Nonparametric and semiparametric estimation of quantile residual lifetime for length‐biased and right‐censored data

Abstract

Quantile residual lifetime models are often of concern in survival analysis, especially when studying a chronic or irreversible disease like dementia. In the past several decades residual life models have been studied extensively with right‐censored survival data. However these methods are not suitable to analyze the length‐biased and right‐censored data from the prevalent cohort sampling. In this article we propose nonparametric and semiparametric model‐based procedures to estimate the quantile residual lifetime with censored length‐biased data. Two test statistics are established for comparing the quantile residual lifetimes of two groups, evaluated, respectively, on ratio and difference in terms of type I error probabilities and powers. Some simulations are conducted to compare the proposed method with existing approaches. Real dementia data from the National Alzheimer's Coordinating Center are used to illustrate the proposed estimation methods by estimating the quantile residual lifetimes of the dementia patients. The Canadian Journal of Statistics 45: 220–250; 2017 © 2017 Statistical Society of Canada

Inference on quantile residual life for length-biased survival data

“…In addition, we have shown how to construct confidence intervals for the quantiles of length-biased right-censored survival data. Moreover, bootstrap-based inference did not provide good coverage when the censoring rates were larger [30%, maximum considered in Wang et al (2017)]. Our influence-function-based variance estimation maintained approximately nominal coverage when censoring rate was as high as 51%.…”

“…We have developed the asymptotic inference procedures for the two estimators and demonstrated how the confidence interval for QRL can be constructed by inverting a proposed test statistic. Our methods are similar to those described as TJW and HQ methods in Wang et al (2017) where variance of these methods were estimated using a bootstrap approach. In contrast, we have provided explicit variance estimators based on influence functions and implemented it in the data analysis and simulation.…”

“…Since it is based on survival distribution estimate which does not have a closed-form expression, computation of this estimator and its asymptotic properties is relatively complicated. Although Liu et al (2015) approach can be extended to censored length-biased data, but this method does not utilize the information of the truncation variable, making it less efficient than that proposed in Wang et al (2017).…”

“…Specifically, we propose two estimators of quantile residual life function based on the survival functions estimated using truncation product limit method and Huang and Qin (2011) method, and show that the latter is more efficient than the QRL function estimated using the truncation product limit estimator. Our method is similar to those described as TJW and HQ methods in Wang et al (2017), where the variance was estimated using a bootstrap approach. In contrast, we provide explicit variance estimator based on influence functions and implement it.…”