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

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.