Confidence intervals for the ratio of two median residual lifetimes with left-truncated and right-censored data.
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.
Department of Statistics, National Cheng Kung University, Tainan, Taiwan.
Tsung-Hsien
TH
Tsai
Department of Biostatistics, Columbia University, New York City, U.S.A.
Wei-Yann
WY
Tsai
Department of Statistics, National Cheng Kung University, Tainan, Taiwan.
Yunchan
Y
Chi
Department of Statistics, National Cheng Kung University, Tainan, Taiwan.
Sheng-Mao
SM
Chang
D000368:Aged; D000369:Aged, 80 and over; D003198:Computer Simulation; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D008017:Life Expectancy; D008297:Male; D008875:Middle Aged; D015233:Models, Statistical; D016017:Odds Ratio; D016016:Proportional Hazards Models; D015203:Reproducibility of Results; D018401:Sample Size; D012680:Sensitivity and Specificity; D016019:Survival Analysis; D013624:Taiwan / Q000453:epidemiology
Confidence interval; Empirical likelihood; Left-truncated and right-censored data; Median residual lifetime