Comparison of Several Confidence Intervals for Median Residual Lifetime with Left-Truncated and Right-Censored Data

• Activity Number: 253
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Tsung-Hsien Tsai*+ and Yunchan Chi and Yi-Hsuan Tu and Wen-Yan Tsai
• Companies: National Cheng Kung University and National Cheng Kung University and National Cheng Kung University and Columbia University
• Keywords: Kaplan-Meier estimator ; left-truncated and right-censored data ; median residual lifetime ; point-wise confidence interval

Abstract

For left-truncated and right-censored data, the technique in Brookmeyer and Crowley (1982) is extended to construct a point-wise confidence interval for median residual lifetime in a homogenous population by inverting the acceptance region of a size a test. The test statistic is based on a conditional survival function estimator (Lynden-Bell (1971)), which is an analogue of Kaplan-Meier estimator. This procedure is computational simpler than the score type confidence interval in Jeong et al. (2008) and empirical likelihood confidence interval in Zhou and Jeong (2010). These procedures do not involve a nonparametric estimation of the probability density function of failure times. Further, transformations of conditional survival function estimator are applied to improve the approximation to the asymptotic distribution for small sample size, such as arcsine square root transformation. A simulation study is conducted to investigate the accuracy of these confidence intervals and the implementation of these confidence intervals to one real data set is illustrated.