Abstract
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.