Confidence intervals for the ratio of two median residual lifetimes with left-truncated and right-censored data

Tsung Hsien Tsai, Wei Yann Tsai, Yun-Chan Chi, Sheng-Mao Chang

Research output: Contribution to journalArticle

Abstract

The confidence intervals for the ratio of two median residual lifetimes are developed for left-truncated and right-censored data. The approach of Su and Wei (1993) is first extended by replacing the Kaplan-Meier survival estimator with the estimator of the conditional survival function (Lynden-Bell, 1971). This procedure does not involve a nonparametric estimation of the probability density function of the failure time. However, the Su and Wei type confidence intervals are very conservative even for larger sample size. Therefore, this article proposes an alternative confidence interval for the ratio of two median residual lifetimes, which is not only without nonparametric estimation of the density function of failure times but is also computationally simpler than the Su and Wei type confidence interval. A simulation study is conducted to examine the accuracy of these confidence intervals and the implementation of these confidence intervals to two real data sets is illustrated.

Original languageEnglish
Pages (from-to)232-241
Number of pages10
JournalBiometrics
Volume72
Issue number1
DOIs
Publication statusPublished - 2016 Mar 1

Fingerprint

Residual Lifetime
Right-censored Data
Probability density function
Confidence interval
confidence interval
Confidence Intervals
Failure Time
Nonparametric Estimation
Kaplan-Meier
Estimator
Survival Function
Density Function
Sample Size
Simulation Study
Alternatives

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

Cite this

@article{3c7868759d8c46f9aa4411c93b9e1ab1,
title = "Confidence intervals for the ratio of two median residual lifetimes with left-truncated and right-censored data",
abstract = "The confidence intervals for the ratio of two median residual lifetimes are developed for left-truncated and right-censored data. The approach of Su and Wei (1993) is first extended by replacing the Kaplan-Meier survival estimator with the estimator of the conditional survival function (Lynden-Bell, 1971). This procedure does not involve a nonparametric estimation of the probability density function of the failure time. However, the Su and Wei type confidence intervals are very conservative even for larger sample size. Therefore, this article proposes an alternative confidence interval for the ratio of two median residual lifetimes, which is not only without nonparametric estimation of the density function of failure times but is also computationally simpler than the Su and Wei type confidence interval. A simulation study is conducted to examine the accuracy of these confidence intervals and the implementation of these confidence intervals to two real data sets is illustrated.",
author = "Tsai, {Tsung Hsien} and Tsai, {Wei Yann} and Yun-Chan Chi and Sheng-Mao Chang",
year = "2016",
month = "3",
day = "1",
doi = "10.1111/biom.12378",
language = "English",
volume = "72",
pages = "232--241",
journal = "Biometrics",
issn = "0006-341X",
publisher = "Wiley-Blackwell",
number = "1",

}

Confidence intervals for the ratio of two median residual lifetimes with left-truncated and right-censored data. / Tsai, Tsung Hsien; Tsai, Wei Yann; Chi, Yun-Chan; Chang, Sheng-Mao.

In: Biometrics, Vol. 72, No. 1, 01.03.2016, p. 232-241.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Confidence intervals for the ratio of two median residual lifetimes with left-truncated and right-censored data

AU - Tsai, Tsung Hsien

AU - Tsai, Wei Yann

AU - Chi, Yun-Chan

AU - Chang, Sheng-Mao

PY - 2016/3/1

Y1 - 2016/3/1

N2 - The confidence intervals for the ratio of two median residual lifetimes are developed for left-truncated and right-censored data. The approach of Su and Wei (1993) is first extended by replacing the Kaplan-Meier survival estimator with the estimator of the conditional survival function (Lynden-Bell, 1971). This procedure does not involve a nonparametric estimation of the probability density function of the failure time. However, the Su and Wei type confidence intervals are very conservative even for larger sample size. Therefore, this article proposes an alternative confidence interval for the ratio of two median residual lifetimes, which is not only without nonparametric estimation of the density function of failure times but is also computationally simpler than the Su and Wei type confidence interval. A simulation study is conducted to examine the accuracy of these confidence intervals and the implementation of these confidence intervals to two real data sets is illustrated.

AB - The confidence intervals for the ratio of two median residual lifetimes are developed for left-truncated and right-censored data. The approach of Su and Wei (1993) is first extended by replacing the Kaplan-Meier survival estimator with the estimator of the conditional survival function (Lynden-Bell, 1971). This procedure does not involve a nonparametric estimation of the probability density function of the failure time. However, the Su and Wei type confidence intervals are very conservative even for larger sample size. Therefore, this article proposes an alternative confidence interval for the ratio of two median residual lifetimes, which is not only without nonparametric estimation of the density function of failure times but is also computationally simpler than the Su and Wei type confidence interval. A simulation study is conducted to examine the accuracy of these confidence intervals and the implementation of these confidence intervals to two real data sets is illustrated.

UR - http://www.scopus.com/inward/record.url?scp=84941313345&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84941313345&partnerID=8YFLogxK

U2 - 10.1111/biom.12378

DO - 10.1111/biom.12378

M3 - Article

VL - 72

SP - 232

EP - 241

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 1

ER -