The Joint Modeling of Longitudinal Covariates and Censored Quantile Regression for Health Applications

The overall theme of this thesis focuses on the joint modeling of longitudinal covariates and a censored survival outcome, where a survival outcome is modeled using a conditional quantile regression. In traditional joint modeling approaches, a survival outcome is usually parametrically modeled as a Cox regression. Censored quantile regressions can model a survival outcome without pre-specifying a parametric likelihood function or assuming a proportional hazard ratio. Existing censored quantile methods are mostly limited to fixed cross-sectional covariates, while in many longitudinal studies, researchers wish to investigate the associations between longitudinal covariates and a survival outcome. The first part considers the problem of joint modeling with a survival outcome under a mixture of censoring: left censoring, interval censoring or right censoring. We pose a linear mixed effect model for a longitudinal covariate and a conditional quantile regression for a censored survival outcome, assuming that a longitudinal covariate and a survival outcome are conditional independent on individual level random effects. We propose a Gibbs sampling approach as an extension of a censored qua