Semiparametric Analysis of Failure Time Data in the Presence of Dependent Censoring

Open Access
Author:
Cho, Youngjoo
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
April 28, 2015
Committee Members:
  • Debashis Ghosh, Dissertation Advisor
  • Debashis Ghosh, Committee Chair
  • David Russell Hunter, Committee Member
  • Runze Li, Committee Member
  • Christopher Jon Zorn, Committee Member
Keywords:
  • Bivariate Data
  • Failure Times
  • Perturbation Method
  • Resampling
  • U-statistics
  • Causal Inference
  • Observational Study
Abstract:
Survival analysis is a well-established field in statistics. It has many applications to biology, economics, industrial engineering, and so on. Independent censoring is one of the crucial assumptions in survival analysis. However, this is impractical in many medical studies. For example, in many medical studies, disease occurrence and dependent censoring exist simultaneously, where the presence of dependent censoring leads to the difficulty in analyzing covariate effects on disease outcomes. Such a data structure has been termed `semicompeting risks data'. Much research have been performed on modeling semicompeting risks data. One approach to handle the dependent censoring is to use semiparametric accelerated failure time (AFT) model. This dissertation focuses on addressing restrictions on previous methodology of the semiparametric AFT model and provide solutions. In the first part of the dissertation, we propose a new weighted estimator for the AFT model under dependent censoring. One of the advantages in our approach is that these weights are optimal among all the linear combinations of the previously mentioned two estimators. To calculate these weights, a novel resampling-based scheme is employed. Attendant asymptotic statistical results for the estimator are established. In addition, simulation studies, as well as an application to real data, show the gains in efficiency for our estimator. Goodness of fit procedures are essential tools for assessing model adequacy in statistics. While many authors have proposed goodness of fit tests for U-statistics of order 1, little has been developed for higher order U-statistics. In the second part of the dissertation, we develop a general theory and approach to goodness of fit techniques based on U-processes for the AFT model. Many of the examples will focus on U-statistics of order 2. We propose goodness of fit tests for U-statistics of order 2 by using theoretical results from U-process theory. For numerical summary of hypothesis testing, a generalization of resampling approach adapted from goodness of fit tests based on U-statistics of order 1 is developed. Simulation studies are used to illustrate the proposed methods. In many medical studies, estimation of treatment effects is often of primary scientific interest. As mentioned before, standard methods for evaluating the treatment effect in survival analysis typically require the assumption of independent censoring. In semicompeting risks framework, estimating treatment effect for the disease occurrence is difficult due to the dependent censoring. The approach to use semiparametric AFT model to adjust the dependent censoring requires an artificial censoring technique. However, when covariates are continuous and have large variability, this can lead to excessive artificial censoring resulting in numerically unstable estimates. In the third part of the dissertation, we propose a strategy for weighted estimation of treatment effect that adjusts for covariates. Weights are based on propensity score modeling of the treatment conditional on confounder variables. This novel application of propensity scores avoids excess artificial censoring caused by continuous covariates. Simulation studies and an application to data from the Radiation Therapy Oncology Group (RTOG) are used to illustrate the methodology.