastic optimization to identify relevant variables and estimate parameters.

Contribution

It proposes a novel method combining non-linear mixed-effects models with Cox models, incorporating l1-penalization and adaptive stochastic gradient for variable selection in high-dimensional settings.

Findings

Effective variable selection demonstrated through simulations

Method handles censoring and correlation in data

Accurate parameter estimation in complex joint models

Abstract

We consider a joint survival and mixed-effects model to explain the survival time from longitudinal data and high-dimensional covariates in a population. The longitudinal data is modeled using a non linear mixed-effects model to account for the inter-individual variability in the population. The corresponding regression function serves as a link function incorporated into the survival model. In that way, the longitudinal data is related to the survival time. We consider a Cox model that takes into account both high-dimensional covariates and the link function. There are two main objectives: first, identify the relevant covariates that contribute to explaining survival time, and second, estimate all unknown parameters of the joint model. For the first objective, we consider the estimate defined by maximizing the marginal log-likelihood regularized with a l1-penalty term. To tackle the optimization problem, we implement an adaptive stochastic gradient to handle the latent variables of the non linear mixed-effects model associated with a proximal operator to manage the non-differentiability of the penalty. We rely on an eBIC model choice criterion to select an optimal value for the regularization parameter. Once the relevant covariates are selected, we re-estimate the parameters in the reduced model by maximizing the likelihood using an adaptive stochastic gradient descent. We provide relevant simulations that showcase the performance of the proposed variable selection and parameter estimation method in the joint model. We investigate the effect of censoring and of the presence of correlation between the individual parameters in the mixed model.