| Summary: | 碩士 === 國立政治大學 === 統計研究所 === 94 === Analyzing censored survival data with high-dimensional covariates arising from the microarray data has been an important issue. The main goal is to find genes that have pivotal influence with patient's survival time or other important clinical outcomes. Threshold Gradient Directed Regularization (TGDR) method has been used for simultaneous variable selection and model building in high-dimensional regression problems. However, the TGDR method adopts a gradient-projection type of method and would have slow convergence rate. In this thesis, we proposed Modified TGDR algorithms which incorporate Newton-Raphson type of search algorithm. Our proposed approaches have the similar characteristics with TGDR but faster convergence rates. A real cancer microarray data with censored survival times is used for demonstration.
The second part of this thesis is about a proposed resampling based Peto-Peto test for survival functions on interval censored data. The proposed resampling based Peto-Peto test can evaluate the power of survival function estimation methods, such as Turnbull’s Procedure and Kaplan-Meier estimate. The test shows that the power based on Kaplan-Meier estimate is lower than that based on Turnbull’s estimation on interval censored data. This proposed test is demonstrated on simulated data and a real interval censored data from a breast cancer study.
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