Antoine Caillebotte | Searcharxiv

arXiv2025

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

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.

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arXiv2025

Estimation and variable selection in high dimension in nonlinear mixed-effects models

We consider nonlinear mixed effects models including high-dimensional covariates to model individual parameters variability. The objective is to identify relevant covariates among a large set under sparsity assumption and to estimate model parameters. To face the high dimensional setting we consider a regularized estimator namely the maximum likelihood estimator penalized with the l1-penalty. We rely on the use of the eBIC model choice criteria to select an optimal reduced model. Then we estimate the parameters by maximizing the likelihood of the reduced model. We calculate in practice the maximum likelihood estimator penalized with the l1-penalty though a weighted proximal stochastic gradient descent algorithm with an adaptive learning rate. This choice allows us to consider very general models, in particular models that do not belong to the curved exponential family. We demonstrate first in a simple linear toy model through a simulation study the good convergence properties of this optimization algorithm. We compare then the performance of the proposed methodology with those of the \glmmLasso procedure in a linear mixed effects model in a simulation study. We illustrate also its performance in a nonlinear mixed-effects logistic growth model through simulation. We finally highlight the beneficit of the proposed procedure relying on an integrated single step approach regarding two others two steps approaches for variable selection objective.

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