From regression rank scores to robust inference for censored quantile regression

Quantile regression for right- or left-censored outcomes has attracted attention due to its ability to accommodate heterogeneity in regression analysis of survival times. Rank-based inferential methods have desirable properties for quantile regression analysis, but censored data poses challenges to the general concept of ranking. In this article, we propose a notion of censored quantile regression rank scores, which enables us to construct rank-based tests for quantile regression coefficients at a single quantile or over a quantile region. A model-based bootstrap algorithm is proposed to implement the tests. We also illustrate the advantage of focusing on a quantile region instead of a single quantile level when testing the effect of certain covariates in a quantile regression framework.