臺灣博碩士論文加值系統

在生物醫學上，檢定雙樣本存活曲線的問題是常見的。其中，最常被使用的檢定方法為log-rank test。然而，當兩條存活曲線有交叉的情況發生時，log-rank test可能會導致錯誤的結果。此外，我們很難找到一種檢定方法適合所有可能的交叉情況。因此，我們提出一種方法，我們稱它為費雪精確檢定的延伸。以及一種策略，我們稱它為策略一和策略二。然後，我們對提出的方法和策略做模擬分析來探討它們的檢定力和型I誤差。接著，從Li et al. (2015)選出五種具有競爭力的方法來跟我們提出的方法在兩條存活曲線不同的交叉情況下做模擬比較。從模擬結果，我們建議使用策略二來檢定兩條存活曲線。因為策略二有合適的型I誤差以及在每個情況下都有較高的檢定力。最後，我們使用我們所提出的方法分析兩筆實際資料。

In biomedical studies, two sample survival curves testing problem is commonly seen. The most popular approach is the log-rank test. However, the log-rank test may lead to misleading results when two survival curves cross each other. Moreover, it is difficult to find an appropriate method for all situations. Hence, we propose an approach, which is the extension of Fisher exact test and two strategies, Strategy 1 and Strategy 2. Then, we conduct simulations to investigate the power and type I error rate and compare the proposed methods with five competitive approaches from Li et al. (2015) under various crossing situations of two survival curves. From the results, we suggest the Strategy 2 for the two survival curves testing problem, which has higher power and appropriate type I error for each situation. Finally, we analyze two real data examples with the proposed methods for illustrations.

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Data and Hypothesis Test . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Right Censored Data . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Two Sample Hypothesis Test . . . . . . . . . . . . . . . . . . . . . . . 5
3 Literature Review . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . 6
3.1 Log-rank Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.2 Gehan-Wilcoxon Test . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.3 Tarone-Ware Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.4 Fleming-Harrington Test . . . . . . . . . . . . . . . . . . . . . . . . 8
3.5 Two-stage Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4 The Proposed Inference Procedure . . . . . . . . . . . . . . . . . . . . . 13
4.1 The Extension of Fisher Exact Test . . . . . . . . . . . . . . . . . . 13
4.2 Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2.1 Strategy 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2.2 Strategy 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.1 Simulation Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.2 Estimation of Statistical Power and Type I Error . . . . . . . . . . . 23
6 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
6.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
6.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

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