Deep Nonparametric Inference for Conditional Hazard Function

TL;DR

This paper introduces a deep learning-based nonparametric method for estimating the conditional hazard function in survival analysis, offering flexible modeling, theoretical guarantees, and improved testing procedures.

Contribution

It develops a novel DNN-based estimator for the conditional hazard function with theoretical error bounds and asymptotic properties, along with new goodness-of-fit and treatment comparison tests.

Findings

Estimator achieves superior accuracy in simulations.

Tests demonstrate improved power over existing methods.

Method effectively handles right-censored survival data.

Abstract

We propose a novel deep learning approach to nonparametric statistical inference for the conditional hazard function of survival time with right-censored data. We use a deep neural network (DNN) to approximate the logarithm of a conditional hazard function given covariates and obtain a DNN likelihood-based estimator of the conditional hazard function. Such an estimation approach renders model flexibility and hence relaxes structural and functional assumptions on conditional hazard or survival functions. We establish the nonasymptotic error bound and functional asymptotic normality of the proposed estimator. Subsequently, we develop new one-sample tests for goodness-of-fit evaluation and two-sample tests for treatment comparison. Both simulation studies and real application analysis show superior performances of the proposed estimators and tests in comparison with existing methods.