A new kernel estimator of hazard ratio and its asymptotic mean squared error

TL;DR

This paper introduces a new kernel estimator for the hazard ratio in survival analysis, demonstrating reduced asymptotic mean squared error and improved numerical performance over existing methods.

Contribution

It proposes a novel kernel estimator of the hazard ratio based on a modification of existing methods, with theoretical analysis and bias reduction techniques.

Findings

The new estimator has smaller asymptotic variance than naive estimators.

Bias reduction improves the estimator's mean squared error.

Numerical results show enhanced performance of the proposed method.

Abstract

The hazard function is a ratio of a density and survival function, and it is a basic tool of the survival analysis. In this paper we propose a kernel estimator of the hazard ratio function, which are based on a modification of \'{C}wik and Mielniczuk's method. We study nonparametric estimators of the hazard function and compare those estimators by means of asymptotic mean squared error ($AMSE$). We obtain asymptotic bias and variance of the new estimator, and compare them with a naive estimator. The asymptotic variance of the new estimator is always smaller than the naive estimator's, so we also discuss an improvement of $AMSE$ using Terrell and Scott's bias reduction method. The new modified estimator ensures the non-negativity, and we demonstrate the numerical improvement.