在醫學研究中，生物指標因素(prognosis factor)和其相對應的預測模 型已經被廣泛使用。存活樹(Survival tree)和森林(Survival forest)是當 前非常熱門用於存活數據(Survival data)開發預測模型的非參數方法。它們 具有很高的彈性，可以合理地檢測某些變數間的交互作用而不需要太多模型 假設。此外，一棵存活樹可以根據其二元分類及不斷遞迴的特性產生多個指 標因素並將樣本分為多個組別。在本文中，我們點名的存活樹在高維度變數 下的實施困難原因及解決辦法。此外，我們還指出，用於檢測樹節點在傳統 logrank test 下具有致命的缺點。為了解決上述問題，我們提出了穩定單變 量score statistics 來找出樹的節點。進階來說，我們可以在沒有任何迭代 優化的情況下執行高維度變數的篩選和提出決策，在某些特殊運算下能提升 效率。本文也提出對於當logrank test 無法提供適量的統計決策時，我們提 出的方法能適當解決這個問題並產生更有預測能力的存活樹。;Analysis of prognostic factors and prediction models has been considered extensively in medical research. Survival trees and forests are popular non-parametric tools for developing prognostic models for survival data. They offer great flexibility and can automatically detect certain types of interactions without the need to specify them beforehand. Moreover, a single tree can naturally classify subjects into different groups according to their survival prognosis based on their covariates. In this thesis, we point out the difficulty of tree-based model fitting a high dimensional covariate. Furthermore, we also point out that the traditional logrank tests for detecting the nodes of a tree have fatal drawbacks. In order to overcome these difficulties, we propose a stabilized univariate score statistics to find the nodes of a tree. We show that the high dimensional score tests can be performed without any iteration and optimization, leading to a computationally efficient test procedures. We also show that the proposed method can resolve the drawbacks of the logrank tests, leading to a highly precise tree. Simulation studies are performed to see the relative performance of the proposed method with the existing method. The lung cancer dataset is analyzed for illustration.
