在臨床研究中，將連續的生物指標進行二分法是一個普遍的做法。二分法使得臨床醫生更容易在制定治療決策時，使用事件與生物指標之間的相關資訊。在過去的文獻中存在多種對連續生物指標進行二分法，其中最常用的兩種方法，一種是最小p值法，另一種則是以概似函數為基礎的方法。最小p值法是對一個連續生物指標的所有值進行二分法，並進行一系列檢定統計量分析後，再選擇與最大檢定統計量（或等價地，最小p值）相關的“最佳”切點。而以概似函數為基礎的方法則是將切點視為一個未知參數，並藉由概似函數值的最大值來找出最佳的切點。在風險迴歸中也可以運用前述的兩種方法來尋找生物指標的切點。方法是將生物指標透過切點區分成兩個風險組作為我們的共變量來進行風險迴歸。本文希望能夠使用EH擴充風險模型，並運用前述的最小p值法及以概似函數為基礎的方法來尋找生物指標最佳的切點。

Dichotomizing a continuous biomarker is a common practice in clinical research.
Dichotomizing make it easier for clinicians to use information about the relationship between an outcome and a baseline biomarker in making treatment decisions. Various methods exist in the literature for dichotomizing continuous biomarkers, of which the two most commonly used methods, one is the minimum p-value approach, and the other is likelihood-based approach. Minimum p-value approach uses a sequence of test statistics for all possible dichotomizations of a continuous biomarker, and it chooses the cutpoint that is associated with the maximum test statistic, or equivalently, the minimum p-value of the test. On the other hand, likelihood-based approach considers the cutpoint as an unknown parameter and find the best cutpoint by maximum likelihood. These two methods can be incorporated in the hazard regression by dividing the biomarkers into two groups through a cutpoint and treated as a hazard regression model. In this thesis, a semiparametric extended hazards model, which includes the Cox model and the AFT model as special cases is incorporated in the two methods to find the best cutpoint of a biomarker.

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