Detecting Outliers in Mixture Hazard Models with Weibull Baselines

• Main Authors: Ho, Li-Wei, 何莉維
• Other Authors: Chang, Shao-Tung
• Format: Others
• Language: zh-TW
• Online Access: http://ndltd.ncl.edu.tw/handle/r2hkw3

碩士 === 國立臺灣師範大學 === 數學系 === 106 === Outlier detection is an important issue in statistical analysis. It is a method to identify the data or observations which have extreme abnormalities in the dataset. Detecting these observations and treating them appropriately can improve the result of estimation and reasonably interpret models. Outlier detection is commonly applied to structural defects, medical problems, and other types of problems. In the medical problem, the Cox proportional hazard model is the most widely used model in survival analysis. It is mainly used to explore the relationship between survival time and covariate. Although many approaches have been proposed for the outliers detection in survival model, few of them consider the about outlier detection in mixture hazard model. However, the analysis of mixture hazard model is popular recently because the diseases would often be divided into many groups based on the causes in medicine. As a result, it is very important to develop a method for detecting outliers and fitting the estimation of the mixture hazard models, and this thesis is discussing about this issue. In this thesis, we focus on the detection of the mixture hazard model based on the Weibull mixture hazard model. We introduce the shrinkage parameters in the penalized likelihood function to detect the outliers, and develop EM algorithm to estimate the shrinkage parameter. After detecting possible outliers, we refit the model parameters either by weighting or deleting the outliers. The simulation results reveal that the proposed method can detect the outliers of the mixture hazard model effectively. Additionally, using the outlier-deleting method can obtain better parameter estimates, in the sense of smaller bias, generally.