Two-piece distribution based semi-parametric quantile regression for right censored data

Abstract

Widely used methods such as Cox proportional hazards, accelerated failure time, and Bennet proportional odds models do not model the quantiles directly, but rather allow to assess the influence of the covariates only on the location of the distribution. Quantile regression allows to assess the effects of covariates, not only on a location parameter (such as a mean or median) but also on specific percentiles of the conditional distribution. In recent years, a large family of flexible two-piece asymmetric distributions where the location parameter coincides with a specific quantile of the distribution has been studied. In a conditional (regression) setting the use of such a family of two-piece asymmetric distributions has only been investigated in the complete data case in the literature. In this paper, we propose a semi-parametric procedure to estimate the conditional quantile curves of two-piece asymmetric distributions based on right censored survival data. We use a local likelihood estimation technique in a multi-parameter functional form, via which the effect of a covariate on the location, scale, and index of the conditional survival distribution can be assessed. The finite sample performance of the estimators is investigated via simulations, and the methodology is illustrated on real data examples.