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 accommodate heterogeneity in analysis of survival times. Rank-based inferential methods have desirable properties quantile analysis, but censored data poses challenges the general concept ranking. In this article, we propose a notion rank scores, which enables us construct rank-based tests coefficients at single over region. A model-based bootstrap algorithm is proposed implement tests. We also illustrate advantage focusing on region instead level when testing effect certain covariates framework. En analyse de survie pour données censurées à gauche ou droite, la régression suscité beaucoup d'attention en raison sa capacité accommoder l'hétérogénéité dans le cadre d'analyses régression. Les méthodes inférentielles fondées sur les rangs ont nombreuses propriétés attrayantes des quantile, mais elles sont confrontées défis posés par d'ordre présence censure. Pour contourner cette difficulté, auteurs ce travail proposent un scores censurés. Cette approche permet construire du modèle question, que soit seul tout ensemble quantiles. L'implantation tels repose algorithme fondé modèle. Enfin, illustrent l'avantage cibler une région plutôt qu'un unique lorsqu'il est question tester l'effet certaines covariables quantile. Since first by Koenker & Bassett (1978), emerged as powerful tool study relationship between response variable and set covariates. By modelling function τ ∈ ( 0 , 1 ), particularly useful varies across different regions . This phenomenon often observed biomedical studies, where treatments heterogeneous population dependant unobserved characteristics subjects. responses/outcomes (commonly known times) are from right because participating subjects may drop out clinical trial terminate after period time. The accelerated failure time (AFT) model Cox proportional hazards popular models outcomes. However, AFT works conditional mean responses unable capture possible changes treatment requires quantiles follow specific form discussed Section 3 Portnoy (2003), precludes types (e.g., negative zero low positive high ). focus statistical inference with outcomes, allowing vary level. Censored was studied Powell (1984, 1986), censoring assumed be known. Wang Fygenson (2009) developed longitudinal fixed censoring. Ying, Jung Wei (1995), Zhou (2006), Bang Tsiatis (2002), among others, estimating equations assuming independent outcome. less stringent assumption literature assumes conditionally outcome given Several estimation been under assumption, they can classified into two groups whether linear (or more generally, parametric) hold locally one globally all Under local (2009), Leng Tong (2013), Backer, Ghouch Keilegom (2019) constructed various forms adapted loss functions regression, share same feature that distribution either needs estimated non-parametrically carry estimation. global model, (2003) an iterative self-consistency based idea redistribution mass, while Peng Huang (2008) their equation through Martingale related counting process signs residuals. determined coefficient so explicit distributions not needed. present article region, special case. To distinguish it just level, call former “regional inference”. applications, typically meaningful evaluate impact covariate many levels than He, Hsu Hu (2010) detection effects upper ≥ 75) trials. Park He (2017), Sun (2021), Chen et al. (2021) showed regional inferences stable hypothesis natural approach consider test statistic characterizes take forms, including averaging taking supremum norm. As demonstrated earlier work (Gutenbrunner Jurečková, 1992; Kocherginsky, Mu, 2005), statistics robustness analysis. motivates random address major developing article. First, without censoring, solutions dual problem optimizing function. score naturally defined observations. (generalized) utilizing mass observations used (2009). Second, do simple limiting critical values easily available. If use method framework, sample should generated null ensure consistency. Resampling schemes like paired generalized (done perturbing weights each observation) generate full therefore applicable our method. new procedure approximates generating satisfying hypothesis. other words, main contributions construction development framework inference. remaining parts organized follows. 2 presents results. More specifically, introduce setting 2.1, 2.2, then tests, algorithm, relevant large-sample Sections 2.3, 2.4, 2.5, respectively. give simulated results demonstrate power test. 4, apply mortality bighorn sheep illustrative example methodology. 5, conclude summary comments. One implication β ) identifiable some At U highest identifiable. Regional will obviously limited any subset within ]. Due triples Y i x Δ = min T C