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Ties Between Event Times and Covariate Change Times in Cox Models

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Title: Ties Between Event Times and Covariate Change Times in Cox Models
Author: Xin, Xin
Department: Department of Mathematics and Statistics
Program: Mathematics and Statistics
Advisor: Horrocks, JulieDarlington, Gerarda
Abstract: This thesis comprises three research developments with respect to handling ties between event times and the times that a time-varying covariate changes in the Cox model. Ties of this type are denoted as Type 2 ties in contrast to Type 1 ties that exist between the event times of different individuals. All ties need to be considered when fitting a Cox model as the Cox partial likelihood was originally proposed to accommodate distinct/continuous time values. Type 1 ties have been systematically studied and methods are well established, but the impact of Type 2 ties has not been extensively considered in the statistical literature. Previous work (Xin et al., 2013) studied Type 2 ties for the first time and demonstrated that these ties can lead to biased Cox model estimation if not appropriately modeled. Two methods, the random jitter (RJ) method and equally weighted (EW) method, were proposed as appropriate approaches to treat Type 2 ties within the framework of the Cox model. This thesis presents a systematic investigation of the RJ and EW methods for Type 2 ties in the Cox model. Specifically, a novel partial likelihood is proposed. Three appropriate methods for the EW standard error estimation are proposed. In addition, two competing methods for estimating the regression coefficients of the Cox model in the presence of Type 2 ties are discussed and comparison studies are conducted. In addition, an investigation of the analogy between the RJ method and missing data imputation methodology is conducted. Inspired by multiple imputation, the multiple random jitter (MRJ) method is proposed as a potential improvement to the RJ method. However, it is shown that the MRJ method does not outperform the RJ method. Finally, a novel partial likelihood inspired by the Efron approximation was constructed for accommodating both Type 1 and Type 2 ties at the same time in Cox models. This partial likelihood can be easily maximized for coefficient estimation and conveniently expanded to accommodate more complex covariates.
Date: 2014-03
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