A new reproducing kernel based nonlinear dimension reduction method for survival data

TL;DR

This paper introduces RDSIR, a novel nonlinear dimension reduction method for survival data based on RKHS and SIR theories, capable of capturing complex nonlinear relationships while adjusting for censoring bias.

Contribution

The paper proposes RDSIR, a new RKHS-based double slicing approach for nonlinear dimension reduction in survival analysis, with theoretical properties and practical efficiency.

Findings

RDSIR effectively captures nonlinear structures in survival data.

The method is computationally efficient with fast calculation speed.

RDSIR performs comparably to linear SDR methods on real and simulated data.

Abstract

Based on the theories of sliced inverse regression (SIR) and reproducing kernel Hilbert space (RKHS), a new approach RDSIR (RKHS-based Double SIR) to nonlinear dimension reduction for survival data is proposed and discussed. An isometrically isomorphism is constructed based on RKHS property, then the nonlinear function in the RKHS can be represented by the inner product of two elements which reside in the isomorphic feature space. Due to the censorship of survival data, double slicing is used to estimate weight function or conditional survival function to adjust for the censoring bias. The sufficient dimension reduction (SDR) subspace is estimated by a generalized eigen-decomposition problem. Our method is computationally efficient with fast calculation speed and small computational burden. The asymptotic property and the convergence rate of the estimator are also discussed based on the perturbation theory. Finally, we illustrate the performance of RDSIR on simulated and real data to confirm that RDSIR is comparable with linear SDR method. The most important is that RDSIR can also extract nonlinearity in survival data effectively.