Regression Modeling of Complex Survival Data based on Pseudo-Observations

The restricted mean survival time (RMST) is a clinically meaningful summary measure in studies with survival outcomes. Statistical methods have been developed for regression analysis of RMST to investigate impacts of covariates on RMST, which is a useful alternative to the Cox regression analysis. However, existing methods for regression modeling of RMST are not applicable to left-truncated right-censored data that arise frequently in prevalent cohort studies, for which the sampling bias due to left truncation and informative censoring induced by the prevalent sampling scheme must be properly addressed. Meanwhile, statistical methods have been developed for regression modeling of the cumulative incidence function for left-truncated right-censored competing risks data. Nevertheless, existing methods typically involve complicated weighted estimating equations or nonparametric conditional likelihood function and often require a restrictive assumption that censoring and/or truncation times are independent of failure time. Andersen et al. introduced an approach of using pseudo observations (POs) in regression analysis of right-censored data. In this dissertation, we develop statistical methods for regression modeling of complex survival data based on POs. In Chapter 1, we propose to directly model RMST as a function of baseline covariates based on POs for left-truncated right-censored data under general censoring mechanisms. We adjust for the potential covariate-dependent censoring or dependent censoring by the inverse probability of censoring weighting method. We establish large sample properties of the proposed estimators and assess their finite sample performances by simulation studies under various scenarios. We apply the proposed methods to a prevalent cohort of women diagnosed with stage IV breast cancer identified from Surveillance, Epidemiology, and End Results-Medicare linked database. In Chapter 2, we extend the PO approach to left-truncated right-censored competing risks data and propose to directly model the cumulative incidence as a function of baseline covariates based on POs, under general truncation and censoring mechanisms. We adjust for potential covariate-dependent truncation and/or covariate-dependent censoring by incorporating covariate-adjusted weights into the inverse probability weighted estimator of the cumulative incidence function. We derive large sample properties of the proposed estimators under reasonable model assumptions and regularity conditions and assess their finite sample performances by simulation studies under various scenarios. We apply the proposed methods to a cohort study on HIV disease progression and a cohort study on pregnancy exposed to coumarin derivatives for illustration