This paper considers a power-transformed linear quantile regression model for censored competing risks data, based on conditional quantiles defined by using the cumulative incidence function. We propose a two-stage estimating procedure for the regression coefficients and the transformation parameter. In the first step, for a given transformation parameter, we develop an unbiased monotone estimating equation for regression parameters in the quantile model, which can be solved by minimizing a $L_1$ type convex objective function. In the second step, the transformation parameter can be estimated by constructing the cumulative sum processes. The consistency and asymptotic normality of the regression parameters and transformation parameter are derived. The finite-sample performances of the proposed approach are illustrated by simulation studies and an application to the follicular type lymphoma data set.
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