Quantile regression presents a flexible approach to the analysis of survival data, allowing for modeling quantile-specific covariate effect. Qian and Peng (2010) proposed profile estimating equations and a readily and stably implemented iterative algorithm for censored quantile regression tailored to the partially functional effect setting with a mixture of varying and constant effects and demonstrated improved efficiency of estimation over a naive two stage procedure. The aim of this study is to use the same algorithm on a quantile regression setting where some covariate effects follow general parametric pattern (e.g. normal, gamma or logistic distribution) rather than a constant function or value and to determine the strength of using the algorithm in such regression settings through simulation. Simulation studies demonstrate that the method works well, for moderately censored data, if the parametric pattern g(:) is a known function with unknown parameter(s). A sensitivity analysis is performed to check the consequences of misspecification of such parametric pattern.