Nonparametric inference for rates with censored survival data
type: Item
instance of: scholarly article
title: Nonparametric inference for rates with censored survival data
zbMATH Open document ID: 0598.62050
author: Brian S. Yandell
published in: The Annals of Statistics
publication date: 1983-01-01T00:00:00Z
review text: This paper develops asymptotic confidence bands and hypotheses tests for the hazard rate function h(x) under the random censorship model which assumes that the lifetimes and censoring times for the n sampled individuals constitute independent and identically distributed random pairs. Attention is focused on estimators of the form \[ h_ n(x)=\int K_ b(x,y)dH_ n(y), \] where \(H_ n(\cdot)\) is the Nelson-Aalen empirical cumulative hazard rate, \(K_ b\) is a kernel of the form w[(x- y)/b]/b with w(\(\cdot)\) a density, and the band-width \(b\to 0\) and nb\(\to \infty\) as \(n\to \infty\). Strong approximation results are derived for the pivot process \[ W_ n(x)=[nb/V_ h(x)]^{1/2}[h_ n(x)-E h_ n(x)], \] where \(V_ h(x)=\lim nb Var(h_ n(x))\). The limiting process is then inverted to derive simultaneous asymptotic confidence bands for h(x). Further applications of the strong approximation include a goodness-of-fit test for hypotheses of the form \(h(x)=h_ 0(x,\theta)\), and a two-sample test for the equality of the hazard rates. The effects of censoring on the bias, variance and maximum absolute deviation are investigated by simulations with exponential survival and censoring distributions. An application is illustrated with a data set from a survival experiment with serial sacrifice.
Mathematics Subject Classification ID: 62G15
Mathematics Subject Classification ID: 62N05
Mathematics Subject Classification ID: 62G10
Mathematics Subject Classification ID: 62G05
zbMATH DE Number: 3965206
zbMATH Keywords: life testing
zbMATH Keywords: censored survival data
zbMATH Keywords: asymptotic confidence bands
zbMATH Keywords: hazard rate function
zbMATH Keywords: random censorship model
zbMATH Keywords: censoring
zbMATH Keywords: estimators
zbMATH Keywords: Nelson- Aalen empirical cumulative hazard rate
zbMATH Keywords: Strong approximation results
zbMATH Keywords: pivot process
zbMATH Keywords: goodness-of-fit test
zbMATH Keywords: two-sample test for the equality of the hazard rates
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346326
OpenAlex ID: W1581735175
DOI: 10.1214/AOS/1176346326
description: scientific article; zbMATH DE number 3965206