Quantile regression for sequentially observed bivariate survival data

Abstract

Quantile regression is an extension to the traditional linear regression. It offers a flexible way to assess the effects of covariates on the quantiles of the conditional distribution of a random variable for a given set of covariates. Since the effects of covariates can be assessed at any quantile of the conditional distribution of the response variable, it provides a better understanding of the effects of covariates comparing with traditional regression models. In this study, we consider a parametric conditional quantile regression model for survival data with time-fixed covariates. We propose a multi-stage estimation procedure to estimate the effects of covariates on the quantiles of marginal distributions of sequentially observed bivariate survival times. We model the dependency between survival times with a Clayton copula. Our estimation method is based on the martingale estimating equations. We study the bias and precision of the parameter estimates obtained with the proposed method, as well as investigate their large sample properties with simulation studies. Finally, the method is illustrated by analyzing a colon cancer data set.