Double bias correction for high-dimensional sparse additive hazards regression with covariate measurement errors

Xiaobo Wang (), Jiayu Huang (), Guosheng Yin (), Jian Huang () and Yuanshan Wu ()
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Xiaobo Wang: Wuhan University
Jiayu Huang: Wuhan University
Guosheng Yin: University of Hong Kong
Jian Huang: University of Iowa
Yuanshan Wu: Zhongnan University of Economics and Law

Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, 2023, vol. 29, issue 1, No 5, 115-141

Abstract: Abstract We propose an inferential procedure for additive hazards regression with high-dimensional survival data, where the covariates are prone to measurement errors. We develop a double bias correction method by first correcting the bias arising from measurement errors in covariates through an estimating function for the regression parameter. By adopting the convex relaxation technique, a regularized estimator for the regression parameter is obtained by elaborately designing a feasible loss based on the estimating function, which is solved via linear programming. Using the Neyman orthogonality, we propose an asymptotically unbiased estimator which further corrects the bias caused by the convex relaxation and regularization. We derive the convergence rate of the proposed estimator and establish the asymptotic normality for the low-dimensional parameter estimator and the linear combination thereof, accompanied with a consistent estimator for the variance. Numerical experiments are carried out on both simulated and real datasets to demonstrate the promising performance of the proposed double bias correction method.

Keywords: Bias correction; Confidence interval; Error-in-variable; Estimating equation; High dimensions; Survival analysis (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10985-022-09568-2

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