如何藉由DNA微陣列資料跟存活資料的資訊來找出基因表現定型一直是個重要的議題。這些研究的主要目標是從大量的基因中找出那些真正跟存活時間或其它重要的臨床結果有顯著關係的小部分。Threshold Gradient Directed Regularization (TGDR)是ㄧ種已經被應用在高維度迴歸問題中能同時處理變數選取以及模型配適的演算法。然而，TGDR採用一種梯度投影型態的演算法使得收斂速率緩慢。在本篇論文中，我們建議新的包含Newton-Raphson求解演算法類型的改良版TGDR方法。我們建議的方法有類似TGDR的特性但卻有比較快的收斂速率。文中並利用一筆附有設限存活時間的真實微陣列癌症資料來做示範。 本篇論文的第二部份是關於適用於區間設限存活資料的重複抽樣Peto-Peto檢定。這個重複抽樣Peto-Peto檢定能夠評估存活函數估計方法的檢定力，例如Turnbull的估計方法以及Kaplan-Meier的估計方法。這個檢定方法顯示出在區間設限資料時Kaplan-Meier的估計方法的檢定力要比Turnbull的估計方法的檢定力來得低。這個檢定方法將以模擬的區間設限資料以及一筆真實關於乳癌研究的區間設限資料來說明。 / 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.

本文所探討的中心為貝氏模型運用於加速壽命試驗，並且假設受測項目之壽命服從Weibull分配。加速實驗環境有三種，其中第二種環境代表正常狀態，採用加速壽命試驗的方式涵蓋了三種：固定應力、漸進之逐步應力和變量曲線之逐步應力。對於先驗參數，並不是直接給予特定的值，而是透過專家評估，給定各種環境之下的產品可靠度之中位數或百分位數，再利用這些資訊經過數值運算解出先驗參數。資料的型態分成兩種，一為區間資料，另一為型一設限資料，透過蒙地卡羅法模擬出後驗分配，並且估計正常環境狀態的可靠度。 / This article develops a Bayes inference model for accelerated life testing assuming failure times at each stress level are Weibull distributed. Using the approach, there are three stressed to be used, and the three testing scenarios to be adapted are as follows：fixed-stress, progressive step-stress and profile step-stress. Prior information is used to indirectly define a multivariate prior distribution for the scale parameters at the various stress levels. The inference procedure accommodates both the interval data sampling strategy and type I censored sampling strategy for the collection of ALT test data. The inference procedure uses the well-known Markov Chain Monte Carlo methods to derive posterior approximations.