Confidence Band Estimation for Survival Random Forests

TL;DR

This paper introduces a statistically valid and computationally feasible method for estimating confidence bands for survival random forests by extending infinite-order incomplete U-statistics and modeling the cumulative hazard as a Gaussian process.

Contribution

It proposes a novel approach to confidence band estimation for survival random forests using variance-covariance estimation and Gaussian process simulation, addressing a key gap in the field.

Findings

Accurately estimates confidence bands with proper coverage.

Computationally efficient when subsampling size is controlled.

Validated through numerical studies and real data application.

Abstract

Survival random forest is a popular machine learning tool for modeling censored survival data. However, there is currently no statistically valid and computationally feasible approach for estimating its confidence band. This paper proposes an unbiased confidence band estimation by extending recent developments in infinite-order incomplete U-statistics. The idea is to estimate the variance-covariance matrix of the cumulative hazard function prediction on a grid of time points. We then generate the confidence band by viewing the cumulative hazard function estimation as a Gaussian process whose distribution can be approximated through simulation. This approach is computationally easy to implement when the subsampling size of a tree is no larger than half of the total training sample size. Numerical studies show that our proposed method accurately estimates the confidence band and achieves desired coverage rate. We apply this method to veterans' administration lung cancer data.