在各種資料中，常會出現只有兩種水準的解釋變數，且在許多狀況下，
這兩個水準分別代表“有”與“無”某種性質。考慮一筆包含兩個此類解釋
變數A 與B 以及二元型反應變數Y 的資料，若要辨識是否具有協同或拮
抗交互作用，Lin (2015) 建議可在使用Helmert coding 之廣義線性模型下
作檢定。本論文亦採用此模型，但將此問題透過交聯集檢定法和等效性檢
定法重新定義。此問題包含多個假設檢定，可以先使用Wald 檢定或概似
比檢定進行個別檢定，再透過交聯集檢定法建構level-alpha 的檢定。在Wald
檢定中，其參數在大樣本下服從多變量常態分配，故可使用Chen (2016)
的方法，建構出一個size-alpha 的檢定；而在概似比檢定中，會碰到虛無假設
下的參數空間與整個參數空間的維度相等的問題，因此將虛無假設轉換成
僅包含邊界點，可推得其檢定統計量在大樣本下仍服從卡方分配，並依此
性質建構出level-alpha 的檢定。接下來我們用電腦模擬來驗證此新檢定法之效
力，並比較此兩種方法。最後分析一筆大腸癌的真實資料，辨識是否具有
合成致死效應。

In real data analyses, it is very common to encounter variables with two
levels representing conditions with or without a certain property. In this
thesis, we consider a data with two 2-level explanatory variables A and B
and a binary response Y. For such data, we discuss how to identify whether
A and B have a synergistic or antagonistic interaction on Y. To identify
such intersections, Lin (2015) suggested a generalized linear model based on
Helmert coding. In this thesis, we adopt this model and utilize the methods
of intersection-union test (IUT) and equivalence test to resolve the problem
of identifying the intersections. We apply the method of IUT to write our
test problem as a combination of three sub-tests. The whole rejection region
is the intersection of the rejection regions of the three sub-tests. For each
sub-tests, we construct their rejection regions by using the Wald test and
the likelihood ratio test. Because the asymptotic distribution of the effect
estimators under the generalized linear model is a multivariate normal with
a known covariance matrix, the Wald test is consistent with the method
used in Chen (2016) to construct a size-alpha test for normal responses. For
the likelihood ratio test, we replace the null hypothesis by the parameter
values on the boundary of the null and the alternative spaces to derive the
asymptotic null distribution of test statistics for constructing a level-alpha test.
A simulation study is conducted to validate our method, and to compare
the performances of the Wald and the likelihood ratio tests. Our method is
also applied to a CRC real data to identify the synthetic lethal effects.

1 緒論1
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 廣義線性模型的參數估計與其分配. . . . . . . . . . . . . . . . . . 8
3 分析方法9
3.1 Wald 檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 概似比檢定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2.1 包含三個子檢定的概似比檢定. . . . . . . . . . . . . . . . . 12
3.2.2 包含二個子檢定的概似比檢定. . . . . . . . . . . . . . . . . 15
3.3 單獨對協同(或拮抗) 交互作用之檢定. . . . . . . . . . . . . . . . 18
4 電腦計算與模擬20
4.1 參數設定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.2 模擬結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.3 檢定法之比較. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5 真實資料之分析23
5.1 資料分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.2 合成致死效應之辨識. . . . . . . . . . . . . . . . . . . . . . . . . . 24
6 結論32
參考文獻33
附錄34

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