Quantile regression has become a widely used tool for analysing competing risk data. However, quantile regression for competing risk data with a continuous mark is still scarce. The mark variable is an extension of cause of failure in a classical competing risk model where cause of failure is replaced by a continuous mark only observed at uncensored failure times. An example of the continuous mark variable is the genetic distance that measures dissimilarity between the infecting virus and the virus contained in the vaccine construct. In this article, we propose a novel mark-specific quantile regression model. The proposed estimation method borrows strength from data in a neighbourhood of a mark and is based on an induced smoothed estimation equation, which is very different from the existing methods for competing risk data with discrete causes. The asymptotic properties of the resulting estimators are established across mark and quantile continuums. In addition, a mark-specific quantile-type vaccine efficacy is proposed and its statistical inference procedures are developed. Simulation studies are conducted to evaluate the finite sample performances of the proposed estimation and hypothesis testing procedures. An application to the first HIV vaccine efficacy trial is provided.  

　　Publication:  

　　Biometrika, 2023, asad039, https://doi.org/10.1093/biomet/asad039  

　　Author:  

　　Lianqiang Qu  

　　School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, China  

　　Liuquan Sun  

　　Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China  

　　Email: slq@amt.ac.cn  

　　Yanqing Sun  

　　Department of Mathematics and Statistics, University of North Carolina at Charlotte, 9201 University City Boulevard, Charlotte, North Carolina 28223, USA