Statistical Approaches for Missing Covariates and a Novel Joint Model for Ordered Bivariate Survival Times

Abstract

This dissertation develops and evaluates methods for some common statistical challenges arising from clinical and epidemiological studies.

Missing covariates is a very common problem in clinical and epidemiologic studies and and may lead to biased estimates and inference if we do not account for missingness. Chapters II and III study the problem of missing covariates. Specifically, Chapter II focuses on estimating the causal treatment effect in randomized clinical trials when covariate adjustment is used for improving efficacy, but covariates are possibly missing. We adopt the robust augmentation framework for covariate adjustment and propose three different implementation strategies when multiple baseline covariates are likely missing. Without assuming the data are MAR, the proposed methods lead to consistent and asymptotically normal estimators of the treatment effects, as long as the treatment assignment is independent of the missingness. Chapter III focuses on handling missing covariates in the Cox regression model, which is challenging as the outcome is subject to censoring. Existing methods generally require MAR, but this assumption may not be plausible in survival analysis. Instead of MAR, two alternative missing assumptions are proposed. However, the performance of commonly used imputation methods in this context is relatively less studied. We conducted extensive simulation studies to evaluate the performance of some popular methods, for example, the multiple imputation by chained equations (MICE), complete-case analysis (CC), and single imputation (SI), under various missingness mechanisms and levels of missingness.

Chapter IV develops methods for analyzing ordered bivariate survival times, motivated by the Prostate, Lung, Colorectal, and Ovarian (PLCO) Cancer Screening Trial, to study the effect of screening on cancer mortality. We aim to jointly model the time to cancer diagnosis and the time to death to improve efficiency. Our joint model accounts for the ordering of events, where cancer diagnosis must occur before death. A copula is a function that links two random variables by specifying their dependence structure. Copulas have been extensively applied in bivariate survival models. However, traditional copulas do not account for the order restrictions between random variables. To address this limitation, we propose a novel joint model for ordered bivariate survival times based on copulas.