Adaptive estimation of the baseline hazard function in the Cox model by model selection, with high-dimensional covariates
نویسندگان
چکیده
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.
منابع مشابه
Tire demand planning based on reliability and operating environment
Tires represent a critical spare part in mines. There is a shortage of medium and large tires. In addition, with increased mining activities and the creation of new mines, the demand for tires has increased significantly. Thus, it is particularly important for mining engineers to identify tire characteristics and correctly manage the spare part inventory. Spare parts management is critical from...
متن کاملPenalized Estimators in Cox Regression Model
The proportional hazard Cox regression models play a key role in analyzing censored survival data. We use penalized methods in high dimensional scenarios to achieve more efficient models. This article reviews the penalized Cox regression for some frequently used penalty functions. Analysis of medical data namely ”mgus2” confirms the penalized Cox regression performs better than the cox regressi...
متن کاملPath consistent model selection in additive risk model via Lasso.
As a flexible alternative to the Cox model, the additive risk model assumes that the hazard function is the sum of the baseline hazard and a regression function of covariates. For right censored survival data when variable selection is needed along with model estimation, we propose a path consistent model selector using a modified Lasso approach, under the additive risk model assumption. We sho...
متن کاملAdaptive kernel estimation of the baseline function in the Cox model with high-dimensional covariates
We propose a novel kernel estimator of the baseline function in a general highdimensional Cox model, for which we derive non-asymptotic rates of convergence. To construct our estimator, we first estimate the regression parameter in the Cox model via a LASSO procedure. We then plug this estimator into the classical kernel estimator of the baseline function, obtained by smoothing the so-called Br...
متن کاملبرآورد خطای پیش بینی برای وضعیت بقا و کاربرد آن درتحلیل بقای بیماران مبتلا به سرطان روده بزرگ
Introduction: Colorectal cancer is one of the most widespread and killer among cancers. It is important that we predict what status people have in the future. The purpose of this study was comparison of the Cox model and Kaplan-Meier curve with IBS and also identifying the factors about predicted survival time of patients with colon cancer. Materials & Methods: This paper is related to colore...
متن کامل