Nearest Neighbor and Kernel Survival Analysis: Nonasymptotic Error Bounds and Strong Consistency Rates

TL;DR

This paper provides the first nonasymptotic error bounds and strong consistency rates for Kaplan-Meier-based nearest neighbor and kernel survival estimators in metric spaces, supported by experimental comparisons.

Contribution

It introduces nonasymptotic error bounds and strong consistency results for survival estimators in metric spaces, extending theoretical guarantees to kernel and nearest neighbor methods.

Findings

Kernel survival estimator performs well with kernels learned from random survival forests.

Theoretical bounds match existing lower bounds up to a log factor.

Experimental results validate the effectiveness of proposed estimators.

Abstract

We establish the first nonasymptotic error bounds for Kaplan-Meier-based nearest neighbor and kernel survival probability estimators where feature vectors reside in metric spaces. Our bounds imply rates of strong consistency for these nonparametric estimators and, up to a log factor, match an existing lower bound for conditional CDF estimation. Our proof strategy also yields nonasymptotic guarantees for nearest neighbor and kernel variants of the Nelson-Aalen cumulative hazards estimator. We experimentally compare these methods on four datasets. We find that for the kernel survival estimator, a good choice of kernel is one learned using random survival forests.