Counting process-based dimension reduction methods for censored outcomes. (7th January 2019)

• Record Type: Journal Article
• Authors: Sun, Qiang; Zhu, Ruoqing; Wang, Tao; Zeng, Donglin
• Is Part Of: Biometrika. Volume 106:Number 1(2019:Mar.)
• Page Start: 181
• Page End: 196
• Publication Date: 2019-01-07
• Subjects: Estimating equation -- Semiparametric inference -- Sliced inverse regression -- Sufficient dimension reduction -- Survival analysis; Biometry -- Periodicals; 570.1519505
• DOI: 10.1093/biomet/asy064
• Languages: English
• ISSNs: 0006-3444

Abstract

SUMMARY: We propose counting process-based dimension reduction methods for right-censored survival data. Semiparametric estimating equations are constructed to estimate the dimension reduction subspace for the failure time model. Our methods address two limitations of existing approaches. First, using the counting process formulation, they do not require estimation of the censoring distribution to compensate for the bias in estimating the dimension reduction subspace. Second, the nonparametric estimation involved adapts to the structural dimension, so our methods circumvent the curse of dimensionality. Asymptotic normality is established for the estimators. We propose a computationally efficient approach that requires only a singular value decomposition to estimate the dimension reduction subspace. Numerical studies suggest that our new approaches exhibit significantly improved performance. The methods are implemented in the $\texttt{R}$ package $\texttt{orthoDr}$ .