Premium
Confidence intervals for the ratio of two median residual lifetimes with left‐truncated and right‐censored data
Author(s) -
Tsai TsungHsien,
Tsai WeiYann,
Chi Yunchan,
Chang ShengMao
Publication year - 2016
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.12378
Subject(s) - confidence interval , cdf based nonparametric confidence interval , statistics , mathematics , robust confidence intervals , nonparametric statistics , estimator , residual , coverage probability , confidence distribution , confidence and prediction bands , survival function , tolerance interval , algorithm
Summary 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.