Sufficient dimension reduction with simultaneous estimation of effective dimensions for time-to-event data.

Area of Science:

• Statistics
• Biostatistics
• Survival Analysis

Background:

• Sufficient dimension reduction (SDR) offers a flexible, parsimonious nonparametric approach for analyzing covariate-outcome associations when regression models are unknown.
• Existing SDR methods often rely on inverse probability weighting, which can cause instability in small sample sizes.

Purpose of the Study:

• To propose a novel, adaptive estimator for low-dimensional composite scores summarizing covariate contributions to right-censored survival outcomes.
• To simultaneously estimate structural dimension, central subspace, and smoothing bandwidth adaptively from data.

Main Methods:

• The methodology is formulated within a counting process framework.
• The proposed estimator avoids inverse probability weighting, enhancing stability.
• Estimation is implemented using a forward selection algorithm, supported by asymptotic convexity properties.

Main Results:

• The study derives large sample properties for the estimated central subspace, considering data-adaptive structural dimension and bandwidth.
• Numerical simulations and two real-world examples demonstrate the method's effectiveness.

Conclusions:

• The novel SDR estimator provides a stable and adaptive approach for analyzing right-censored survival data.
• The method simplifies the summarization of covariate effects, offering practical advantages over existing techniques.