Statistical Analysis for Clustered Survival Data with a Hierarchical Structure or in Presence of Cure

• Main Authors: Su, Chien-Lin, 蘇健霖
• Other Authors: Wang, Wei-jing
• Format: Others
• Language: en_US
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/06252602567753491103

博士 === 國立交通大學 === 統計學研究所 === 103 === Clustered data are commonly seen in real-world applications. The thesis considers two directions of statistical analysis for clustered data. The first data type is clustered data with a two-level hierarchical structure. In the second direction, we study clustered survival data in the presence of cure. To model the two-level clustered data, we adopt the hierarchical Kendall copula proposed by Brechmann (2014). We develop statistical inference methods, including a three-stage estimation procedure and a goodness-of-fit test. The proposed methods are suitable for handling censored data. Large-sample properties of the proposed methods are derived. Simulation and data analysis results are also presented. For the second topic of the thesis, we propose a class of mixed-effects parametric models to fit clustered survival data in the presence of cure. Possible model candidates can be the generalized Gompertz distribution or four-parameter log-logistic distribution which permit improper distributions. The model parameters are specified as a function of observed covariates and random effects. Simulation studies are performed to evaluate finite-sample performances of the proposed estimators. Two real datasets are analyzed for illustration purposes.