Abstract
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.