Analysis on censored quantile residual life model via spline smoothing

Abstract

We propose a general class of quantile residual life models, where a specific quantile of the residual life time, conditional on an individual has survived up to time t, is a function of certain covariates with their coefficients varying over time. The varying coefficients are assumed to be smooth unspecified functions of t. We propose to estimate the coefficient functions using spline approximation. Incorporating the spline representation directly into a set of unbiased estimating equations, we obtain a one-step estimation procedure, and we show that this leads to a uniformly consistent estimator. To obtain further computational simplification, we propose a two-step estimation approach in which we estimate the coefficients on a series of time points first, and follow this with spline smoothing. We compare the two methods in terms of their asymptotic efficiency and computational complexity. We further develop inference tools to test the significance of the covariate effect on residual life. The finite sample performance of the estimation and testing procedures are further illustrated through numerical experiments. We also apply the methods to a data set from a neurological study.

Quantile regression analysis of length‐biased survival data

“…The inverse probability principle was also adopted by Bang & Tsiatis (), Jung et al . (), Ma & Wei (), Peng & Fine (), Ma & Yin () and Leng & Tong (), to name a few, for censored quantile regression in various contexts where the data are not subject to length‐bias sampling.…”

“…Ma & Yin (), Jung et al . () and Ma & Wei () studied quantile residual life models. However, all these work assumes that the sample under analysis is a random sample from the population of interest.…”

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

“…Meanwhile quantile residual lifetime models provide more complete and informative interpretations than mean residual lifetime models, especially when the distribution of the residual lifetime is nonsymmetric or skewed. Some quantile residual lifetime models have been studied by Jeong, Jung, & Costantiono (), Jeong & Fine (, ), Jung, Jeong, & Bandos (), Ma & Yin (), and Ma & Wei () among others. Recently Lin, Zhang, & Zhou () proposed an estimator of conditional quantile residual lifetime based on the Cox proportional hazard model with right‐censored data.…”

Pseudo-value approach for conditional quantile residual lifetime analysis for clustered survival and competing risks data with applications to bone marrow transplant data

“…Quantile residual lifetime analysis is often preferred when the distribution of the residual lifetime is skewed (Ma and Wei, 2012). Statistical methods for residual lifetime analysis with survival data have been recently developed as in Kim, Zhou and Jeong (2012) and Lin, Zhang and Zhou (2014).…”