Nonparametric estimation for length-biased and right-censored data

Chiung Yu Huang, Jing Qin

Research output: Contribution to journalArticle

Abstract

This paper considers survival data arising from length-biased sampling, where the survival times are left truncated by uniformly distributed random truncation times. We propose a nonparametric estimator that incorporates the information about the length-biased sampling scheme. The new estimator retains the simplicity of the truncation product-limit estimator with a closed-form expression, and has a small efficiency loss compared with the nonparametric maximum likelihood estimator, which requires an iterative algorithm. Moreover, the asymptotic variance of the proposed estimator has a closed form, and a variance estimator is easily obtained by plug-in methods. Numerical simulation studies with practical sample sizes are conducted to compare the performance of the proposed method with its competitors. A data analysis of the Canadian Study of Health and Aging is conducted to illustrate the methods and theory.

Original languageEnglish (US)
Pages (from-to)177-186
Number of pages10
JournalBiometrika
Volume98
Issue number1
DOIs
StatePublished - Mar 2011
Externally publishedYes

Fingerprint

Biased Sampling
Right-censored Data
Nonparametric Estimation
Truncation
Biased
Closed-form
Plug-in Method
Product-limit Estimator
Sampling
Nonparametric Maximum Likelihood Estimator
Estimator
Variance Estimator
Survival Data
Survival Time
Nonparametric Estimator
Asymptotic Variance
Iterative Algorithm
Maximum likelihood
Simplicity
Data analysis

Keywords

  • Backward and forward recurrence time
  • Cross-sectional sampling
  • Partial likelihood
  • Random truncation
  • Renewal process

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics
  • Statistics, Probability and Uncertainty

Cite this

Nonparametric estimation for length-biased and right-censored data. / Huang, Chiung Yu; Qin, Jing.

In: Biometrika, Vol. 98, No. 1, 03.2011, p. 177-186.

Research output: Contribution to journalArticle

Huang, Chiung Yu ; Qin, Jing. / Nonparametric estimation for length-biased and right-censored data. In: Biometrika. 2011 ; Vol. 98, No. 1. pp. 177-186.
@article{aeab301c60a642b8b0cedcbfc2e4d13b,
title = "Nonparametric estimation for length-biased and right-censored data",
abstract = "This paper considers survival data arising from length-biased sampling, where the survival times are left truncated by uniformly distributed random truncation times. We propose a nonparametric estimator that incorporates the information about the length-biased sampling scheme. The new estimator retains the simplicity of the truncation product-limit estimator with a closed-form expression, and has a small efficiency loss compared with the nonparametric maximum likelihood estimator, which requires an iterative algorithm. Moreover, the asymptotic variance of the proposed estimator has a closed form, and a variance estimator is easily obtained by plug-in methods. Numerical simulation studies with practical sample sizes are conducted to compare the performance of the proposed method with its competitors. A data analysis of the Canadian Study of Health and Aging is conducted to illustrate the methods and theory.",
keywords = "Backward and forward recurrence time, Cross-sectional sampling, Partial likelihood, Random truncation, Renewal process",
author = "Huang, {Chiung Yu} and Jing Qin",
year = "2011",
month = "3",
doi = "10.1093/biomet/asq069",
language = "English (US)",
volume = "98",
pages = "177--186",
journal = "Biometrika",
issn = "0006-3444",
publisher = "Oxford University Press",
number = "1",

}

TY - JOUR

T1 - Nonparametric estimation for length-biased and right-censored data

AU - Huang, Chiung Yu

AU - Qin, Jing

PY - 2011/3

Y1 - 2011/3

N2 - This paper considers survival data arising from length-biased sampling, where the survival times are left truncated by uniformly distributed random truncation times. We propose a nonparametric estimator that incorporates the information about the length-biased sampling scheme. The new estimator retains the simplicity of the truncation product-limit estimator with a closed-form expression, and has a small efficiency loss compared with the nonparametric maximum likelihood estimator, which requires an iterative algorithm. Moreover, the asymptotic variance of the proposed estimator has a closed form, and a variance estimator is easily obtained by plug-in methods. Numerical simulation studies with practical sample sizes are conducted to compare the performance of the proposed method with its competitors. A data analysis of the Canadian Study of Health and Aging is conducted to illustrate the methods and theory.

AB - This paper considers survival data arising from length-biased sampling, where the survival times are left truncated by uniformly distributed random truncation times. We propose a nonparametric estimator that incorporates the information about the length-biased sampling scheme. The new estimator retains the simplicity of the truncation product-limit estimator with a closed-form expression, and has a small efficiency loss compared with the nonparametric maximum likelihood estimator, which requires an iterative algorithm. Moreover, the asymptotic variance of the proposed estimator has a closed form, and a variance estimator is easily obtained by plug-in methods. Numerical simulation studies with practical sample sizes are conducted to compare the performance of the proposed method with its competitors. A data analysis of the Canadian Study of Health and Aging is conducted to illustrate the methods and theory.

KW - Backward and forward recurrence time

KW - Cross-sectional sampling

KW - Partial likelihood

KW - Random truncation

KW - Renewal process

UR - http://www.scopus.com/inward/record.url?scp=79952124267&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952124267&partnerID=8YFLogxK

U2 - 10.1093/biomet/asq069

DO - 10.1093/biomet/asq069

M3 - Article

C2 - 23049126

AN - SCOPUS:79952124267

VL - 98

SP - 177

EP - 186

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 1

ER -