QUANTILE REGRESSION MODELS WITH PARTIALLY FUNCTIONAL EFFECTS FOR RANDOMLY RIGHT CENSORED DATA: A SIMULATION STUDY

Abstract

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.