在資料分析時，常會出現只包含兩水準的解釋變數，其二水準分別代表
「有」或「無」某種性質。考慮一筆包含兩個此類解釋變數A、B 與一個二元型
反應變數X 的資料，若欲辨識是否存在協同或拮抗交互作用，Lin（2015）建議
可在Helmert coding 之廣義線性模型下作檢定。本文亦採用此模型，但將此問
題以交聯集檢定法和等效性檢定法重新定義。此問題可拆成三個假設檢定，本
文提出一個序列法來進行此三個檢定。針對第一個檢定，我們應用費雪精確等
效性檢定建構其拒絕域；針對第二及第三個檢定，為了方便計算檢定統計量的
虛無分配以決定臨界值，我們做了一些調整，使其可分別應用費雪精確等效性
檢定和費雪精確檢定來建構拒絕域。然而在這樣的調整下，此序列式檢定之整
體最大型一錯誤機率值，在某些參數點上無法被控制在alpha內。本文將透過電腦
模擬探討型一錯誤機率值可能高於alpha的情況，而由模擬結果中發現最大型一錯
誤機率值皆與alpha相去不遠。我們亦將此檢定法應用於判定合成致死效應的真實
資料上，發現其可比Lin（2015）辨識出更多合理的合成致死效應蛋白質對。

In practical data analyses, it is common to encounter explanatory variables with two levels representing conditions with or without a certain property. In this thesis, we consider a generalized linear model with a binary response and two such explanatory variables. To identify whether a synergistic or antagonistic interaction exists under the model, Lin（2015）suggested to use the Helmert coding. We also adopt this approach to develop tests for identifying the interactions, but redefine the problem by introducing the methods of intersection-union test (IUT)
and equivalence test. We utilize the method of IUT to write our test problem as a combination of three tests, and propose a sequential method to develop the rejection region. For the first test, we apply Fisher’s exact equivalence test to construct the rejection region. For the second and the third tests, we modify their null and alternative models so that the Fisher’s exact equivalence test and the Fisher’s exact test can be respectively applied to construct the rejection regions. However, a drawback of this modification is that the probability of type I error would be larger than alpha on some parameter values. We use a computer simulation to study the severity of this drawback, and find that the maximum probability of type I error in the simulation is still close to alpha. We also apply the sequential method on a real data to identify the synthetic-lethal interactions (which are synergistic interactions) between pairs of genes, and find that our method can identify more reasonable pairs than the other methods.

1 緒論1
1.1 協同與拮抗交互作用. . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 問題陳述. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 問題界定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 交聯集檢定法與等效性檢定. . . . . . . . . . . . . . . . . . . . . . 5
2 文獻回顧7
2.1 交聯集檢定法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 等效性檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 費雪精確檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 費雪精確等效性檢定. . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 分析方法11
3.1 序列式檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 檢定方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.3 檢定力函數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.4 單獨檢定協同（拮抗）交互作用. . . . . . . . . . . . . . . . . . . 18
4 電腦模擬20
4.1 參數設定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.2 模擬結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5 真實資料分析24
5.1 資料介紹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.2 合成致死效應之辨識結果. . . . . . . . . . . . . . . . . . . . . . . 25
6 結論與討論29
6.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.2 討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
參考文獻31
附錄32

[1] Berger, R. L. (1982). Multiparameter hypothesis testing and acceptance sampling.
Technometrics, 24(4), 295-300.
[2] Berger, R. L. and Hsu, J. C. (1996). Bioequivalence trials, intersection-union
tests and equivalence confidence sets. Statistical Science, 11(4), 283-319.
[3] Chen, T.-C. (2016). Intersection-union test for identifying synergistic and
antagonistic interactions under linear model with known variance, Master
thesis, National Tsing Hua University, Hsinchu, Taiwan.
[4] Lin, W.-T. (2015). Identification of synergistic and antagonistic interactions,
Master thesis, National Tsing Hua University, Hsinchu, Taiwan.
[5] Lydersen, S., Pradhan, V., Senchaudhuri, P. and Laake, P. (2007). Choice
of test for association in small sample unordered rc tables. Statistics in
medicine, 26(23), 4328-4343.
[6] McCullagh, P. and Nelder, J. A. (1989). Generalized linear models, 2nd edition,
London: Chapman and Hall.
[7] 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. and Shieh, G. S.
(2014). CSNK1E/CTNNB1 are synthetic lethal to TP53 in colorectal cancer
and are markers for prognosis. Neoplasia, 16(5), 441-450.
[8] Wellek, S. (2010). Testing statistical hypotheses of equivalence and noninferiority,
2nd edition, Boca Raton: CRC Press.