Quantile regression of right-censored length-biased data using the Buckley–James-type method

Length-biased data are encountered frequently due to prevalent cohort sampling in follow-up studies. Quantile regression provides great flexibility for assessing covariate effects on survival time, and is a useful alternative to Cox’s proportional hazards model and the accelerated failure time (AFT) model for survival analysis. In this paper, we develop a Buckley–James-type estimator for right-censored length-biased data under a quantile regression model. The problem of informative right-censoring of length-biased data induced by prevalent cohort sampling must be handled. Following on from the generalization of the Buckley–James-type estimator under the AFT model proposed by Ning et al. (Biometrics 67:1369–1378, <CitationRef CitationID="CR14">2011</CitationRef>), we propose a Buckley–James-type estimating equation for regression coefficients in the quantile regression model and develop an iterative algorithm to obtain the estimates. The resulting estimator is consistent and asymptotically normal. We evaluate the performance of the proposed estimator on finite samples using extensive simulation studies. Analysis of real data is presented to illustrate our proposed methodology. Copyright Springer-Verlag Berlin Heidelberg 2014