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Abstract: Quantile regression has been advocated in survival analysis to assessevolving covariate effects. However, challenges arise when the censoring timeis not always observed and may be covariate-dependent, particularly in thepresence of continuously-distributed covariates. In spite of several recentadvances, existing methods either involve algorithmic complications or impose aprobability grid. The former leads to difficulties in the implementation andasymptotics, whereas the latter introduces undesirable grid dependence. Toresolve these issues, we develop fundamental and general quantile calculus oncumulative probability scale in this article, upon recognizing that probabilityand time scales do not always have a one-to-one mapping given a survivaldistribution. These results give rise to a novel estimation procedure forcensored quantile regression, based on estimating integral equations. Anumerically reliable and efficient Progressive Localized Minimization PLMINalgorithm is proposed for the computation. This procedure reduces exactly tothe Kaplan-Meier method in the $k$-sample problem, and to standard uncensoredquantile regression in the absence of censoring. Under regularity conditions,the proposed quantile coefficient estimator is uniformly consistent andconverges weakly to a Gaussian process. Simulations show good statistical andalgorithmic performance. The proposal is illustrated in the application to aclinical study.

Autor: Yijian Huang

Fuente: https://arxiv.org/

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