在數據分析時，常會出現兩水準的解釋變數，其兩個水準分別代表“有”或“無” 某種性質，例如: 是否服用某種藥物、某基因是否發生突變而造成蛋白質的變異、是否添加某種化學成分、等，皆為此類解釋變數。對兩個此類的解釋變數A和B，我們在本論文中探討其是否具有協同交互作用或拮抗交互作用的辨識法。此兩種交互作用，一為正向，另一為負向，比如基因研究中所稱的合成致死(synthetic lethal) 效應，即為一種協同交互作用。
對於用來了解協同或拮抗交互作用是否存在的資料，目前仍有許多分析，採用檢定A 與B 之傳統主效應及交互作用是否顯著，來辨識協同或拮抗交互作用是否存在。在本文中，我們將指出此種分析方法不適合之處，並對應變數Y 為連續型或離散型之數據，分別使用線性模型與廣義線性模型，在Helmert coding system 下，提出更適用於判別協同或拮抗交互作用是否存在的分析方法。
我們亦利用電腦模擬，檢驗此新分析方法之功效，並與傳統分析方法相比較。並將此方法應用於用來判定合成致死的真實數據上，發現其可比舊方法發現更多的合成致死蛋白質對(protein pair)。

In data analysis, it is very common to encounter variables with 2 levels. The 2 levels of such variables may represent conditions with or without a certain property. For example, a variable indicating whether taking a medicine, a variable indicating whether a gene is mutated and protein expression is abnormal, and a variable indicating whether a chemical is applied, are such variables. For two such variables $A$ and $B$, we discuss how to identify whether they have synergistic or antagonistic interactions. The former is a positive interaction while the latter is a negative one. The synthetic lethal effect, for example, in genetic research is a synergistic interaction.

The conventional method to identity synergistic and/or antagonistic interactions is based on the test significance of the main effects and interaction defined under sum coding system. In the work, we discuss the inadequacy of the approach. The main purpose of this study is to propose a more appropriate analysis method for the identification of synergistic and/or antagonistic interactions. Our method adopts the Helmert coding system to define effects. For quantitative and qualitative responses, we use linear models and generalized linear models respectively to develop a new identification method.

A simulation study is conducted to validate the new method and to compare its performance to previous methods. The new method is also applied to a CRC real data. It identifies more synthetic lethal protein pairs than the previous method.

目錄
1 緒論與文獻回顧 1
1.1 緒論 1
1.2 文獻回顧 3
1.2.1 線性模型 3
1.2.2 廣義線性模型 3
1.2.3 列聯表之分析方式 4
2 效應編碼及參數意義之比較 7
2.1 線性模型下參數之意義 7
2.1.1 sum coding 7
2.1.2 Helmert coding 8
2.2 廣義線性模型下參數之意義 9
2.2.1 sum coding 9
2.2.2 Helmert coding 10
2.3 廣義線性模型下參數之檢定與費雪精確檢定之對應關係 11
3 協同與拮抗交互作用之檢定方法 14
3.1 分析方法 14
3.1.1 建構虛無與對立假設 14
3.1.2 檢定方法 16
3.2 模擬研究 18
3.2.1 模擬參數之設定 19
3.2.2 常態型資料模擬結果與結論 20
3.2.3 二元型資料模擬結果與結論 23
4 真實資料之分析 30
4.1 資料介紹 30
4.2 合成致死效應之辨識 31
5 結論 34
參考文獻 35

参考文獻
[1] Draper, N. R., and Smith, H. (1998). Applied regression analysis; 3rd edition. John
Wiley & Sons.
[2] McCullagh, P., and Nelder, J. A. (1989). Generalized linear models; 2nd edition. CRC press.
[3] Tiong, K. L., Chang, K. C., Yeh, K. T., Liu, T. Y., Wu, J. H., Hsieh, P. H., Lin, S. H., Lai, W. Y., Hsu, Y. C., Chen, J. Y., Chang, J. G., Shieh, G. S. (2014).
“CSNK1E/CTNNB1 are synthetic lethal to TP53 in colorectal cancer and are markers for prognosis.” Neoplasia, 16(5), 441-450.