Adaptive estimation of the baseline hazard function in the Cox model by model selection, with high-dimensional covariates

Agathe Guilloux (1) , Sarah Lemler (2) , Marie-Luce Taupin (2)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée
2 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry

The purpose of this article is to provide an adaptive estimator of the baseline function in the Cox model with high-dimensional covariates. We consider a two-step procedure : first, we estimate the regression parameter of the Cox model via a Lasso procedure based on the partial log-likelihood, secondly, we plug this Lasso estimator into a least-squares type criterion and then perform a model selection procedure to obtain an adaptive penalized contrast estimator of the baseline function. Using non-asymptotic estimation results stated for the Lasso estimator of the regression parameter , we establish a non-asymptotic oracle inequality for this penalized contrast estimator of the baseline function, which highlights the discrepancy of the rate of convergence when the dimension of the covariates increases.

Mots clés: Conditional hazard rate function; Survival analysis; Semi-parametric model; Right-censored data; Cox's proportional hazards model; Non-asymptotic oracle inequalities; Model selection; High-dimensional covariates; Nonparametric model; Concentration inequalities

Domaines: Théorie [stat.TH]; Applications [stat.AP]

Agathe Guilloux, Sarah Lemler, Marie-Luce Taupin. Adaptive estimation of the baseline hazard function in the Cox model by model selection, with high-dimensional covariates. 2015. ⟨hal-01120683v1⟩